Complexity of the Quantum Adiabatic Algorithm
Hen, Itay
2013-01-01
The Quantum Adiabatic Algorithm (QAA) has been proposed as a mechanism for efficiently solving optimization problems on a quantum computer. Since adiabatic computation is analog in nature and does not require the design and use of quantum gates, it can be thought of as a simpler and perhaps more profound method for performing quantum computations that might also be easier to implement experimentally. While these features have generated substantial research in QAA, to date there is still a lack of solid evidence that the algorithm can outperform classical optimization algorithms.
Quantum Adiabatic Evolution Algorithms versus Simulated Annealing
Farhi, E; Gutmann, S; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam
2002-01-01
We explain why quantum adiabatic evolution and simulated annealing perform similarly in certain examples of searching for the minimum of a cost function of n bits. In these examples each bit is treated symmetrically so the cost function depends only on the Hamming weight of the n bits. We also give two examples, closely related to these, where the similarity breaks down in that the quantum adiabatic algorithm succeeds in polynomial time whereas simulated annealing requires exponential time.
Adiabatic quantum algorithm for search engine ranking
Garnerone, Silvano; Lidar, Daniel A
2011-01-01
We propose an adiabatic quantum algorithm to evaluate the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which provide evidence that this quantum algorithm outputs any component of the PageRank vector-and thus the ranking of the corresponding webpage-in a time which scales polylogarithmically in the number of webpages. This would constitute an exponential speed-up with respect to all known classical algorithms designed to evaluate the PageRank.
Quantum Adiabatic Evolution Algorithms with Different Paths
Farhi, E; Gutmann, S; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam
2002-01-01
In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground state of the final Hamiltonian encodes the solution of the computational problem. These algorithms have generally been studied in the case where the "straight line" path from initial to final Hamiltonian is taken. But there is no reason not to try paths involving terms that are not linear combinations of the initial and final Hamiltonians. We give several proposals for randomly generating new paths. Using one of these proposals, we convert an algorithmic failure into a success.
Quantum adiabatic algorithm for factorization and its experimental implementation.
Peng, Xinhua; Liao, Zeyang; Xu, Nanyang; Qin, Gan; Zhou, Xianyi; Suter, Dieter; Du, Jiangfeng
2008-11-28
We propose an adiabatic quantum algorithm capable of factorizing numbers, using fewer qubits than Shor's algorithm. We implement the algorithm in a NMR quantum information processor and experimentally factorize the number 21. In the range that our classical computer could simulate, the quantum adiabatic algorithm works well, providing evidence that the running time of this algorithm scales polynomially with the problem size.
Limitations of some simple adiabatic quantum algorithms
Ioannou, L M; Ioannou, Lawrence M.; Mosca, Michele
2007-01-01
Let $H(t)=(1-t/T)H_0 + (t/T)H_1$, $t\\in [0,T]$, be the Hamiltonian governing an adiabatic quantum algorithm, where $H_0$ is diagonal in the Hadamard basis and $H_1$ is diagonal in the computational basis. We prove that $H_0$ and $H_1$ must each have at least two large mutually-orthogonal eigenspaces if the algorithm's running time is to be subexponential in the number of qubits. We also reproduce the optimality proof of Farhi and Gutmann's search algorithm in the context of this adiabatic scheme; because we only consider initial Hamiltonians that are diagonal in the Hadamard basis, our result is slightly stronger than the original.
Quantum Adiabatic Algorithms and Large Spin Tunnelling
Boulatov, A.; Smelyanskiy, V. N.
2003-01-01
We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in this paper. The algorithm is applied to a random binary optimization problem (a version of the 3-Satisfiability problem) where the n-bit cost function is symmetric with respect to the permutation of individual bits. The evolution paths are produced, using the generic control Hamiltonians H (r) that preserve the bit symmetry of the underlying optimization problem. In the case where the ground state of H(0) coincides with the totally-symmetric state of an n-qubit system the algorithm dynamics is completely described in terms of the motion of a spin-n/2. We show that different control Hamiltonians can be parameterized by a set of independent parameters that are expansion coefficients of H (r) in a certain universal set of operators. Only one of these operators can be responsible for avoiding the tunnelling in the spin-n/2 system during the quantum adiabatic algorithm. We show that it is possible to select a coefficient for this operator that guarantees a polynomial complexity of the algorithm for all problem instances. We show that a successful evolution path of the algorithm always corresponds to the trajectory of a classical spin-n/2 and provide a complete characterization of such paths.
Adiabatic quantum algorithm for search engine ranking.
Garnerone, Silvano; Zanardi, Paolo; Lidar, Daniel A
2012-06-08
We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which provide evidence that this algorithm can prepare the quantum PageRank state in a time which, on average, scales polylogarithmically in the number of web pages. We argue that the main topological feature of the underlying web graph allowing for such a scaling is the out-degree distribution. The top-ranked log(n) entries of the quantum PageRank state can then be estimated with a polynomial quantum speed-up. Moreover, the quantum PageRank state can be used in "q-sampling" protocols for testing properties of distributions, which require exponentially fewer measurements than all classical schemes designed for the same task. This can be used to decide whether to run a classical update of the PageRank.
Adiabatic Quantum Algorithm for Search Engine Ranking
Garnerone, Silvano; Zanardi, Paolo; Lidar, Daniel A.
2012-06-01
We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which provide evidence that this algorithm can prepare the quantum PageRank state in a time which, on average, scales polylogarithmically in the number of web pages. We argue that the main topological feature of the underlying web graph allowing for such a scaling is the out-degree distribution. The top-ranked log(n) entries of the quantum PageRank state can then be estimated with a polynomial quantum speed-up. Moreover, the quantum PageRank state can be used in “q-sampling” protocols for testing properties of distributions, which require exponentially fewer measurements than all classical schemes designed for the same task. This can be used to decide whether to run a classical update of the PageRank.
A quantum search algorithm based on partial adiabatic evolution
Zhang Ying-Yu; Hu He-Ping; Lu Song-Feng
2011-01-01
This paper presents and implements a specified partial adiabatic search algorithm on a quantum circuit. It studies the minimum energy gap between the first excited state and the ground state of the system Hamiltonian and it finds that, in the case of M=1, the algorithm has the same performance as the local adiabatic algorithm. However, the algorithm evolves globally only within a small interval, which implies that it keeps the advantages of global adiabatic algorithms without losing the speedup of the local adiabatic search algorithm.
How to Make the Quantum Adiabatic Algorithm Fail
Farhi, E; Gutmann, S; Nagaj, D; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam; Nagaj, Daniel
2005-01-01
The quantum adiabatic algorithm is a Hamiltonian based quantum algorithm designed to find the minimum of a classical cost function whose domain has size N. We show that poor choices for the Hamiltonian can guarantee that the algorithm will not find the minimum if the run time grows more slowly than square root of N. These poor choices are nonlocal and wash out any structure in the cost function to be minimized and the best that can be hoped for is Grover speedup. These failures tell us what not to do when designing quantum adiabatic algorithms.
On Models of Nonlinear Evolution Paths in Adiabatic Quantum Algorithms
SUN Jie; LU Song-Feng; Samuel L.Braunstein
2013-01-01
In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model — an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.
Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning
Smelyanskiy, Vadius; vonToussaint, Udo V.; Timucin, Dogan A.; Clancy, Daniel (Technical Monitor)
2002-01-01
We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum exitation gap, gmin = O(n2(sup -n/2)), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.
Quantum Adiabatic Algorithms, Small Gaps, and Different Paths
Farhi, Edward; Gosset, David; Gutmann, Sam; Meyer, Harvey B; Shor, Peter
2011-01-01
We construct a set of instances of 3SAT which are not solved efficiently using the simplest quantum adiabatic algorithm. These instances are obtained by picking random clauses all consistent with two disparate planted solutions and then penalizing one of them with a single additional clause. We argue that by randomly modifying the beginning Hamiltonian, one obtains (with substantial probability) an adiabatic path that removes this difficulty. This suggests that the quantum adiabatic algorithm should in general be run on each instance with many different random paths leading to the problem Hamiltonian. We do not know whether this trick will help for a random instance of 3SAT (as opposed to an instance from the particular set we consider), especially if the instance has an exponential number of disparate assignments that violate few clauses. We use a continuous imaginary time Quantum Monte Carlo algorithm in a novel way to numerically investigate the ground state as well as the first excited state of our system...
Random Matrix Approach to Quantum Adiabatic Evolution Algorithms
Boulatov, Alexei; Smelyanskiy, Vadier N.
2004-01-01
We analyze the power of quantum adiabatic evolution algorithms (Q-QA) for solving random NP-hard optimization problems within a theoretical framework based on the random matrix theory (RMT). We present two types of the driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that the failure mechanism of the QAA is due to the interaction of the ground state with the "cloud" formed by all the excited states, confirming that in the driven RMT models. the Landau-Zener mechanism of dissipation is not important. We show that the QAEA has a finite probability of success in a certain range of parameters. implying the polynomial complexity of the algorithm. The second model corresponds to the standard QAEA with the problem Hamiltonian taken from the Gaussian Unitary RMT ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. However, the driven RMT model always leads to the exponential complexity of the algorithm due to the presence of the long-range intertemporal correlations of the eigenvalues. Our results indicate that the weakness of effective transitions is the leading effect that can make the Markovian type QAEA successful.
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
Farhi, E; Gutmann, S; Lapan, J; Lundgren, A; Preda, D; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam; Lapan, Joshua; Lundgren, Andrew; Preda, Daniel
2001-01-01
A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We test one such algorithm by applying it to randomly generated, hard, instances of an NP-complete problem. For the small examples that we can simulate, the quantum adiabatic algorithm works well, and provides evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.
Mitra, Avik; Ghosh, Arindam; Das, Ranabir; Patel, Apoorva; Kumar, Anil
2005-12-01
Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required output state. In some cases, such as the adiabatic versions of Grover's search algorithm and Deutsch-Jozsa algorithm, applying the global adiabatic evolution yields a complexity similar to their classical algorithms. However, using the local adiabatic evolution, the algorithms given by J. Roland and N.J. Cerf for Grover's search [J. Roland, N.J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65 (2002) 042308] and by Saurya Das, Randy Kobes, and Gabor Kunstatter for the Deutsch-Jozsa algorithm [S. Das, R. Kobes, G. Kunstatter, Adiabatic quantum computation and Deutsh's algorithm, Phys. Rev. A 65 (2002) 062301], yield a complexity of order N (where N=2(n) and n is the number of qubits). In this paper, we report the experimental implementation of these local adiabatic evolution algorithms on a 2-qubit quantum information processor, by Nuclear Magnetic Resonance.
Ultrafast adiabatic quantum algorithm for the NP-complete exact cover problem.
Wang, Hefeng; Wu, Lian-Ao
2016-02-29
An adiabatic quantum algorithm may lose quantumness such as quantum coherence entirely in its long runtime, and consequently the expected quantum speedup of the algorithm does not show up. Here we present a general ultrafast adiabatic quantum algorithm. We show that by applying a sequence of fast random or regular signals during evolution, the runtime can be reduced substantially, whereas advantages of the adiabatic algorithm remain intact. We also propose a randomized Trotter formula and show that the driving Hamiltonian and the proposed sequence of fast signals can be implemented simultaneously. We illustrate the algorithm by solving the NP-complete 3-bit exact cover problem (EC3), where NP stands for nondeterministic polynomial time, and put forward an approach to implementing the problem with trapped ions.
Adiabatic quantum computation along quasienergies
Tanaka, Atushi
2009-01-01
The parametric deformations of quasienergies and eigenvectors of unitary operators are applied to the design of quantum adiabatic algorithms. The conventional, standard adiabatic quantum computation proceeds along eigenenergies of parameter-dependent Hamiltonians. By contrast, discrete adiabatic computation utilizes adiabatic passage along the quasienergies of parameter-dependent unitary operators. For example, such computation can be realized by a concatenation of parameterized quantum circuits, with an adiabatic though inevitably discrete change of the parameter. A design principle of adiabatic passage along quasienergy is recently proposed: Cheon's quasienergy and eigenspace anholonomies on unitary operators is available to realize anholonomic adiabatic algorithms [Tanaka and Miyamoto, Phys. Rev. Lett. 98, 160407 (2007)], which compose a nontrivial family of discrete adiabatic algorithms. It is straightforward to port a standard adiabatic algorithm to an anholonomic adiabatic one, except an introduction of...
Quantum adiabatic algorithm and scaling of gaps at first-order quantum phase transitions.
Laumann, C R; Moessner, R; Scardicchio, A; Sondhi, S L
2012-07-20
Motivated by the quantum adiabatic algorithm (QAA), we consider the scaling of the Hamiltonian gap at quantum first-order transitions, generally expected to be exponentially small in the size of the system. However, we show that a quantum antiferromagnetic Ising chain in a staggered field can exhibit a first-order transition with only an algebraically small gap. In addition, we construct a simple classical translationally invariant one-dimensional Hamiltonian containing nearest-neighbor interactions only, which exhibits an exponential gap at a thermodynamic quantum first-order transition of essentially topological origin. This establishes that (i) the QAA can be successful even across first-order transitions but also that (ii) it can fail on exceedingly simple problems readily solved by inspection, or by classical annealing.
Pinski, Sebastian D
2011-01-01
Adiabatic Quantum Computing (AQC) is a relatively new subject in the world of quantum computing, let alone Physics. Inspiration for this project has come from recent controversy around D-Wave Systems in British Columbia, Canada, who claim to have built a working AQC which is now commercially available and hope to be distributing a 1024 qubit chip by the end of 2008. Their 16 qubit chip was demonstrated online for the Supercomputing 2007 conference within which a few small problems were solved; although the explanations that journalists and critics received were minimal and very little was divulged in the question and answer session. This 'unconvincing' demonstration has caused physicists and computer scientists to hit back at D-Wave. The aim of this project is to give an introduction to the historic advances in classical and quantum computing and to explore the methods of AQC. Through numerical simulations an algorithm for the Max Independent Set problem is empirically obtained.
A Numerical Study of the Performance of a Quantum Adiabatic Evolution Algorithm for Satisfiability
Farhi, E; Gutmann, S; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam
2000-01-01
Quantum computation by adiabatic evolution, as described in quant-ph/0001106, will solve satisfiability problems if the running time is long enough. In certain special cases (that are classically easy) we know that the quantum algorithm requires a running time that grows as a polynomial in the number of bits. In this paper we present numerical results on randomly generated instances of an NP-complete problem and of a problem that can be solved classically in polynomial time. We simulate a quantum computer (of up to 16 qubits) by integrating the Schrodinger equation on a conventional computer. For both problems considered, for the set of instances studied, the required running time appears to grow slowly as a function of the number of bits.
Lobe, Elisabeth; Stollenwerk, Tobias; Tröltzsch, Anke
2015-01-01
In the recent years, the field of adiabatic quantum computing has gained importance due to the advances in the realisation of such machines, especially by the company D-Wave Systems. These machines are suited to solve discrete optimisation problems which are typically very hard to solve on a classical computer. Due to the quantum nature of the device it is assumed that there is a substantial speedup compared to classical HPC facilities. We explain the basic principles of adiabatic ...
Quantum adiabatic machine learning
Pudenz, Kristen L
2011-01-01
We develop an approach to machine learning and anomaly detection via quantum adiabatic evolution. In the training phase we identify an optimal set of weak classifiers, to form a single strong classifier. In the testing phase we adiabatically evolve one or more strong classifiers on a superposition of inputs in order to find certain anomalous elements in the classification space. Both the training and testing phases are executed via quantum adiabatic evolution. We apply and illustrate this approach in detail to the problem of software verification and validation.
Adiabatic Quantum Search in Open Systems.
Wild, Dominik S; Gopalakrishnan, Sarang; Knap, Michael; Yao, Norman Y; Lukin, Mikhail D
2016-10-07
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.
Adiabatic Quantum Search in Open Systems
Wild, Dominik S.; Gopalakrishnan, Sarang; Knap, Michael; Yao, Norman Y.; Lukin, Mikhail D.
2016-10-01
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.
Biamonte, J D; Whitfield, J D; Fitzsimons, J; Aspuru-Guzik, A
2010-01-01
In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator would be error resistant, easily controllable, and built using existing technology. Moving away from gate-model and projective measurement based implementations of quantum computing may offer a less resource-intensive, and consequently a more feasible solution. Here we consider an adiabatic quantum simulator which simulates the ground state properties of sparse Hamiltonians consisting of one- and two-body interaction terms, using sparse Hamiltonians with at most three-body interactions. Properties of such Hamiltonians can be well approximated with Hamiltonians containing only two-local terms. The register holding the simulated ground state is brought adiabatically into interaction with a probe qubit, followed by a single diabatic gate operation on the probe which then undergoes...
Adiabatic quantum computation and quantum phase transitions
Latorre, J I; Latorre, Jose Ignacio; Orus, Roman
2003-01-01
We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass gap becomes small, suggesting that the system passes near a quantum phase transition. Such a large scaling of entanglement suggests that the effective connectivity of the system diverges as the number of qubits goes to infinity and that this algorithm cannot be efficiently simulated by classical means. On the other hand, entanglement in Grover's algorithm is bounded by a constant.
Adiabatic quantum simulation of quantum chemistry.
Babbush, Ryan; Love, Peter J; Aspuru-Guzik, Alán
2014-10-13
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-body, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions.
J. D. Biamonte
2011-06-01
Full Text Available In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator would be controllable, and built using existing technology. In some cases, moving away from gate-model-based implementations of quantum computing may offer a more feasible solution for particular experimental implementations. Here we consider an adiabatic quantum simulator which simulates the ground state properties of sparse Hamiltonians consisting of one- and two-local interaction terms, using sparse Hamiltonians with at most three-local interactions. Properties of such Hamiltonians can be well approximated with Hamiltonians containing only two-local terms. The register holding the simulated ground state is brought adiabatically into interaction with a probe qubit, followed by a single diabatic gate operation on the probe which then undergoes free evolution until measured. This allows one to recover e.g. the ground state energy of the Hamiltonian being simulated. Given a ground state, this scheme can be used to verify the QMA-complete problem LOCAL HAMILTONIAN, and is therefore likely more powerful than classical computing.
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
Aharonov, D; Kempe, J; Landau, Z; Lloyd, S; Regev, O; Aharonov, Dorit; Dam, Wim van; Kempe, Julia; Landau, Zeph; Lloyd, Seth; Regev, Oded
2004-01-01
Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power has been unknown. We settle this question and describe an efficient adiabatic simulation of any given quantum algorithm, which implies that the adiabatic computation model and the conventional quantum circuit model are polynomially equivalent. Our result can be extended to the physically realistic setting of particles arranged on a two-dimensional grid with nearest neighbor interactions. The equivalence between the models provides a new vantage point from which to tackle the central issues in quantum computation, namely designing new quantum algorithms and constructing fault tolerant quantum computers. In particular, by translating the main open questions in quantum algorithms to the language of spectral gaps of sparse matrices, the result makes quantum algorithmic questions accessible to a wider scientific audience, acquainted with mathematical physics, expander theory a...
Quantum Computation by Adiabatic Evolution
Farhi, E; Gutmann, S; Sipser, M; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam; Sipser, Michael
2000-01-01
We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that interpolates between an initial Hamiltonian, whose ground state is easy to construct, and a final Hamiltonian, whose ground state encodes the satisfying assignment. To ensure that the system evolves to the desired final ground state, the evolution time must be big enough. The time required depends on the minimum energy difference between the two lowest states of the interpolating Hamiltonian. We are unable to estimate this gap in general. We give some special symmetric cases of the satisfiability problem where the symmetry allows us to estimate the gap and we show that, in these cases, our algorithm runs in polynomial time.
Partial evolution based local adiabatic quantum search
Sun Jie; Lu Song-Feng; Liu Fang; Yang Li-Ping
2012-01-01
Recently,Zhang and Lu provided a quantum search algorithm based on partial adiabatic evolution,which beats the time bound of local adiabatic search when the number of marked items in the unsorted database is larger than one.Later,they found that the above two adiabatic search algorithms had the same time complexity when there is only one marked item in the database.In the present paper,following the idea of Roland and Cerf [Roland J and Cerf N J 2002Phys.Rev.A 65 042308],if within the small symmetric evolution interval defined by Zhang et al.,a local adiabatic evolution is performed instead of the original “global” one,this “new” algorithm exhibits slightly better performance,although they are progressively equivalent with M increasing.In addition,the proof of the optimality for this partial evolution based local adiabatic search when M =1 is also presented.Two other special cases of the adiabatic algorithm obtained by appropriately tuning the evolution interval of partial adiabatic evolution based quantum search,which are found to have the same phenomenon above,are also discussed.
Ramsey numbers and adiabatic quantum computing.
Gaitan, Frank; Clark, Lane
2012-01-06
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.
Fixed-point adiabatic quantum search
Dalzell, Alexander M.; Yoder, Theodore J.; Chuang, Isaac L.
2017-01-01
Fixed-point quantum search algorithms succeed at finding one of M target items among N total items even when the run time of the algorithm is longer than necessary. While the famous Grover's algorithm can search quadratically faster than a classical computer, it lacks the fixed-point property—the fraction of target items must be known precisely to know when to terminate the algorithm. Recently, Yoder, Low, and Chuang [Phys. Rev. Lett. 113, 210501 (2014), 10.1103/PhysRevLett.113.210501] gave an optimal gate-model search algorithm with the fixed-point property. Previously, it had been discovered by Roland and Cerf [Phys. Rev. A 65, 042308 (2002), 10.1103/PhysRevA.65.042308] that an adiabatic quantum algorithm, operating by continuously varying a Hamiltonian, can reproduce the quadratic speedup of gate-model Grover search. We ask, can an adiabatic algorithm also reproduce the fixed-point property? We show that the answer depends on what interpolation schedule is used, so as in the gate model, there are both fixed-point and non-fixed-point versions of adiabatic search, only some of which attain the quadratic quantum speedup. Guided by geometric intuition on the Bloch sphere, we rigorously justify our claims with an explicit upper bound on the error in the adiabatic approximation. We also show that the fixed-point adiabatic search algorithm can be simulated in the gate model with neither loss of the quadratic Grover speedup nor of the fixed-point property. Finally, we discuss natural uses of fixed-point algorithms such as preparation of a relatively prime state and oblivious amplitude amplification.
Finding cliques by quantum adiabatic evolution
Childs, A M; Goldstone, J; Gutmann, S; Childs, Andrew M.; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam
2002-01-01
Quantum adiabatic evolution provides a general technique for the solution of combinatorial search problems on quantum computers. We present the results of a numerical study of a particular application of quantum adiabatic evolution, the problem of finding the largest clique in a random graph. An n-vertex random graph has each edge included with probability 1/2, and a clique is a completely connected subgraph. There is no known classical algorithm that finds the largest clique in a random graph with high probability and runs in a time polynomial in n. For the small graphs we are able to investigate (n <= 18), the quantum algorithm appears to require only a quadratic run time.
How detrimental is decoherence in adiabatic quantum computation?
Albash, Tameem
2015-01-01
Recent experiments with increasingly larger numbers of qubits have sparked renewed interest in adiabatic quantum computation, and in particular quantum annealing. A central question that is repeatedly asked is whether quantum features of the evolution can survive over the long time-scales used for quantum annealing relative to standard measures of the decoherence time. We reconsider the role of decoherence in adiabatic quantum computation and quantum annealing using the adiabatic quantum master equation formalism. We restrict ourselves to the weak-coupling and singular-coupling limits, which correspond to decoherence in the energy eigenbasis and in the computational basis, respectively. We demonstrate that decoherence in the instantaneous energy eigenbasis does not necessarily detrimentally affect adiabatic quantum computation, and in particular that a short single-qubit $T_2$ time need not imply adverse consequences for the success of the quantum adiabatic algorithm. We further demonstrate that boundary canc...
Active quantum walks: a framework for quantum walks with adiabatic quantum evolution
Wu, Nan; Song, Fangmin; Li, Xiangdong
2016-05-01
We study a new methodology for quantum walk based algorithms. Different from the passive quantum walk, in which a walker is guided by a quantum walk procedure, the new framework that we developed allows the walker to move by an adiabatic procedure of quantum evolution, as an active way. The use of this active quantum walk is helpful to develop new quantum walk based searching and optimization algorithms.
Adiabatic quantum computation and quantum annealing theory and practice
McGeoch, Catherine C
2014-01-01
Adiabatic quantum computation (AQC) is an alternative to the better-known gate model of quantum computation. The two models are polynomially equivalent, but otherwise quite dissimilar: one property that distinguishes AQC from the gate model is its analog nature. Quantum annealing (QA) describes a type of heuristic search algorithm that can be implemented to run in the ``native instruction set'''' of an AQC platform. D-Wave Systems Inc. manufactures {quantum annealing processor chips} that exploit quantum properties to realize QA computations in hardware. The chips form the centerpiece of a nov
Generalized Ramsey numbers through adiabatic quantum optimization
Ranjbar, Mani; Macready, William G.; Clark, Lane; Gaitan, Frank
2016-09-01
Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey numbers r( G, H), the emergent order is characterized by graphs G and H. In this paper we: (i) present a quantum algorithm for computing generalized Ramsey numbers by reformulating the computation as a combinatorial optimization problem which is solved using adiabatic quantum optimization; and (ii) determine the Ramsey numbers r({{T}}m,{{T}}n) for trees of order m,n = 6,7,8, most of which were previously unknown.
Non-adiabatic geometrical quantum gates in semiconductor quantum dots
Solinas, P; Zanghì, N; Rossi, F; Solinas, Paolo; Zanardi, Paolo; Zanghì, Nino; Rossi, Fausto
2003-01-01
In this paper we study the implementation of non-adiabatic geometrical quantum gates with in semiconductor quantum dots. Different quantum information enconding/manipulation schemes exploiting excitonic degrees of freedom are discussed. By means of the Aharanov-Anandan geometrical phase one can avoid the limitations of adiabatic schemes relying on adiabatic Berry phase; fast geometrical quantum gates can be in principle implemented
Approximability of optimization problems through adiabatic quantum computation
Cruz-Santos, William
2014-01-01
The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is l
Adiabatic quantum gates and Boolean functions
Andrecut, M; Ali, M K [Department of Physics, University of Lethbridge, Lethbridge, AB, T1K 3M4 (Canada)
2004-06-25
We discuss the logical implementation of quantum gates and Boolean functions in the framework of quantum adiabatic method, which uses the language of ground states, spectral gaps and Hamiltonians instead of the standard unitary transformation language. (letter to the editor)
Adiabatic rotation, quantum search, and preparation of superposition states
Siu, M. Stewart
2007-06-01
We introduce the idea of using adiabatic rotation to generate superpositions of a large class of quantum states. For quantum computing this is an interesting alternative to the well-studied “straight line” adiabatic evolution. In ways that complement recent results, we show how to efficiently prepare three types of states: Kitaev’s toric code state, the cluster state of the measurement-based computation model, and the history state used in the adiabatic simulation of a quantum circuit. We also show that the method, when adapted for quantum search, provides quadratic speedup as other optimal methods do with the advantages that the problem Hamiltonian is time independent and that the energy gap above the ground state is strictly nondecreasing with time. Likewise the method can be used for optimization as an alternative to the standard adiabatic algorithm.
Quantum Pumping and Adiabatic Transport in Nanostructures
Wakker, G.M.M.
2011-01-01
This thesis consists of a theoretical exploration of quantum transport phenomena and quantum dynamics in nanostructures. Specifically, we investigate adiabatic quantum pumping of charge in several novel types of nanostructures involving open quantum dots or graphene. For a bilayer of graphene we fin
Digitized adiabatic quantum computing with a superconducting circuit.
Barends, R; Shabani, A; Lamata, L; Kelly, J; Mezzacapo, A; Las Heras, U; Babbush, R; Fowler, A G; Campbell, B; Chen, Yu; Chen, Z; Chiaro, B; Dunsworth, A; Jeffrey, E; Lucero, E; Megrant, A; Mutus, J Y; Neeley, M; Neill, C; O'Malley, P J J; Quintana, C; Roushan, P; Sank, D; Vainsencher, A; Wenner, J; White, T C; Solano, E; Neven, H; Martinis, John M
2016-06-09
Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.
Digitized adiabatic quantum computing with a superconducting circuit
Barends, R.; Shabani, A.; Lamata, L.; Kelly, J.; Mezzacapo, A.; Heras, U. Las; Babbush, R.; Fowler, A. G.; Campbell, B.; Chen, Yu; Chen, Z.; Chiaro, B.; Dunsworth, A.; Jeffrey, E.; Lucero, E.; Megrant, A.; Mutus, J. Y.; Neeley, M.; Neill, C.; O'Malley, P. J. J.; Quintana, C.; Roushan, P.; Sank, D.; Vainsencher, A.; Wenner, J.; White, T. C.; Solano, E.; Neven, H.; Martinis, John M.
2016-06-01
Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.
Xu, Kebiao; Xie, Tianyu; Li, Zhaokai; Xu, Xiangkun; Wang, Mengqi; Ye, Xiangyu; Kong, Fei; Geng, Jianpei; Duan, Changkui; Shi, Fazhan; Du, Jiangfeng
2017-03-31
The adiabatic quantum computation is a universal and robust method of quantum computing. In this architecture, the problem can be solved by adiabatically evolving the quantum processor from the ground state of a simple initial Hamiltonian to that of a final one, which encodes the solution of the problem. Adiabatic quantum computation has been proved to be a compatible candidate for scalable quantum computation. In this Letter, we report on the experimental realization of an adiabatic quantum algorithm on a single solid spin system under ambient conditions. All elements of adiabatic quantum computation, including initial state preparation, adiabatic evolution (simulated by optimal control), and final state read-out, are realized experimentally. As an example, we found the ground state of the problem Hamiltonian S_{z}I_{z} on our adiabatic quantum processor, which can be mapped to the factorization of 35 into its prime factors 5 and 7.
A Diffusion Equation for Quantum Adiabatic Systems
Jain, S R
1998-01-01
For ergodic adiabatic quantum systems, we study the evolution of energy distribution as the system evolves in time. Starting from the von Neumann equation for the density operator, we obtain the quantum analogue of the Smoluchowski equation on coarse-graining over the energy spectrum. This result brings out the precise notion of quantum diffusion.
Adiabatic Quantum Computation: Coherent Control Back Action
Goswami, Debabrata
2013-01-01
Though attractive from scalability aspects, optical approaches to quantum computing are highly prone to decoherence and rapid population loss due to nonradiative processes such as vibrational redistribution. We show that such effects can be reduced by adiabatic coherent control, in which quantum interference between multiple excitation pathways is used to cancel coupling to the unwanted, non-radiative channels. We focus on experimentally demonstrated adiabatic controlled population transfer experiments wherein the details on the coherence aspects are yet to be explored theoretically but are important for quantum computation. Such quantum computing schemes also form a back-action connection to coherent control developments. PMID:23788822
Hierarchical theory of quantum adiabatic evolution
Zhang, Qi; Gong, Jiangbin; Wu, Biao
2014-12-01
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between nondegenerate instantaneous energy eigenstates in such a dynamical evolution. However, this is true only when the driving rate is infinitesimally small. For a small nonzero driving rate, there are generally small transition probabilities between the energy eigenstates. We develop a classical mechanics framework to address the small deviations from the quantum adiabatic theorem order by order. A hierarchy of Hamiltonians is constructed iteratively with the zeroth-order Hamiltonian being determined by the original system Hamiltonian. The kth-order deviations are governed by a kth-order Hamiltonian, which depends on the time derivatives of the adiabatic parameters up to the kth-order. Two simple examples, the Landau-Zener model and a spin-1/2 particle in a rotating magnetic field, are used to illustrate our hierarchical theory. Our analysis also exposes a deep, previously unknown connection between classical adiabatic theory and quantum adiabatic theory.
Abrams, D.; Williams, C.
1999-01-01
This thesis describes several new quantum algorithms. These include a polynomial time algorithm that uses a quantum fast Fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases for which all know classical algorithms require exponential time.
Hypercomputability of quantum adiabatic processes: Fact versus Prejudices
Kieu, T D
2005-01-01
We give an overview of a quantum adiabatic algorithm for Hilbert's tenth problem, including some discussions on its fundamental aspects and the emphasis on the probabilistic correctness of its findings. For the purpose of illustration, the numerical simulation results of some simple Diophantine equations are presented. We also discuss some prejudicial misunderstandings as well as some plausible difficulties faced by the algorithm in its physical implementation.
Markovian quantum master equation beyond adiabatic regime
Yamaguchi, Makoto; Yuge, Tatsuro; Ogawa, Tetsuo
2017-01-01
By introducing a temporal change time scale τA(t ) for the time-dependent system Hamiltonian, a general formulation of the Markovian quantum master equation is given to go well beyond the adiabatic regime. In appropriate situations, the framework is well justified even if τA(t ) is faster than the decay time scale of the bath correlation function. An application to the dissipative Landau-Zener model demonstrates this general result. The findings are applicable to a wide range of fields, providing a basis for quantum control beyond the adiabatic regime.
Adiabatic Quantum Optimization for Associative Memory Recall
Hadayat eSeddiqi
2014-12-01
Full Text Available Hopfield networks are a variant of associative memory that recall patterns stored in the couplings of an Ising model. Stored memories are conventionally accessed as fixed points in the network dynamics that correspond to energetic minima of the spin state. We show that memories stored in a Hopfield network may also be recalled by energy minimization using adiabatic quantum optimization (AQO. Numerical simulations of the underlying quantum dynamics allow us to quantify AQO recall accuracy with respect to the number of stored memories and noise in the input key. We investigate AQO performance with respect to how memories are stored in the Ising model according to different learning rules. Our results demonstrate that AQO recall accuracy varies strongly with learning rule, a behavior that is attributed to differences in energy landscapes. Consequently, learning rules offer a family of methods for programming adiabatic quantum optimization that we expect to be useful for characterizing AQO performance.
Adiabatic Theorem for Quantum Spin Systems
Bachmann, S.; De Roeck, W.; Fraas, M.
2017-08-01
The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ɛ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.
Adiabatic Quantum Optimization for Associative Memory Recall
Seddiqi, Hadayat; Humble, Travis
2014-12-01
Hopfield networks are a variant of associative memory that recall patterns stored in the couplings of an Ising model. Stored memories are conventionally accessed as fixed points in the network dynamics that correspond to energetic minima of the spin state. We show that memories stored in a Hopfield network may also be recalled by energy minimization using adiabatic quantum optimization (AQO). Numerical simulations of the underlying quantum dynamics allow us to quantify AQO recall accuracy with respect to the number of stored memories and noise in the input key. We investigate AQO performance with respect to how memories are stored in the Ising model according to different learning rules. Our results demonstrate that AQO recall accuracy varies strongly with learning rule, a behavior that is attributed to differences in energy landscapes. Consequently, learning rules offer a family of methods for programming adiabatic quantum optimization that we expect to be useful for characterizing AQO performance.
Ehrenfest's adiabatic hypothesis in Bohr's quantum theory
Pérez, Enric
2015-01-01
It is widely known that Paul Ehrenfest formulated and applied his adiabatic hypothesis in the early 1910s. Niels Bohr, in his first attempt to construct a quantum theory in 1916, used it for fundamental purposes in a paper which eventually did not reach the press. He decided not to publish it after having received the new results by Sommerfeld in Munich. Two years later, Bohr published "On the quantum theory of line-spectra." There, the adiabatic hypothesis played an important role, although it appeared with another name: the principle of mechanical transformability. In the subsequent variations of his theory, Bohr never suppressed this principle completely. We discuss the role of Ehrenfest's principle in the works of Bohr, paying special attention to its relation to the correspondence principle. We will also consider how Ehrenfest faced Bohr's uses of his more celebrated contribution to quantum theory, as well as his own participation in the spreading of Bohr's ideas.
Adiabatic quantum computing with spin qubits hosted by molecules.
Yamamoto, Satoru; Nakazawa, Shigeaki; Sugisaki, Kenji; Sato, Kazunobu; Toyota, Kazuo; Shiomi, Daisuke; Takui, Takeji
2015-01-28
A molecular spin quantum computer (MSQC) requires electron spin qubits, which pulse-based electron spin/magnetic resonance (ESR/MR) techniques can afford to manipulate for implementing quantum gate operations in open shell molecular entities. Importantly, nuclear spins, which are topologically connected, particularly in organic molecular spin systems, are client qubits, while electron spins play a role of bus qubits. Here, we introduce the implementation for an adiabatic quantum algorithm, suggesting the possible utilization of molecular spins with optimized spin structures for MSQCs. We exemplify the utilization of an adiabatic factorization problem of 21, compared with the corresponding nuclear magnetic resonance (NMR) case. Two molecular spins are selected: one is a molecular spin composed of three exchange-coupled electrons as electron-only qubits and the other an electron-bus qubit with two client nuclear spin qubits. Their electronic spin structures are well characterized in terms of the quantum mechanical behaviour in the spin Hamiltonian. The implementation of adiabatic quantum computing/computation (AQC) has, for the first time, been achieved by establishing ESR/MR pulse sequences for effective spin Hamiltonians in a fully controlled manner of spin manipulation. The conquered pulse sequences have been compared with the NMR experiments and shown much faster CPU times corresponding to the interaction strength between the spins. Significant differences are shown in rotational operations and pulse intervals for ESR/MR operations. As a result, we suggest the advantages and possible utilization of the time-evolution based AQC approach for molecular spin quantum computers and molecular spin quantum simulators underlain by sophisticated ESR/MR pulsed spin technology.
Shortcuts to adiabaticity for quantum annealing
Takahashi, Kazutaka
2017-01-01
We study the Ising Hamiltonian with a transverse field term to simulate the quantum annealing. Using shortcuts to adiabaticity, we design the time dependence of the Hamiltonian. The dynamical invariant is obtained by the mean-field ansatz, and the Hamiltonian is designed by the inverse engineering. We show that the time dependence of physical quantities such as the magnetization is independent of the speed of the Hamiltonian variation in the infinite-range model. We also show that rotating transverse magnetic fields are useful to achieve the ideal time evolution.
An Integrated Development Environment for Adiabatic Quantum Programming
Humble, Travis S [ORNL; McCaskey, Alex [ORNL; Bennink, Ryan S [ORNL; Billings, Jay Jay [ORNL; D' Azevedo, Eduardo [ORNL; Sullivan, Blair D [ORNL; Klymko, Christine F [ORNL; Seddiqi, Hadayat [ORNL
2014-01-01
Adiabatic quantum computing is a promising route to the computational power afforded by quantum information processing. The recent availability of adiabatic hardware raises the question of how well quantum programs perform. Benchmarking behavior is challenging since the multiple steps to synthesize an adiabatic quantum program are highly tunable. We present an adiabatic quantum programming environment called JADE that provides control over all the steps taken during program development. JADE captures the workflow needed to rigorously benchmark performance while also allowing a variety of problem types, programming techniques, and processor configurations. We have also integrated JADE with a quantum simulation engine that enables program profiling using numerical calculation. The computational engine supports plug-ins for simulation methodologies tailored to various metrics and computing resources. We present the design, integration, and deployment of JADE and discuss its use for benchmarking adiabatic quantum programs.
Quantum-Classical Correspondence of Shortcuts to Adiabaticity
Okuyama, Manaka; Takahashi, Kazutaka
2017-04-01
We formulate the theory of shortcuts to adiabaticity in classical mechanics. For a reference Hamiltonian, the counterdiabatic term is constructed from the dispersionless Korteweg-de Vries (KdV) hierarchy. Then the adiabatic theorem holds exactly for an arbitrary choice of time-dependent parameters. We use the Hamilton-Jacobi theory to define the generalized action. The action is independent of the history of the parameters and is directly related to the adiabatic invariant. The dispersionless KdV hierarchy is obtained from the classical limit of the KdV hierarchy for the quantum shortcuts to adiabaticity. This correspondence suggests some relation between the quantum and classical adiabatic theorems.
High Fidelity Adiabatic Quantum Computation via Dynamical Decoupling
Quiroz, Gregory
2012-01-01
We introduce high-order dynamical decoupling strategies for open system adiabatic quantum computation. Our numerical results demonstrate that a judicious choice of high-order dynamical decoupling method, in conjunction with an encoding which allows computation to proceed alongside decoupling, can dramatically enhance the fidelity of adiabatic quantum computation in spite of decoherence.
Sufficient Condition for Validity of Quantum Adiabatic Theorem
TAO Yong
2012-01-01
In this paper, we attempt to give a sufficient condition of guaranteeing the validity of the proof of the quantum adiabatic theorem. The new sufficient condition can clearly remove the inconsistency and the counterexample of the quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 （2004） 160408].
Quantum CPU and Quantum Algorithm
Wang, An Min
1999-01-01
Making use of an universal quantum network -- QCPU proposed by me\\upcite{My1}, it is obtained that the whole quantum network which can implement some the known quantum algorithms including Deutsch algorithm, quantum Fourier transformation, Shor's algorithm and Grover's algorithm.
Generating shortcuts to adiabaticity in quantum and classical dynamics
Jarzynski, Christopher
2013-01-01
Transitionless quantum driving achieves adiabatic evolution in a hurry, using a counter-diabatic Hamiltonian to stifle non-adiabatic transitions. Here this strategy is cast in terms of a generator of adiabatic transport, leading to a classical analogue: dissipationless classical driving. For the single-particle piston, this approach yields simple and exact expressions for both the classical and quantal counter-diabatic terms. These results are further generalized to even-power-law potentials in one degree of freedom.
Investigating the Performance of an Adiabatic Quantum Optimization Processor
Rose, Geordie; Dickson, Neil G; Hamze, Firas; Amin, M H S; Drew-Brook, Marshall; Chudak, Fabian A; Bunyk, Paul I; Macready, William G
2010-01-01
We calculate median adiabatic times (in seconds) of a specific superconducting adiabatic quantum processor for an NP-hard Ising spin glass instance class with up to N=128 binary variables. To do so, we ran high performance Quantum Monte Carlo simulations on a large-scale Internet-based computing platform. We compare the median adiabatic times with the median running times of two classical solvers and find that, for problems with up to 128 variables, the adiabatic times for the simulated processor architecture are about 4 and 6 orders of magnitude shorter than the two classical solvers' times. This performance difference shows that, even in the potential absence of a scaling advantage, adiabatic quantum optimization may outperform classical solvers.
Entanglement, quantum phase transitions and quantum algorithms
Orus, R
2006-01-01
The work that we present in this thesis tries to be at the crossover of quantum information science, quantum many-body physics, and quantum field theory. We use tools from these three fields to analyze problems that arise in the interdisciplinary intersection. More concretely, in Chapter 1 we consider the irreversibility of renormalization group flows from a quantum information perspective by using majorization theory and conformal field theory. In Chapter 2 we compute the entanglement of a single copy of a bipartite quantum system for a variety of models by using techniques from conformal field theory and Toeplitz matrices. The entanglement entropy of the so-called Lipkin-Meshkov-Glick model is computed in Chapter 3, showing analogies with that of (1+1)-dimensional quantum systems. In Chapter 4 we apply the ideas of scaling of quantum correlations in quantum phase transitions to the study of quantum algorithms, focusing on Shor's factorization algorithm and quantum algorithms by adiabatic evolution solving a...
Towards robust dynamical decoupling and high fidelity adiabatic quantum computation
Quiroz, Gregory
Quantum computation (QC) relies on the ability to implement high-fidelity quantum gate operations and successfully preserve quantum state coherence. One of the most challenging obstacles for reliable QC is overcoming the inevitable interaction between a quantum system and its environment. Unwanted interactions result in decoherence processes that cause quantum states to deviate from a desired evolution, consequently leading to computational errors and loss of coherence. Dynamical decoupling (DD) is one such method, which seeks to attenuate the effects of decoherence by applying strong and expeditious control pulses solely to the system. Provided the pulses are applied over a time duration sufficiently shorter than the correlation time associated with the environment dynamics, DD effectively averages out undesirable interactions and preserves quantum states with a low probability of error, or fidelity loss. In this study various aspects of this approach are studied from sequence construction to applications of DD to protecting QC. First, a comprehensive examination of the error suppression properties of a near-optimal DD approach is given to understand the relationship between error suppression capabilities and the number of required DD control pulses in the case of ideal, instantaneous pulses. While such considerations are instructive for examining DD efficiency, i.e., performance vs the number of control pulses, high-fidelity DD in realizable systems is difficult to achieve due to intrinsic pulse imperfections which further contribute to decoherence. As a second consideration, it is shown how one can overcome this hurdle and achieve robustness and recover high-fidelity DD in the presence of faulty control pulses using Genetic Algorithm optimization and sequence symmetrization. Thirdly, to illustrate the implementation of DD in conjunction with QC, the utilization of DD and quantum error correction codes (QECCs) as a protection method for adiabatic quantum
Quantum algorithmic information theory
Svozil, Karl
1995-01-01
The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental atoms processed by quantum computation are the quantum bits which are dealt with in quantum information theory. The theory of quantum computation will be based upon a model of universal quantum computer whose elementary unit is a two-port interferometer capa...
Relaxation versus adiabatic quantum steady-state preparation
Venuti, Lorenzo Campos; Albash, Tameem; Marvian, Milad; Lidar, Daniel; Zanardi, Paolo
2017-04-01
Adiabatic preparation of the ground states of many-body Hamiltonians in the closed-system limit is at the heart of adiabatic quantum computation, but in reality systems are always open. This motivates a natural comparison between, on the one hand, adiabatic preparation of steady states of Lindbladian generators and, on the other hand, relaxation towards the same steady states subject to the final Lindbladian of the adiabatic process. In this work we thus adopt the perspective that the goal is the most efficient possible preparation of such steady states, rather than ground states. Using known rigorous bounds for the open-system adiabatic theorem and for mixing times, we are then led to a disturbing conclusion that at first appears to doom efforts to build physical quantum annealers: relaxation seems to always converge faster than adiabatic preparation. However, by carefully estimating the adiabatic preparation time for Lindbladians describing thermalization in the low-temperature limit, we show that there is, after all, room for an adiabatic speedup over relaxation. To test the analytically derived bounds for the adiabatic preparation time and the relaxation time, we numerically study three models: a dissipative quasifree fermionic chain, a single qubit coupled to a thermal bath, and the "spike" problem of n qubits coupled to a thermal bath. Via these models we find that the answer to the "which wins" question depends for each model on the temperature and the system-bath coupling strength. In the case of the "spike" problem we find that relaxation during the adiabatic evolution plays an important role in ensuring a speedup over the final-time relaxation procedure. Thus, relaxation-assisted adiabatic preparation can be more efficient than both pure adiabatic evolution and pure relaxation.
(Hybrid) Baryons Quantum Numbers and Adiabatic Potentials
Page, P R
1999-01-01
We construct (hybrid) baryons in the flux-tube model of Isgur and Paton. In the limit of adiabatic quark motion, we build proper eigenstates of orbital angular momentum and indicate the flavour, spin, chirality and J^P of (hybrid) baryons. The adiabatic potential is calculated as a function of the quark positions.
A Random Matrix Model of Adiabatic Quantum Computing
Mitchell, D R; Lue, W; Williams, C P; Mitchell, David R.; Adami, Christoph; Lue, Waynn; Williams, Colin P.
2004-01-01
We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of Random Matrix Theory (RMT). We determine the global regularity of the spectral fluctuations of the instantaneous Hamiltonians encountered during the interpolation between the starting Hamiltonians and the ones whose ground states encode the solutions to the computational problems of interest. At each interpolation point, we quantify the degree of regularity of the average spectral distribution via its Brody parameter, a measure that distinguishes regular (i.e., Poissonian) from chaotic (i.e., Wigner-type) distributions of normalized nearest-neighbor spacings. We find that for hard problem instances, i.e., those having a critical ratio of clauses to variables, the spectral fluctuations typically become irregular across a contiguous region of the interpolation parameter, while the spectrum is regular for easy instances. Within the hard region, RMT may be applied to obtain a mathemat...
Quantum state preparation in semiconductor dots by adiabatic rapid passage
Wu, Yanwen; Piper, I.M.; Ediger, M.; Brereton, P.; Schmidgall, E. R.; Hugues, M.; Hopkinson, M.; Phillips, R.T.
2010-01-01
Preparation of a specific quantum state is a required step for a variety of proposed practical uses of quantum dynamics. We report an experimental demonstration of optical quantum state preparation in a semiconductor quantum dot with electrical readout, which contrasts with earlier work based on Rabi flopping in that the method is robust with respect to variation in the optical coupling. We use adiabatic rapid passage, which is capable of inverting single dots to a specified upper level. We d...
Systematic Analysis of Majorization in Quantum Algorithms
Orus, R; Martín-Delgado, M A; Orus, Roman; Latorre, Jose I.; Martin-Delgado, Miguel A.
2002-01-01
Motivated by the need to uncover some underlying mathematical structure of efficient quantum computation, we carry out a systematic analysis of a wide variety of quantum algorithms from the majorization theory point of view. We conclude that step-by-step majorization is found in the known instances of efficient algorithms, namely in the quantum Fourier transform, in Grover's algorithm, in the hidden affine function problem, in searching by quantum adiabatic evolution and in deterministic quantum walks in continuous time solving a classically hard problem. On the other hand, the optimal quantum algorithm for parity determination, which does not provide any computational speed up, does not show step-by-step majorization. Furthermore, the efficient quantum algorithm for the hidden affine function problem does not make use of any entanglement while it does obey majorization. All the above results give support to a step-by-step Majorization Principle necessary for efficient quantum computation.
Adame, J.; Warzel, S., E-mail: warzel@ma.tum.de [Zentrum Mathematik, TU München, Boltzmannstr. 3, 85747 Garching (Germany)
2015-11-15
In this note, we use ideas of Farhi et al. [Int. J. Quantum. Inf. 6, 503 (2008) and Quantum Inf. Comput. 11, 840 (2011)] who link a lower bound on the run time of their quantum adiabatic search algorithm to an upper bound on the energy gap above the ground-state of the generators of this algorithm. We apply these ideas to the quantum random energy model (QREM). Our main result is a simple proof of the conjectured exponential vanishing of the energy gap of the QREM.
Algorithms for Quantum Computers
Smith, Jamie
2010-01-01
This paper surveys the field of quantum computer algorithms. It gives a taste of both the breadth and the depth of the known algorithms for quantum computers, focusing on some of the more recent results. It begins with a brief review of quantum Fourier transform based algorithms, followed by quantum searching and some of its early generalizations. It continues with a more in-depth description of two more recent developments: algorithms developed in the quantum walk paradigm, followed by tensor network evaluation algorithms (which include approximating the Tutte polynomial).
Cleve, R; Henderson, L; Macchiavello, C; Mosca, M
1998-01-01
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle) interferometers. We show how most known quantum algorithms, including quantum algorithms for factorising and counting, may be cast in this manner. Quantum searching is described as inducing a desired relative phase between two eigenvectors to yield constructive interference on the sought elements and destructive interference on the remaining terms.
Fidelity of adiabatic holonomic quantum gates
Malinovsky, Vladimir; Rudin, Sergey
2016-05-01
During last few years non-Abelian geometric phases are attracting increasing interest due to possible experimental applications in quantum computation. Here we discuss universal set of holonomic quantum gates using the geometric phase that the qubit wave function acquires after a cyclic evolution. The proposed scheme utilizes ultrafast pulses and provides a possibility to substantially suppress transient population of the ancillary states. Fidelity of the holonomic quantum gates in the presence of dephasing and dissipation is discussed. Example of electron spin qubit system in the InGaN/GaN, GaN/AlN quantum dot is considered in details.
New Dynamical Scaling Universality for Quantum Networks Across Adiabatic Quantum Phase Transitions
Acevedo, Oscar L.; Rodriguez, Ferney J.; Quiroga, Luis; Johnson, Neil F.; Rey, Ana M.
2014-05-01
We reveal universal dynamical scaling behavior across adiabatic quantum phase transitions in networks ranging from traditional spatial systems (Ising model) to fully connected ones (Dicke and Lipkin-Meshkov-Glick models). Our findings, which lie beyond traditional critical exponent analysis and adiabatic perturbation approximations, are applicable even where excitations have not yet stabilized and, hence, provide a time-resolved understanding of quantum phase transitions encompassing a wide range of adiabatic regimes. We show explicitly that even though two systems may traditionally belong to the same universality class, they can have very different adiabatic evolutions. This implies that more stringent conditions need to be imposed than at present, both for quantum simulations where one system is used to simulate the other and for adiabatic quantum computing schemes.
Quantum tunneling, adiabatic invariance and black hole spectroscopy
Li, Guo-Ping; Zu, Xiao-Tao [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Pu, Jin [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); China West Normal University, College of Physics and Space Science, Nanchong (China); Jiang, Qing-Quan [China West Normal University, College of Physics and Space Science, Nanchong (China)
2017-05-15
In the tunneling framework, one of us, Jiang, together with Han has studied the black hole spectroscopy via adiabatic invariance, where the adiabatic invariant quantity has been intriguingly obtained by investigating the oscillating velocity of the black hole horizon. In this paper, we attempt to improve Jiang-Han's proposal in two ways. Firstly, we once again examine the fact that, in different types (Schwarzschild and Painleve) of coordinates as well as in different gravity frames, the adiabatic invariant I{sub adia} = circular integral p{sub i}dq{sub i} introduced by Jiang and Han is canonically invariant. Secondly, we attempt to confirm Jiang-Han's proposal reasonably in more general gravity frames (including Einstein's gravity, EGB gravity and HL gravity). Concurrently, for improving this proposal, we interestingly find in more general gravity theories that the entropy of the black hole is an adiabatic invariant action variable, but the horizon area is only an adiabatic invariant. In this sense, we emphasize the concept that the quantum of the black hole entropy is more natural than that of the horizon area. (orig.)
Adiabatic swimming in an ideal quantum gas.
Avron, J E; Gutkin, B; Oaknin, D H
2006-04-07
Interference effects are important for swimming of mesoscopic systems that are small relative to the coherence length of the surrounding quantum medium. Swimming is geometric for slow swimmers and the distance covered in each stroke is determined, explicitly, in terms of the on-shell scattering matrix. Remarkably, for a one-dimensional Fermi gas at zero temperature we find that slow swimming is topological: the swimming distance covered in one stroke is quantized in half integer multiples of the Fermi wavelength. In addition, a careful choice of the swimming stroke can eliminate dissipation.
Quantum Central Processing Unit and Quantum Algorithm
王安民
2002-01-01
Based on a scalable and universal quantum network, quantum central processing unit, proposed in our previous paper [Chin. Phys. Left. 18 (2001)166], the whole quantum network for the known quantum algorithms,including quantum Fourier transformation, Shor's algorithm and Grover's algorithm, is obtained in a unitied way.
Analysis of adiabatic transfer in cavity quantum electrodynamics
Joyee Ghosh; R Ghosh; Deepak Kumar
2011-10-01
A three-level atom in a conﬁguration trapped in an optical cavity forms a basic unit in a number of proposed protocols for quantum information processing. This system allows for efﬁcient storage of cavity photons into long-lived atomic excitations, and their retrieval with high ﬁdelity, in an adiabatic transfer process through the ‘dark state’ by a slow variation of the control laser intensity. We study the full quantum mechanics of this transfer process with a view to examine the non-adiabatic effects arising from inevitable excitations of the system to states involving the upper level of , which is radiative. We ﬁnd that the ﬁdelity of storage is better, the stronger the control ﬁeld and the slower the rate of its switching off. On the contrary, unlike the adiabatic notion, retrieval is better with faster rates of switching on of an optimal control ﬁeld. Also, for retrieval, the behaviour with dissipation is non-monotonic. These results lend themselves to experimental tests. Our exact computations, when applied to slow variations of the control intensity for strong atom–photon couplings, are in very good agreement with Berry’s superadiabatic transfer results without dissipation.
Particle creation and non-adiabatic transitions in quantum cosmology
Massar, S
1998-01-01
The aim of this paper is to compute transitions amplitudes in quantum cosmology, and in particular pair creation amplitudes and radiative transitions. To this end, we apply a double adiabatic development to the solutions of the Wheeler-DeWitt equation restricted to mini-superspace wherein gravity is described by the scale factor $a$. The first development consists in working with instantaneous eigenstates, in $a$, of the matter Hamiltonian. The second development is applied to the gravitational part of the wave function and generalizes the usual WKB approximation. We then obtain an exact equation which replaces the Wheeler-DeWitt equation and determines the evolution, i.e. the dependence in $a$, of the coefficients of this double expansion. When working in the gravitational adiabatic approximation, the simplified equation delivers the unitary evolution of transition amplitudes occurring among instantaneous eigenstates. Upon abandoning this approximation, one finds that there is an additional coupling among ma...
Dattani, Nike; Tanburn, Richard; Lunt, Oliver
We introduce two methods for speeding up adiabatic quantum computations by increasing the energy between the ground and first excited states. Our methods are even more general. They can be used to shift a Hamiltonian's density of states away from the ground state, so that fewer states occupy the low-lying energies near the minimum, hence allowing for faster adiabatic passages to find the ground state with less risk of getting caught in an undesired low-lying excited state during the passage. Even more generally, our methods can be used to transform a discrete optimization problem into a new one whose unique minimum still encodes the desired answer, but with the objective function's values forming a different landscape. Aspects of the landscape such as the objective function's range, or the values of certain coefficients, or how many different inputs lead to a given output value, can be decreased *or* increased. One of the many examples for which these methods are useful is in finding the ground state of a Hamiltonian using NMR. We apply our methods to an AQC algorithm for integer factorization, and the first method reduces the maximum runtime in our example by up to 754%, and the second method reduces the maximum runtime of another example by up to 250%.
Adiabatic pipelining: a key to ternary computing with quantum dots.
Pečar, P; Ramšak, A; Zimic, N; Mraz, M; Lebar Bajec, I
2008-12-10
The quantum-dot cellular automaton (QCA), a processing platform based on interacting quantum dots, was introduced by Lent in the mid-1990s. What followed was an exhilarating period with the development of the line, the functionally complete set of logic functions, as well as more complex processing structures, however all in the realm of binary logic. Regardless of these achievements, it has to be acknowledged that the use of binary logic is in computing systems mainly the end result of the technological limitations, which the designers had to cope with in the early days of their design. The first advancement of QCAs to multi-valued (ternary) processing was performed by Lebar Bajec et al, with the argument that processing platforms of the future should not disregard the clear advantages of multi-valued logic. Some of the elementary ternary QCAs, necessary for the construction of more complex processing entities, however, lead to a remarkable increase in size when compared to their binary counterparts. This somewhat negates the advantages gained by entering the ternary computing domain. As it turned out, even the binary QCA had its initial hiccups, which have been solved by the introduction of adiabatic switching and the application of adiabatic pipeline approaches. We present here a study that introduces adiabatic switching into the ternary QCA and employs the adiabatic pipeline approach to successfully solve the issues of elementary ternary QCAs. What is more, the ternary QCAs presented here are sizewise comparable to binary QCAs. This in our view might serve towards their faster adoption.
Use of non-adiabatic geometric phase for quantum computing by NMR.
Das, Ranabir; Kumar, S K Karthick; Kumar, Anil
2005-12-01
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of error. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using the non-adiabatic geometric phase we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system.
Nonadiabatic corrections to a quantum dot quantum computer working in adiabatic limit
M Ávila
2014-07-01
The time of operation of an adiabatic quantum computer must be less than the decoherence time, otherwise the computer would be nonoperative. So far, the nonadiabatic corrections to an adiabatic quantum computer are merely theoretical considerations. By the above reason, we consider the particular case of a quantum-dot-confined electron spin qubit working adiabatically in the nanoscale regime (e.g., in the MeV range of energies) and include nonadiabatic corrections in it. If the decoherence times of a quantum dot computer are ∼100 ns [J M Kikkawa and D D Awschalom, Phys. Rev. Lett. 80, 4313 (1998)] then the predicted number of one qubit gate (primitive) operations of the Loss–DiVincenzo quantum computer in such an interval of time must be > 1010. However, if the quantum-dot-confined electron spin qubit is very excited (i.e., the semiclassical limit) the number of operations of such a computer would be approximately the same as that of a classical computer. Our results suggest that for an adiabatic quantum computer to operate successfully within the decoherence times, it is necessary to take into account nonadiabatic corrections.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.
Goto, Hayato
2016-02-22
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network
Goto, Hayato
2016-02-01
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Duality in adiabatic level crossing Quantum coherence and complete reflection
Fujikawa, K; Fujikawa, Kazuo; Suzuki, Hiroshi
1997-01-01
A field dependent su(2) gauge transformation connects between the adiabatic and diabatic pictures in the (Landau-Zener-Stueckelberg) level crossing problem. It is pointed out that weak and strong level crossing interactions are interchanged under this transformation, and thus realizing a naive strong and weak duality. A reliable perturbation theory is thus formulated in the both limits of weak and strong interactions. Main characteristics of the level crossing phenomena such as the Landau-Zener formula including its numerical coefficient are well-described by simple perturbation theory without referring to Stokes phenomena. We also show that quantum coherence in a double well potential is generally suppressed by the effect of level crossing, which is analogous to the effect of Ohmic dissipation on quantum coherence.
Effect of Poisson noise on adiabatic quantum control
Kiely, A.; Muga, J. G.; Ruschhaupt, A.
2017-01-01
We present a detailed derivation of the master equation describing a general time-dependent quantum system with classical Poisson white noise and outline its various properties. We discuss the limiting cases of Poisson white noise and provide approximations for the different noise strength regimes. We show that using the eigenstates of the noise superoperator as a basis can be a useful way of expressing the master equation. Using this, we simulate various settings to illustrate different effects of Poisson noise. In particular, we show a dip in the fidelity as a function of noise strength where high fidelity can occur in the strong-noise regime for some cases. We also investigate recent claims [J. Jing et al., Phys. Rev. A 89, 032110 (2014), 10.1103/PhysRevA.89.032110] that this type of noise may improve rather than destroy adiabaticity.
Differential geometric treewidth estimation in adiabatic quantum computation
Wang, Chi; Jonckheere, Edmond; Brun, Todd
2016-10-01
The D-Wave adiabatic quantum computing platform is designed to solve a particular class of problems—the Quadratic Unconstrained Binary Optimization (QUBO) problems. Due to the particular "Chimera" physical architecture of the D-Wave chip, the logical problem graph at hand needs an extra process called minor embedding in order to be solvable on the D-Wave architecture. The latter problem is itself NP-hard. In this paper, we propose a novel polynomial-time approximation to the closely related treewidth based on the differential geometric concept of Ollivier-Ricci curvature. The latter runs in polynomial time and thus could significantly reduce the overall complexity of determining whether a QUBO problem is minor embeddable, and thus solvable on the D-Wave architecture.
Wu, Jin-Lei; Ji, Xin; Zhang, Shou
2017-01-01
We propose a dressed-state scheme to achieve shortcuts to adiabaticity in atom-cavity quantum electrodynamics for speeding up adiabatic two-atom quantum state transfer and maximum entanglement generation. Compared with stimulated Raman adiabatic passage, the dressed-state scheme greatly shortens the operation time in a non-adiabatic way. By means of some numerical simulations, we determine the parameters which can guarantee the feasibility and efficiency both in theory and experiment. Besides, numerical simulations also show the scheme is robust against the variations in the parameters, atomic spontaneous emissions and the photon leakages from the cavity.
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.
Kent, A; Kent, Adrian; Elwaine, Jim Mc
1997-01-01
The consistent histories formulation of the quantum theory of a closed system with pure initial state defines an infinite number of incompatible consistent sets, each of which gives a possible description of the physics. We investigate the possibility of using the properties of the Schmidt decomposition to define an algorithm which selects a single, physically natural, consistent set. We explain the problems which arise, set out some possible algorithms, and explain their properties with the aid of simple models. Though the discussion is framed in the language of the consistent histories approach, it is intended to highlight the difficulty in making any interpretation of quantum theory based on decoherence into a mathematically precise theory.
The theory of variational hybrid quantum-classical algorithms
McClean, Jarrod R; Babbush, Ryan; Aspuru-Guzik, Alán
2015-01-01
Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as "the quantum variational eigensolver" was developed with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through relaxation of exponential splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this proced...
Quantum algorithm for data fitting.
Wiebe, Nathan; Braun, Daniel; Lloyd, Seth
2012-08-03
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)]. In many cases, our algorithm can also efficiently find a concise function that approximates the data to be fitted and bound the approximation error. In cases where the input data are pure quantum states, the algorithm can be used to provide an efficient parametric estimation of the quantum state and therefore can be applied as an alternative to full quantum-state tomography given a fault tolerant quantum computer.
Rapid adiabatic passage in quantum dots: Influence of scattering and dephasing
Schuh, K.; Jahnke, F.; Lorke, Michael
2011-01-01
Theoretical investigations for the realization of population inversion of semiconductor quantum dot ground-state transitions by means of adiabatic passage with chirped optical pulses are presented. While the inversion due to Rabi oscillations depends sensitively on the resonance condition...
Non-adiabatic holonomy operators in classical and quantum completely integrable systems
Giachetta, G; Sardanashvily, G
2002-01-01
Given a completely integrable system, we associate to any connection on its invariant tori fibred over a parameter manifold the classical and quantum holonomy operator (generalized Berry's phase factor), without any adiabatic approximation.
A quantum-quantum Metropolis algorithm.
Yung, Man-Hong; Aspuru-Guzik, Alán
2012-01-17
The classical Metropolis sampling method is a cornerstone of many statistical modeling applications that range from physics, chemistry, and biology to economics. This method is particularly suitable for sampling the thermal distributions of classical systems. The challenge of extending this method to the simulation of arbitrary quantum systems is that, in general, eigenstates of quantum Hamiltonians cannot be obtained efficiently with a classical computer. However, this challenge can be overcome by quantum computers. Here, we present a quantum algorithm which fully generalizes the classical Metropolis algorithm to the quantum domain. The meaning of quantum generalization is twofold: The proposed algorithm is not only applicable to both classical and quantum systems, but also offers a quantum speedup relative to the classical counterpart. Furthermore, unlike the classical method of quantum Monte Carlo, this quantum algorithm does not suffer from the negative-sign problem associated with fermionic systems. Applications of this algorithm include the study of low-temperature properties of quantum systems, such as the Hubbard model, and preparing the thermal states of sizable molecules to simulate, for example, chemical reactions at an arbitrary temperature.
Quantum state conversion in opto-electro-mechanical systems via shortcut to adiabaticity
Zhou, Xiao; Liu, Bao-Jie; Shao, L.-B.; Zhang, Xin-Ding; Xue, Zheng-Yuan
2017-09-01
Adiabatic processes have found many important applications in modern physics, the distinct merit of which is that accurate control over process timing is not required. However, such processes are slow, which limits their application in quantum computation, due to the limited coherent times of typical quantum systems. Here, we propose a scheme to implement quantum state conversion in opto-electro-mechanical systems via a shortcut to adiabaticity, where the process can be greatly speeded up while precise timing control is still not necessary. In our scheme, by modifying only the coupling strength, we can achieve fast quantum state conversion with high fidelity, where the adiabatic condition does not need to be met. In addition, the population of the unwanted intermediate state can be further suppressed. Therefore, our protocol presents an important step towards practical state conversion between optical and microwave photons, and thus may find many important applications in hybrid quantum information processing.
Quantum walks and search algorithms
Portugal, Renato
2013-01-01
This book addresses an interesting area of quantum computation called quantum walks, which play an important role in building quantum algorithms, in particular search algorithms. Quantum walks are the quantum analogue of classical random walks. It is known that quantum computers have great power for searching unsorted databases. This power extends to many kinds of searches, particularly to the problem of finding a specific location in a spatial layout, which can be modeled by a graph. The goal is to find a specific node knowing that the particle uses the edges to jump from one node to the next. This book is self-contained with main topics that include: Grover's algorithm, describing its geometrical interpretation and evolution by means of the spectral decomposition of the evolution operater Analytical solutions of quantum walks on important graphs like line, cycles, two-dimensional lattices, and hypercubes using Fourier transforms Quantum walks on generic graphs, describing methods to calculate the limiting d...
Quantum entanglement and quantum computational algorithms
Arvind
2001-02-01
The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum entanglement shows up qualitatively at the level of two qubits. We demonstrate that the one- and the two-bit Deutsch-Jozsa algorithm does not require entanglement and can be mapped onto a classical optical scheme. It is only for three and more input bits that the DJ algorithm requires the implementation of entangling transformations and in these cases it is impossible to implement this algorithm classically
Search for New Quantum Algorithms
2006-05-01
Topological computing for beginners, (slide presentation), Lecture Notes for Chapter 9 - Physics 219 - Quantum Computation. (http...14 II.A.8. A QHS algorithm for Feynman integrals ......................................................18 II.A.9. Non-abelian QHS algorithms -- A...idea is that NOT all environmentally entangling transformations are equally likely. In particular, for spatially separated physical quantum
Non-adiabatic holonomic quantum computation in linear system-bath coupling.
Sun, Chunfang; Wang, Gangcheng; Wu, Chunfeng; Liu, Haodi; Feng, Xun-Li; Chen, Jing-Ling; Xue, Kang
2016-02-05
Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of (N - 2)/N. The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.
Solving the transport without transit quantum paradox of the spatial adiabatic passage technique
Benseny, Albert; Oriols, Xavier; Mompart, Jordi
2011-01-01
We discuss and solve the transport without transit quantum paradox recently introduced in the context of the adiabatic transport of a single particle or a Bose--Einstein condensate between the two extreme traps of a triple-well potential. To this aim, we address the corresponding quantum dynamics in terms of Bohmian trajectories and show that transport always implies transit through the middle well, in full agreement with the quantum continuity equation. This adiabatic quantum transport presents a very counterintuitive effect: by slowing down the total time duration of the transport process, ultra-high Bohmian velocities are achieved such that, in the limit of perfect adiabaticity, relativistic corrections are needed to properly address the transfer process while avoiding superluminal matter wave propagation.
Preconditioned quantum linear system algorithm.
Clader, B D; Jacobs, B C; Sprouse, C R
2013-06-21
We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize generic states, show how simple ancilla measurements can be used to calculate many quantities of interest, and integrate a quantum-compatible preconditioner that greatly expands the number of problems that can achieve exponential speedup over classical linear systems solvers. To demonstrate the algorithm's applicability, we show how it can be used to compute the electromagnetic scattering cross section of an arbitrary target exponentially faster than the best classical algorithm.
An algorithm for minimization of quantum cost
Banerjee, Anindita; Pathak, Anirban
2009-01-01
A new algorithm for minimization of quantum cost of quantum circuits has been designed. The quantum cost of different quantum circuits of particular interest (eg. circuits for EPR, quantum teleportation, shor code and different quantum arithmetic operations) are computed by using the proposed algorithm. The quantum costs obtained using the proposed algorithm is compared with the existing results and it is found that the algorithm has produced minimum quantum cost in all cases.
Quantum state engineering in a cavity by Stark chirped rapid adiabatic passage
Amniat-Talab, M; Guérin, S
2006-01-01
We propose a robust scheme to generate single-photon Fock states and atom-photon and atom-atom entanglement in atom-cavity systems. We also present a scheme for quantum networking between two cavity nodes using an atomic channel. The mechanism is based on Stark-chirped rapid adiabatic passage (SCRAP) and half-SCRAP processes in a microwave cavity. The engineering of these states depends on the design of the adiabatic dynamics through the static and dynamic Stark shifts.
Algorithms on ensemble quantum computers.
Boykin, P Oscar; Mor, Tal; Roychowdhury, Vwani; Vatan, Farrokh
2010-06-01
In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers, e.g., on liquid NMR quantum computers. These algorithms are Shor's factorization algorithm, Grover's search algorithm (with several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation of Toffoli and σ(z)(¼) as these operations cannot be implemented "bitwise", and their standard fault-tolerant implementations require measurement.
Chen, Jingwei [State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-sen University, Guangzhou 510275 (China); Wei, L.F., E-mail: weilianfu@gmail.com [State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-sen University, Guangzhou 510275 (China); Quantum Optoelectronics Laboratory, School of Physics and Technology, Southwest Jiaotong University, Chengdu 610031 (China)
2015-10-23
Highlights: • A specific SCRAP technique is proposed to realize quantum gates in the circuit QED. • These quantum gates are insensitive to the durations of the applied pluses. • The implemented quantum gates are robustness against the operational imperfections. - Abstract: We show that a set of universal quantum gates could be implemented robustly in a circuit QED system by using Stark-chirped rapid adiabatic passage (SCRAP) technique. Under the adiabatic limit we find that the population transfers could be deterministically passaged from one selected quantum states to the others, and thus the desired quantum gates can be implemented. The proposed SCRAP-based gates are insensitive to the details of the operations and thus relax the designs of the applied pulses, operational imperfections, and the decoherence of the system.
Error suppression and error correction in adiabatic quantum computation I: techniques and challenges
Young, Kevin C.; Sarovar, Mohan; Blume-Kohout, Robin
2013-01-01
Adiabatic quantum computation (AQC) is known to possess some intrinsic robustness, though it is likely that some form of error correction will be necessary for large scale computations. Error handling routines developed for circuit-model quantum computation do not transfer easily to the AQC model since these routines typically require high-quality quantum gates, a resource not generally allowed in AQC. There are two main techniques known to suppress errors during an AQC implementation: energy...
Reprint of : Nanomagnet coupled to quantum spin Hall edge: An adiabatic quantum motor
Arrachea, Liliana; von Oppen, Felix
2016-08-01
The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer-Büttiker theory. Scattering theory provides a microscopic derivation of the Landau-Lifshitz-Gilbert equation for the magnetization dynamics of the device, including spin-transfer torque, Gilbert damping, and Langevin torque. We find that the device can be viewed as a Thouless motor, attaining unit efficiency when the chemical potential of the edge states falls into the magnetization-induced gap. For more general parameters, we characterize the device by means of a figure of merit analogous to the ZT value in thermoelectrics.
Using the J1-J2 Quantum Spin Chain as an Adiabatic Quantum Data Bus
Chancellor, Nicholas
2012-01-01
This paper investigates numerically a phenomenon which can be used to transport a single q-bit down a J1-J2 Heisenberg spin chain using a quantum adiabatic process. The motivation for investigating such processes comes from the idea that this method of transport could potentially be used as a means of sending data to various parts of a quantum computer made of artificial spins, and that this method could take advantage of the easily prepared ground state at the so called Majumdar-Ghosh point. We examine several annealing protocols for this process and find similar result for all of them. The annealing process works well up to a critical frustration threshold.
Gossip algorithms in quantum networks
Siomau, Michael
2017-01-01
Gossip algorithms is a common term to describe protocols for unreliable information dissemination in natural networks, which are not optimally designed for efficient communication between network entities. We consider application of gossip algorithms to quantum networks and show that any quantum network can be updated to optimal configuration with local operations and classical communication. This allows to speed-up - in the best case exponentially - the quantum information dissemination. Irrespective of the initial configuration of the quantum network, the update requiters at most polynomial number of local operations and classical communication.
How do quantum numbers generally vary in the adiabatic transformation of an ideal gas?
Yarman, T.; L. Kholmetskii, A.
2011-10-01
We continue to analyse the known law of adiabatic transformation for an ideal gas PV5/3 = Constant, where P is the pressure and V is the volume, and following the approach of non-relativistic quantum mechanics which we suggested in a previous work (Yarman et al. 2010 Int. J. Phys. Sci. 5 1524). We explicitly determine the constant for the general parallelepiped geometry of a container. We also disclose how the quantum numbers associated with molecules of an ideal gas vary through an arbitrary adiabatic transformation. Physical implications of the results obtained are discussed.
How do quantum numbers generally vary in the adiabatic transformation of an ideal gas?
T. Yarman; A. L. Kholmetskii
2011-01-01
We continue to analyse the known law of adiabatic transformation for an ideal gas PV5/3 =Constant,where P is the pressure and V is the volume,and following the approach of non-relativistic quantum mechanics which we suggested in a previous work (Yarman et al.2010 Int.J.Phys.Sci.5 1524).We explicitly determine the constant for the general parallelepiped geometry of a container.We also disclose how the quantum numbers associated with molecules of an ideal gas vary through an arbitrary adiabatic transformation.Physical implications of the results obtained are discussed.
Zlatanov, Kaloyan N.; Vitanov, Nikolay V.
2017-07-01
The common objective of the application of adiabatic techniques in the field of quantum control is to transfer a quantum system from one discrete energy state to another. These techniques feature both high efficiency and insensitivity to variations in the experimental parameters, e.g., variations in the driving field amplitude, duration, frequency, and shape, as well as fluctuations in the environment. Here we explore the potential of adiabatic techniques for creating arbitrary predefined coherent superpositions of two quantum states. We show that an equally weighted coherent superposition can be created by temporal variation of the ratio between the Rabi frequency Ω (t ) and the detuning Δ (t ) from 0 to ∞ (case 1) or vice versa (case 2), as it is readily deduced from the explicit adiabatic solution for the Bloch vector. We infer important differences between cases 1 and 2 in the composition of the created coherent superposition: The latter depends on the dynamical phase of the process in case 2, while it does not depend on this phase in case 1. Furthermore, an arbitrary coherent superposition of unequal weights can be created by using asymptotic ratios of Ω (t )/Δ (t ) different from 0 and ∞ . We supplement the general adiabatic solution with analytic solutions for three exactly soluble models: two trigonometric models and the hyperbolic Demkov-Kunike model. They allow us not only to demonstrate the general predictions in specific cases but also to derive the nonadiabatic corrections to the adiabatic solutions.
Robust quantum logic in neutral atoms via adiabatic Rydberg dressing
Keating, Tyler; Cook, Robert L.; Hankin, Aaron M.; Jau, Yuan-Yu; Biedermann, Grant W.; Deutsch, Ivan H.
2015-01-01
We study a scheme for implementing a controlled-Z (cz) gate between two neutral-atom qubits based on the Rydberg blockade mechanism in a manner that is robust to errors caused by atomic motion. By employing adiabatic dressing of the ground electronic state, we can protect the gate from decoherence due to random phase errors that typically arise because of atomic thermal motion. In addition, the adiabatic protocol allows for a Doppler-free configuration that involves counterpropagating lasers in a σ+/σ- orthogonal polarization geometry that further reduces motional errors due to Doppler shifts. The residual motional error is dominated by dipole-dipole forces acting on doubly excited Rydberg atoms when the blockade is imperfect. For reasonable parameters, with qubits encoded into the clock states of 133Cs, we predict that our protocol could produce a cz gate in <10 μ s with error probability on the order of 10-3.
Quantum state engineering with flux-biased Josephson phase qubits by rapid adiabatic passages
Nie, W.; Huang, J. S.; Shi, X.; Wei, L. F.
2010-09-01
In this article, the scheme of quantum computing based on the Stark-chirped rapid adiabatic passage (SCRAP) technique [L. F. Wei, J. R. Johansson, L. X. Cen, S. Ashhab, and F. Nori, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.100.113601 100, 113601 (2008)] is extensively applied to implement quantum state manipulations in flux-biased Josephson phase qubits. The broken-parity symmetries of bound states in flux-biased Josephson junctions are utilized to conveniently generate the desirable Stark shifts. Then, assisted by various transition pulses, universal quantum logic gates as well as arbitrary quantum state preparations can be implemented. Compared with the usual π-pulse operations widely used in experiments, the adiabatic population passages proposed here are insensitive to the details of the applied pulses and thus the desirable population transfers can be satisfyingly implemented. The experimental feasibility of the proposal is also discussed.
Implementing a Universal Quantum Cloning Machine via Adiabatic Evolution in Ion-Trap System
YI Xiao-Jie; YANG Rong-Can; NIE Yi-You; LI Hong-Cai; ZHOU Nan-Run; LIN Xiu; HUANG Yi-Bing; HUANG Zhi-Ping; HONG Zhi-Hui; XIE Hong; LI Song-Song
2008-01-01
A scheme for the realization of a universal quantum cloning machine is proposed in this paper. The present protocol does not need the vibrational mode to act as the memory and it is robust against small changes of experimental parameters due to adiabatic passages. Furthermore, the scheme may be realized based on current technology.
Unification and limitations of error suppression techniques for adiabatic quantum computing
Young, Kevin C.; Sarovar, Mohan
2012-01-01
While adiabatic quantum computation (AQC) possesses some intrinsic robustness to noise, it is expected that a form of error control will be necessary for large scale computations. Error control ideas developed for circuit-model quantum computation do not transfer easily to the AQC model and to date there have been two main proposals to suppress errors during an AQC implementation: energy gap protection and dynamical decoupling. Here we show that these two methods are fundamentally related and...
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity
Okuyama, Manaka; Takahashi, Kazutaka
2016-08-01
Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic X Y spin chains from the Toda equations are studied in detail.
Scaling-up quantum heat engines efficiently via shortcuts to adiabaticity
Beau, M; del Campo, A
2016-01-01
The finite-time operation of a quantum heat engine that uses a single particle as a working medium generally increases the output power at the expense of inducing friction that lowers the cycle efficiency. We propose to scale up a quantum heat engine utilizing a many-particle working medium in combination with the use of shortcuts to adiabaticity to boost the nonadiabatic performance by eliminating quantum friction and reducing the cycle time. To this end, we first analyze the finite-time thermodynamics of a quantum Otto cycle implemented with a quantum fluid confined in a time-dependent harmonic trap. We show that nonadiabatic effects can be controlled and tailored to match the adiabatic performance using a variety of shortcuts to adiabaticity. As a result, the nonadiabatic dynamics of the scaled-up many-particle quantum heat engine exhibits no friction and the cycle can be run at maximum efficiency with a tunable output power. We demonstrate our results with a working medium consisting of particles with inv...
Scaling-Up Quantum Heat Engines Efficiently via Shortcuts to Adiabaticity
Mathieu Beau
2016-04-01
Full Text Available The finite-time operation of a quantum heat engine that uses a single particle as a working medium generally increases the output power at the expense of inducing friction that lowers the cycle efficiency. We propose to scale up a quantum heat engine utilizing a many-particle working medium in combination with the use of shortcuts to adiabaticity to boost the nonadiabatic performance by eliminating quantum friction and reducing the cycle time. To this end, we first analyze the finite-time thermodynamics of a quantum Otto cycle implemented with a quantum fluid confined in a time-dependent harmonic trap. We show that nonadiabatic effects can be controlled and tailored to match the adiabatic performance using a variety of shortcuts to adiabaticity. As a result, the nonadiabatic dynamics of the scaled-up many-particle quantum heat engine exhibits no friction, and the cycle can be run at maximum efficiency with a tunable output power. We demonstrate our results with a working medium consisting of particles with inverse-square pairwise interactions that includes non-interacting and hard-core bosons as limiting cases.
Quantum robot: structure, algorithms and applications
Dong, Daoyi; Zhang, Chenbin; Chen, Zonghai
2008-01-01
A brand-new paradigm of robots--quantum robots--is proposed through the fusion of quantum theory with robot technology. A quantum robot is essentially a complex quantum system which generally consists of three fundamental components: multi-quantum computing units (MQCU), quantum controller/actuator, and information acquisition units. Corresponding to the system structure, several learning control algorithms, including quantum searching algorithms and quantum reinforcement learning algorithms, are presented for quantum robots. The theoretical results show that quantum robots using quantum searching algorithms can reduce the complexity of the search problem from O(N^2) in classical robots to O(N^3/2). Simulation results demonstrate that quantum robots are also superior to classical robots in efficient learning under novel quantum reinforcement learning algorithms. Considering the advantages of quantum robots, some important potential applications are also analyzed and prospected.
He, Shuang; Su, Shi-Lei; Wang, Dong-Yang; Sun, Wen-Mei; Bai, Cheng-Hua; Zhu, Ai-Dong; Wang, Hong-Fu; Zhang, Shou
2016-08-01
We propose an effective scheme of shortcuts to adiabaticity for generating a three-dimensional entanglement of two atoms trapped in a cavity using the transitionless quantum driving (TQD) approach. The key point of this approach is to construct an effective Hamiltonian that drives the dynamics of a system along instantaneous eigenstates of a reference Hamiltonian to reproduce the same final state as that of an adiabatic process within a much shorter time. In this paper, the shortcuts to adiabatic passage are constructed by introducing two auxiliary excited levels in each atom and applying extra cavity modes and classical fields to drive the relevant transitions. Thereby, the three-dimensional entanglement is obtained with a faster rate than that in the adiabatic passage. Moreover, the influences of atomic spontaneous emission and photon loss on the fidelity are discussed by numerical simulation. The results show that the speed of entanglement implementation is greatly improved by the use of adiabatic shortcuts and that this entanglement implementation is robust against decoherence. This will be beneficial to the preparation of high-dimensional entanglement in experiment and provides the necessary conditions for the application of high-dimensional entangled states in quantum information processing.
Bang-Bang shortcut to adiabaticity in trapped ion quantum simulators
Yoshimura, Bryce; Balasubramanian, Shankar; Han, Shuyang; Freericks, James
2016-05-01
An experimental simulation can prepare a nontrivial ground state via an adiabatic process, however due to experimental constraints this process becomes more and more difficult as the number of ions increase. Instead, we model the bang-bang optimization protocol as a shortcut to adiabaticity in the ground-state preparation of an ion-trap-based quantum simulator. This well known technique in the quantum control community is simple to implement and can be applied without prior knowledge of the Hamiltonian. We apply the bang-bang optimization protocol to the transverse-field Ising model as simulated in a linear Paul trap. We compare our results to a transverse magnetic field that exponential decays and the locally adiabatic approach. The bang-bang protocol produces a significantly higher ground-state probability than the exponential ramp. Although the bang-bang protocol produces a somewhat lower ground-state probability than the locally adiabatic approach, the implementation of the bang-bang protocol is far more simple than the locally adiabatic approach. NSF PHY-1314295.
He, Shuang; Su, Shi-Lei; Wang, Dong-Yang; Sun, Wen-Mei; Bai, Cheng-Hua; Zhu, Ai-Dong; Wang, Hong-Fu; Zhang, Shou
2016-08-08
We propose an effective scheme of shortcuts to adiabaticity for generating a three-dimensional entanglement of two atoms trapped in a cavity using the transitionless quantum driving (TQD) approach. The key point of this approach is to construct an effective Hamiltonian that drives the dynamics of a system along instantaneous eigenstates of a reference Hamiltonian to reproduce the same final state as that of an adiabatic process within a much shorter time. In this paper, the shortcuts to adiabatic passage are constructed by introducing two auxiliary excited levels in each atom and applying extra cavity modes and classical fields to drive the relevant transitions. Thereby, the three-dimensional entanglement is obtained with a faster rate than that in the adiabatic passage. Moreover, the influences of atomic spontaneous emission and photon loss on the fidelity are discussed by numerical simulation. The results show that the speed of entanglement implementation is greatly improved by the use of adiabatic shortcuts and that this entanglement implementation is robust against decoherence. This will be beneficial to the preparation of high-dimensional entanglement in experiment and provides the necessary conditions for the application of high-dimensional entangled states in quantum information processing.
Baksic, Alexandre; Belyansky, Ron; Ribeiro, Hugo; Clerk, Aashish A.
2017-08-01
We present a method for accelerating adiabatic protocols for systems involving a coupling to a continuum, one that cancels both nonadiabatic errors as well as errors due to dissipation. We focus on applications to a generic quantum state transfer problem, where the goal is to transfer a state between a single level or mode, and a propagating temporal mode in a waveguide or transmission line. Our approach enables perfect adiabatic transfer protocols in this setup, despite a finite protocol speed and a finite waveguide coupling. Our approach even works in highly constrained settings, where there is only a single time-dependent control field available.
Adiabatic phase-conserving processes for executing quantum operations with ultracold atoms
Beterov, I. I.; Tret'yakov, D. B.; Entin, V. M.; Yakshina, E. A.; Khamzina, G. N.; Ryabtsev, I. I.
2017-06-01
We have studied the regimes of deterministic single-atom Rydberg excitation in the conditions of Rydberg blockade and the methods of compensation for the dynamic phase of the wave function during the adiabatic passage. Using these methods, we have proposed schemes of single-qubit and two-qubit quantum states with mesoscopic atomic ensembles containing a random number of atoms, considred as quibits. The double adiabatic passage of the Förster resonance for two interacting atoms with a deterministic phase shift can be used for the implementation of two-qubit gates with reduced sensitivity of the gate fidelity to the fluctuations of the interatomic distance.
Entanglement degradation in the solid state: Interplay of adiabatic and quantum noise
Bellomo, B.; Compagno, G.; D'Arrigo, A.; Falci, G.; Lo Franco, R.; Paladino, E.
2010-06-01
We study entanglement degradation of two noninteracting qubits subject to independent baths with broadband spectra typical of solid-state nanodevices. We obtain the analytic form of the concurrence in the presence of adiabatic noise for classes of entangled initial states presently achievable in experiments. We find that adiabatic (low-frequency) noise affects entanglement reduction analogously to pure dephasing noise. Due to quantum (high-frequency) noise, entanglement is totally lost in a state-dependent finite time. The possibility of implementing on-chip local and entangling operations is briefly discussed.
Entanglement degradation in the solid state: interplay of adiabatic and quantum noise
Bellomo, B; D'Arrigo, A; Falci, G; Franco, R Lo; Paladino, E
2010-01-01
We study entanglement degradation of two non-interacting qubits subject to independent baths with broadband spectra typical of solid state nanodevices. We obtain the analytic form of the concurrence in the presence of adiabatic noise for classes of entangled initial states presently achievable in experiments. We find that adiabatic (low frequency) noise affects entanglement reduction analogously to pure dephasing noise. Due to quantum (high frequency) noise, entanglement is totally lost in a state-dependent finite time. The possibility to implement on-chip both local and entangling operations is briefly discussed.
Efficient quantum-state transfer in spin-1 chains by adiabatic passage
Eckert, K; Sanpera, A
2007-01-01
We propose a method for quantum state transfer in spin chains using an adiabatic passage technique. Modifying even and odd nearest-neighbor couplings in time allows to achieve transfer fidelities arbitrarily close to one, without the need for a precise control of coupling strengths and timing. We study in detail transfer by adiabatic passage in a spin-1 chain governed by a generalized Heisenberg Hamiltonian. We consider optimization of the transfer process applying optimal control techniques. We discuss a realistic experimental implementation using cold atomic gases confined in deep optical lattices.
Quantum Algorithms: Database Search and its Variations
Patel, Apoorva
2011-01-01
The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen. Clever quantum algorithms have been discovered in recent years, although not systematically, and the field remains under active investigation. This article is an introduction to the quantum database search algorithm. Its extension to the quantum spatial search algorithm is also described.
Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction.
Gosset, David; Terhal, Barbara M; Vershynina, Anna
2015-04-10
We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.
Non-adiabatic elimination of auxiliary modes in continuous quantum measurements
Yang, Huan; Chen, Yanbei
2011-01-01
When measuring a complex quantum system, we are often interested in only a few degrees of freedom-the plant, while the rest of them are collected as auxiliary modes-the bath. The bath can have finite memory (non-Markovian), and simply ignoring its dynamics, i.e., adiabatically eliminating it, is inadequate to predict the true quantum behavior of the plant. We generalize the technique introduced by Strunz et. al. [Phys. Rev. Lett 82, 1801 (1999)], and develop a formalism that allows us to eliminate the bath non-adiabatically in continuous quantum measurements, and derive a non-Markovian stochastic master equation for the plant alone. We apply this formalism to two interesting examples in cavity QED: (i) a two-level atom (a qubit) coupled to a cavity and (ii) linear optomechanical interaction, both of which can be exactly solved.
Adiabatic quantum pump in a zigzag graphene nanoribbon junction
张林
2015-01-01
The adiabatic electron transport is theoretically studied in a zigzag graphene nanoribbon (ZGNR) junction with two time-dependent pumping electric fields. By modeling a ZGNR p–n junction and applying the Keldysh Green’s function method, we find that a pumped charge current is flowing in the device at a zero external bias, which mainly comes from the photon-assisted tunneling process and the valley selection rule in an even-chain ZGNR junction. The pumped charge current and its ON and OFF states can be efficiently modulated by changing the system parameters such as the pumping frequency, the pumping phase difference, and the Fermi level. A ferromagnetic ZGNR device is also studied to generate a pure spin current and a fully polarized spin current due to the combined spin pump effect and the valley valve effect. Our finding might pave the way to manipulate the degree of freedom of electrons in a graphene-based electronic device.
Adiabatic holonomic quantum gates for a single qubit
Malinovsky, Vladimir S.; Rudin, Sergey
2014-04-01
A universal set of single qubit holonomic quantum gates using the geometric phase that the qubit wave function acquires after a cyclic evolution is discussed. The proposed scheme utilizes ultrafast linearly chirped pulses and provides a possibility to substantially suppress transient population of the ancillary state in a generic three-level system. That provides a possibility to reduce the decoherence effect and achieve a higher fidelity of the quantum gates.
Function Optimization Based on Quantum Genetic Algorithm
Ying Sun; Hegen Xiong
2014-01-01
Optimization method is important in engineering design and application. Quantum genetic algorithm has the characteristics of good population diversity, rapid convergence and good global search capability and so on. It combines quantum algorithm with genetic algorithm. A novel quantum genetic algorithm is proposed, which is called Variable-boundary-coded Quantum Genetic Algorithm (vbQGA) in which qubit chromosomes are collapsed into variable-boundary-coded chromosomes instead of binary-coded c...
Function Optimization Based on Quantum Genetic Algorithm
Ying Sun; Yuesheng Gu; Hegen Xiong
2013-01-01
Quantum genetic algorithm has the characteristics of good population diversity, rapid convergence and good global search capability and so on.It combines quantum algorithm with genetic algorithm. A novel quantum genetic algorithm is proposed ,which is called variable-boundary-coded quantum genetic algorithm (vbQGA) in which qubit chromosomes are collapsed into variableboundary- coded chromosomes instead of binary-coded chromosomes. Therefore much shorter chromosome strings can be gained.The m...
Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem
Pan, Yu; James, Matthew R. [Australian National University, Research School of Engineering, Canberra (Australia); Miao, Zibo [The University of Melbourne, Department of Electrical and Electronic Engineering, Melbourne (Australia); Amini, Nina H. [CNRS, Laboratoire des Signaux et Systemes (L2S) Supelec, Gif-Sur-Yvette (France); Ugrinovskii, Valery [University of New South Wales at ADFA, School of Engineering and Information Technology, Canberra (Australia)
2015-12-15
Quantum control could be implemented by varying the system Hamiltonian. According to adiabatic theorem, a slowly changing Hamiltonian can approximately keep the system at the ground state during the evolution if the initial state is a ground state. In this paper we consider this process as an interpolation between the initial and final Hamiltonians. We use the mean value of a single operator to measure the distance between the final state and the ideal ground state. This measure resembles the excitation energy or excess work performed in thermodynamics, which can be taken as the error of adiabatic approximation. We prove that under certain conditions, this error can be estimated for an arbitrarily given interpolating function. This error estimation could be used as guideline to induce adiabatic evolution. According to our calculation, the adiabatic approximation error is not linearly proportional to the average speed of the variation of the system Hamiltonian and the inverse of the energy gaps in many cases. In particular, we apply this analysis to an example in which the applicability of the adiabatic theorem is questionable. (orig.)
Adapting the traveling salesman problem to an adiabatic quantum computer
Warren, Richard H.
2013-04-01
We show how to guide a quantum computer to select an optimal tour for the traveling salesman. This is significant because it opens a rapid solution method for the wide range of applications of the traveling salesman problem, which include vehicle routing, job sequencing and data clustering.
A Review on Quantum Search Algorithms
Giri, Pulak Ranjan
2016-01-01
The use of superposition of states in quantum computation, known as quantum parallelism, has significant advantage in terms of speed over the classical computation. It can be understood from the early invented quantum algorithms such as Deutsch's algorithm, Deutsch-Jozsa algorithm and its variation as Bernstein-Vazirani algorithm, Simon algorithm, Shor's algorithms etc. Quantum parallelism also significantly speeds up the database search algorithm, which is important in computer science because it comes as a subroutine in many important algorithms. Quantum database search of Grover achieves the task of finding the target element in an unsorted database in a time quadratically faster than the classical computer. We review the Grover quantum search algorithms for a singe and multiple target elements in a database. The partial search algorithm of Grover and Radhakrishnan and its optimization by Korepin, called GRK algorithm are also discussed.
Adiabatic Isometric Mapping Algorithm for Embedding 2-Surfaces in Euclidean 3-Space
Ray, Shannon; Alsing, Paul M; Yau, Shing-Tung
2015-01-01
Alexandrov proved that any simplicial complex homeomorphic to a sphere with strictly non-negative Gaussian curvature at each vertex can be isometrically embedded uniquely in $\\mathbb{R}^3$ as a convex polyhedron. Due to the nonconstructive nature of his proof, there have yet to be any algorithms, that we know of, that realizes the Alexandrov embedding in polynomial time. Following his proof, we developed the adiabatic isometric mapping (AIM) algorithm. AIM uses a guided adiabatic pull-back procedure to produce "smooth" embeddings. Tests of AIM applied to two different polyhedral metrics suggests that its run time is sub cubic with respect to the number of vertices. Although Alexandrov's theorem specifically addresses the embedding of convex polyhedral metrics, we tested AIM on a broader class of polyhedral metrics that included regions of negative Gaussian curvature. One test was on a surface just outside the ergosphere of a Kerr black hole.
Adiabatic isometric mapping algorithm for embedding 2-surfaces in Euclidean 3-space
Ray, Shannon; Miller, Warner A.; Alsing, Paul M.; Yau, Shing-Tung
2015-12-01
Alexandrov proved that any simplicial complex homeomorphic to a sphere with strictly non-negative Gaussian curvature at each vertex can be isometrically embedded uniquely in {{{R}}}3 as a convex polyhedron. Due to the nonconstructive nature of his proof, there have yet to be any algorithms, that we know of, that realizes the Alexandrov embedding in polynomial time. Following his proof, we developed the adiabatic isometric mapping (AIM) algorithm. AIM uses a guided adiabatic pull-back procedure on a given polyhedral metric to produce an embedding that approximates the unique Alexandrov polyhedron. Tests of AIM applied to two different polyhedral metrics suggests that its run time is sub cubic with respect to the number of vertices. Although Alexandrov’s theorem specifically addresses the embedding of convex polyhedral metrics, we tested AIM on a broader class of polyhedral metrics that included regions of negative Gaussian curvature. One test was on a surface just outside the ergosphere of a Kerr black hole.
Algorithmic complexity and entanglement of quantum states.
Mora, Caterina E; Briegel, Hans J
2005-11-11
We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its algorithmic complexity.
Fully quantum non-adiabatic dynamics in electronic-nuclear coherent state basis
Humeniuk, Alexander
2016-01-01
Direct dynamics methods using Gaussian wavepackets have to rely only on local properties, such as gradients and hessians at the center of the wavepacket, so as to be compatible with the usual quantum chemistry methods. Matrix elements of the potential energy surfaces between wavepackets therefore usually have to be approximated. It is shown, that if a modified form of valence bond theory is used instead of the usual MO-based theories, the matrix elements can be obtained exactly. This is so because the molecular Hamiltonian only contains the Coulomb potential, for which matrix elements between different basis functions (consisting of Gaussian nuclear and electronic orbitals) are all well-known. In valence bond theory the self-consistent field calculation can be avoided so that the matrix elements are analytical functions of the nuclear coordinates. A method for simulating non-adiabatic quantum dynamics is sketched, where coherent state trajectories are propagated "on the fly" on adiabatic potential energy surf...
The Quantum-Classical Crossover in the Adiabatic Response of Chaotic Systems
Ausländer, O M; Auslaender, Ophir M.; Fishman, Shmuel
1999-01-01
The autocorrelation function of the force acting on a slow classical system, resulting from interaction with a fast quantum system is calculated following Berry-Robbins and Jarzynski within the leading order correction to the adiabatic approximation. The time integral of the autocorrelation function is proportional to the rate of dissipation. The fast quantum system is assumed to be chaotic in the classical limit for each configuration of the slow system. An analytic formula is obtained for the finite time integral of the correlation function, in the framework of random matrix theory (RMT), for a specific dependence on the adiabatically varying parameter. Extension to a wider class of RMT models is discussed. For the Gaussian unitary and symplectic ensembles for long times the time integral of the correlation function vanishes or falls off as a Gaussian with a characteristic time that is proportional to the Heisenberg time, depending on the details of the model. The fall off is inversely proportional to time ...
Non-adiabatic molecular dynamics with complex quantum trajectories. I. The diabatic representation.
Zamstein, Noa; Tannor, David J
2012-12-14
We extend a recently developed quantum trajectory method [Y. Goldfarb, I. Degani, and D. J. Tannor, J. Chem. Phys. 125, 231103 (2006)] to treat non-adiabatic transitions. Each trajectory evolves on a single surface according to Newton's laws with complex positions and momenta. The transfer of amplitude between surfaces stems naturally from the equations of motion, without the need for surface hopping. In this paper we derive the equations of motion and show results in the diabatic representation, which is rarely used in trajectory methods for calculating non-adiabatic dynamics. We apply our method to the first two benchmark models introduced by Tully [J. Chem. Phys. 93, 1061 (1990)]. Besides giving the probability branching ratios between the surfaces, the method also allows the reconstruction of the time-dependent wavepacket. Our results are in quantitative agreement with converged quantum mechanical calculations.
Spectral-gap analysis for efficient tunneling in quantum adiabatic optimization
Brady, Lucas T.; van Dam, Wim
2016-09-01
We investigate the efficiency of quantum adiabatic optimization when overcoming potential barriers to get from a local to a global minimum. Specifically we look at n qubit systems with symmetric cost functions f :{0,1 } n→R , where the ground state must tunnel through a potential barrier of width nα and height nβ. By the quantum adiabatic theorem the time delay sufficient to ensure tunneling grows quadratically with the inverse spectral gap during this tunneling process. We analyze barrier sizes with 1 /2 ≤α +β and α folklore result by Goldstone from 2002, which used large spin and instanton methods. Parts of our result also refine recent results by Kong and Crosson [arXiv:1511.06991] and Jiang et al. [arXiv:1603.01293] about the exponential gap scaling.
Quantum computation in decoherence-free subspace via cavity-decay-assisted adiabatic passage
FENG Xunli
2015-08-01
Full Text Available In this work,a scheme for quantum computation based on cavity QED in a decoherence-free subspaces via using the technique of stimulated Raman adiabatic passage (STIRAP is proposed.To implement universal quantum logic gates that form basic blocks of quantum computation,we suppose two atoms are trapped in a single-mode cavity with large decay rates and are driven by the laser fields.The relatively large cavity decay can be used for the continuous detection of the cavity mode as so-called ″cavity-decay-induced quantum Zeno effect″.The results show that,decoherence induced by the atomic spontaneous emission and cavity decay can be efficiently suppress with the STIRAP technique and the quantum Zeno effect.
Non-Hermitian heat engine with all-quantum-adiabatic-process cycle
Lin, S.; Song, Z.
2016-11-01
As a quantum device, a quantum heat engine (QHE) is described by a Hermitian Hamiltonian. However, since it is an open system, reservoirs must be imposed phenomenologically without any description in the context of quantum mechanics. A non-Hermitian system is expected to describe an open system that exchanges energy and particles with external reservoirs. Correspondingly, such an exchange can be adiabatic in the context of quantum mechanics. We first propose a non-Hermitian QHE by a concrete simple two-level system, which is an S=1/2 spin in a complex external magnetic field. The non-Hermitian { P }{ T }-symmetric Hamiltonian, as a self-contained one, describes both the working medium and reservoirs. A heat engine cycle is composed of completely quantum adiabatic processes. Surprisingly, the heat efficiency is obtained to be the same as that of the Hermitian quantum Otto cycle. A classical analog of this scheme is also presented. Our finding paves the way for revealing the role of a non-Hermitian Hamiltonian in physics.
Duality quantum algorithm efficiently simulates open quantum systems
Shi-Jie Wei; Dong Ruan; Gui-Lu Long
2016-01-01
Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the op...
Algorithmic approach to quantum physics
Ozhigov, Y
2004-01-01
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the analysis, and a simulation gives a "film" which visualizes many particle quantum dynamics and is demonstrated to a user of the model. Restrictions following from the algorithm theory are considered on a level of fundamental physical laws. Born rule for the calculation of quantum probability as well as the decoherence is derived from the existence of a nonzero minimal value of amplitude module - a grain of amplitude. The limitation on the classical computational resources gives the unified description of quantum dynamics that is not divided to the unitary dynamics and measurements and does not depend on the existence of observer. It is proposed the description of states based on the nesting of particles in each other that permits to account the effects of all levels in the same mode...
A Hybrid Architecture Approach for Quantum Algorithms
Mohammad R.S. Aghaei
2009-01-01
Full Text Available Problem statement: In this study, a general plan of hybrid architecture for quantum algorithms is proposed. Approach: Analysis of the quantum algorithms shows that these algorithms were hybrid with two parts. First, the relationship of classical and quantum parts of the hybrid algorithms was extracted. Then a general plan of hybrid structure was designed. Results: This plan was illustrated the hybrid architecture and the relationship of classical and quantum parts of the algorithms. This general plan was used to increase implementation performance of quantum algorithms. Conclusion/Recommendations: Moreover, simulation results of quantum algorithms on the hybrid architecture proved that quantum algorithms can be implemented on the general plan as well.
A Hybrid Chaotic Quantum Evolutionary Algorithm
Cai, Y.; Zhang, M.; Cai, H.
2010-01-01
A hybrid chaotic quantum evolutionary algorithm is proposed to reduce amount of computation, speed up convergence and restrain premature phenomena of quantum evolutionary algorithm. The proposed algorithm adopts the chaotic initialization method to generate initial population which will form...... and enhance the global search ability. A large number of tests show that the proposed algorithm has higher convergence speed and better optimizing ability than quantum evolutionary algorithm, real-coded quantum evolutionary algorithm and hybrid quantum genetic algorithm. Tests also show that when chaos...... is introduced to quantum evolutionary algorithm, the hybrid chaotic search strategy is superior to the carrier chaotic strategy, and has better comprehensive performance than the chaotic mutation strategy in most of cases. Especially, the proposed algorithm is the only one that has 100% convergence rate in all...
Exponential algorithmic speedup by quantum walk
Childs, A M; Deotto, E; Farhi, E; Gutmann, S; Spielman, D A; Childs, Andrew M.; Cleve, Richard; Deotto, Enrico; Farhi, Edward; Gutmann, Sam; Spielman, Daniel A.
2002-01-01
We construct an oracular problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different technique from previous quantum algorithms based on quantum Fourier transforms. We show how to implement the quantum walk efficiently in our oracular setting. We then show how this quantum walk can be used to solve our problem by rapidly traversing a graph. Finally, we prove that no classical algorithm can solve this problem with high probability in subexponential time.
Recall Performance for Content-addressable Memory Using Adiabatic Quantum Optimization
Imam, Neena [ORNL; Humble, Travis S. [ORNL; McCaskey, Alex [ORNL; Schrock, Jonathan [ORNL; Hamilton, Kathleen E. [ORNL
2017-09-01
A content-addressable memory (CAM) stores key-value associations such that the key is recalled by providing its associated value. While CAM recall is traditionally performed using recurrent neural network models, we show how to solve this problem using adiabatic quantum optimization. Our approach maps the recurrent neural network to a commercially available quantum processing unit by taking advantage of the common underlying Ising spin model. We then assess the accuracy of the quantum processor to store key-value associations by quantifying recall performance against an ensemble of problem sets. We observe that different learning rules from the neural network community influence recall accuracy but performance appears to be limited by potential noise in the processor. The strong connection established between quantum processors and neural network problems supports the growing intersection of these two ideas.
Quantum algorithms for testing Boolean functions
Erika Andersson; Floess, Dominik F.; Mark Hillery
2010-01-01
We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2^n possible linear Boolean functions of n variables; given a linear Boolean function, the Bernstein-Vazirani quantum algorithm can deterministically identify which one of these Boolean functions we are given using just one single function query. The same quantum algorithm can also be used to learn which input variables other types of Boolean functions...
Pulse-driven near-resonant quantum adiabatic dynamics: lifting of quasi-degeneracy
Yatsenko, L P; Jauslin, H R
2003-01-01
We study the quantum dynamics of a two-level system driven by a pulse that starts near-resonant for small amplitudes, yielding nonadiabatic evolution, and induces an adiabatic evolution for larger amplitudes. This problem is analyzed in terms of lifting of degeneracy for rising amplitudes. It is solved exactly for the case of linear and exponential rising. Approximate solutions are given in the case of power law rising. This allows us to determine approximative formulas for the lineshape of resonant excitation by various forms of pulses such as truncated trig-pulses. We also analyze and explain the various superpositions of states that can be obtained by the Half Stark Chirped Rapid Adiabatic Passage (Half-SCRAP) process.
Central charge from adiabatic transport of cusp singularities in the quantum Hall effect
Can, Tankut
2017-04-01
We study quantum Hall (QH) states on a punctured Riemann sphere. We compute the Berry curvature under adiabatic motion in the moduli space in the large N limit. The Berry curvature is shown to be finite in the large N limit and controlled by the conformal dimension of the cusp singularity, a local property of the mean density. Utilizing exact sum rules obtained from a Ward identity, we show that for the Laughlin wave function, the dimension of a cusp singularity is given by the central charge, a robust geometric response coefficient in the QHE. Thus, adiabatic transport of curvature singularities can be used to determine the central charge of QH states. We also consider the effects of threaded fluxes and spin-deformed wave functions. Finally, we give a closed expression for all moments of the mean density in the integer QH state on a punctured disk.
Central charge from adiabatic transport of cusp singularities in the quantum Hall effect
Can, Tankut
2016-01-01
We study quantum Hall (QH) states on a punctured Riemann sphere. We compute the Berry curvature under adiabatic motion in the moduli space in the large N limit. The Berry curvature is shown to be finite in the large N limit and controlled by the conformal dimension of the cusp singularity, a local property of the mean density. Utilizing exact sum rules obtained from a Ward identity, we show that for the Laughlin wave function, the dimension of a cusp singularity is given by the central charge, a robust geometric response coefficient in the QHE. Thus, adiabatic transport of curvature singularities can be used to determine the central charge of QH states. We also consider the effects of threaded fluxes and spin-deformed wave functions. Finally, we give a closed expression for all moments of the mean density in the integer QH state on a punctured disk.
Duality quantum algorithm efficiently simulates open quantum systems.
Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu
2016-07-28
Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d(3)) in contrast to O(d(4)) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm.
Duality quantum algorithm efficiently simulates open quantum systems
Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu
2016-07-01
Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d3) in contrast to O(d4) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm.
Approximate Quantum Adders with Genetic Algorithms: An IBM Quantum Experience
Li Rui
2017-07-01
Full Text Available It has been proven that quantum adders are forbidden by the laws of quantum mechanics. We analyze theoretical proposals for the implementation of approximate quantum adders and optimize them by means of genetic algorithms, improving previous protocols in terms of efficiency and fidelity. Furthermore, we experimentally realize a suitable approximate quantum adder with the cloud quantum computing facilities provided by IBM Quantum Experience. The development of approximate quantum adders enhances the toolbox of quantum information protocols, paving the way for novel applications in quantum technologies.
Approximate Quantum Adders with Genetic Algorithms: An IBM Quantum Experience
Li, Rui; Alvarez-Rodriguez, Unai; Lamata, Lucas; Solano, Enrique
2017-07-01
It has been proven that quantum adders are forbidden by the laws of quantum mechanics. We analyze theoretical proposals for the implementation of approximate quantum adders and optimize them by means of genetic algorithms, improving previous protocols in terms of efficiency and fidelity. Furthermore, we experimentally realize a suitable approximate quantum adder with the cloud quantum computing facilities provided by IBM Quantum Experience. The development of approximate quantum adders enhances the toolbox of quantum information protocols, paving the way for novel applications in quantum technologies.
Ideal quantum gas in expanding cavity: nature of non-adiabatic force
Nakamura, K; Sobirov, Z A; Matrasulov, D U; Monnai, T
2011-01-01
We consider a quantum gas of non-interacting particles confined in the expanding cavity, and investigate the nature of the non-adiabatic force which is generated from the gas and acts on the cavity wall. Firstly, with use of the time-dependent canonical transformation which transforms the expanding cavity to the non-expanding one, we can define the force operator. Secondly, applying the perturbative theory which works when the cavity wall begins to move at time origin, we find that the non-adiabatic force is quadratic in the wall velocity and thereby does not break the time-reversal symmetry, in contrast with the general belief. Finally, using an assembly of the transitionless quantum states, we obtain the nonadiabatic force exactly. The exact result justifies the validity of both the definition of force operator and the issue of the perturbative theory. The mysterious mechanism of nonadiabatic transition with use of transitionless quantum states is also explained. The study is done on both cases of the hard-...
An explicit model for the adiabatic evolution of quantum observables driven by 1D shape resonances
Faraj, A; Nier, F
2010-01-01
This paper is concerned with a linearized version of the transport problem where the Schr\\"{o}dinger-Poisson operator is replaced by a non-autonomous Hamiltonian, slowly varying in time. We consider an explicitly solvable model where a semiclassical island is described by a flat potential barrier, while a time dependent 'delta' interaction is used as a model for a single quantum well. Introducing, in addition to the complex deformation, a further modification formed by artificial interface conditions, we give a reduced equation for the adiabatic evolution of the sheet density of charges accumulating around the interaction point.
Quantum Image Encryption Algorithm Based on Quantum Image XOR Operations
Gong, Li-Hua; He, Xiang-Tao; Cheng, Shan; Hua, Tian-Xiang; Zhou, Nan-Run
2016-07-01
A novel encryption algorithm for quantum images based on quantum image XOR operations is designed. The quantum image XOR operations are designed by using the hyper-chaotic sequences generated with the Chen's hyper-chaotic system to control the control-NOT operation, which is used to encode gray-level information. The initial conditions of the Chen's hyper-chaotic system are the keys, which guarantee the security of the proposed quantum image encryption algorithm. Numerical simulations and theoretical analyses demonstrate that the proposed quantum image encryption algorithm has larger key space, higher key sensitivity, stronger resistance of statistical analysis and lower computational complexity than its classical counterparts.
A realizable quantum encryption algorithm for qubits
Zhou Nan-Run; Zeng Gui-Hua
2005-01-01
A realizable quantum encryption algorithm for qubits is presented by employing bit-wise quantum computation.System extension and bit-swapping are introduced into the encryption process, which makes the ciphertext space expanded greatly. The security of the proposed algorithm is analysed in detail and the schematic physical implementation is also provided. It is shown that the algorithm, which can prevent quantum attack strategy as well as classical attack strategy, is effective to protect qubits. Finally, we extend our algorithm to encrypt classical binary bits and quantum entanglements.
Multiparty Quantum Key Agreement Based on Quantum Search Algorithm.
Cao, Hao; Ma, Wenping
2017-03-23
Quantum key agreement is an important topic that the shared key must be negotiated equally by all participants, and any nontrivial subset of participants cannot fully determine the shared key. To date, the embed modes of subkey in all the previously proposed quantum key agreement protocols are based on either BB84 or entangled states. The research of the quantum key agreement protocol based on quantum search algorithms is still blank. In this paper, on the basis of investigating the properties of quantum search algorithms, we propose the first quantum key agreement protocol whose embed mode of subkey is based on a quantum search algorithm known as Grover's algorithm. A novel example of protocols with 5 - party is presented. The efficiency analysis shows that our protocol is prior to existing MQKA protocols. Furthermore it is secure against both external attack and internal attacks.
Evolutionary algorithms for hard quantum control
Zahedinejad, Ehsan; Schirmer, Sophie; Sanders, Barry C.
2014-09-01
Although quantum control typically relies on greedy (local) optimization, traps (irregular critical points) in the control landscape can make optimization hard by foiling local search strategies. We demonstrate the failure of greedy algorithms as well as the (nongreedy) genetic-algorithm method to realize two fast quantum computing gates: a qutrit phase gate and a controlled-not gate. We show that our evolutionary algorithm circumvents the trap to deliver effective quantum control in both instances. Even when greedy algorithms succeed, our evolutionary algorithm can deliver a superior control procedure, for example, reducing the need for high time resolution.
Heaps, Charles W
2016-01-01
Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic dynamics where excited states are required. In this paper, we employ pseudospectral sampling of time-dependent Gaussian basis functions for the simulation of non-adiabatic dynamics. Unlike other methods, the pseudospectral Gaussian molecular dynamics tests the Schr\\"{o}dinger equation with $N$ Dirac delta functions located at the centers of the Gaussian functions reducing the scaling of potential energy evaluations from $\\mathcal{O}(N^2)$ to $\\mathcal{O}(N)$. By projecting the Gaussian basis onto discrete points in space, the method is capable of efficiently and quantitatively describing nonadiabatic population transfer and intra-surface quantum coherence. We investigate three model systems; the photodissociation of three coupled Morse oscillators, the bound state dynamics of two coupled Morse oscillators, and a two-d...
Hoang, Thai M.; Bharath, Hebbe M.; Boguslawski, Matthew J.; Anquez, Martin; Robbins, Bryce A.; Chapman, Michael S.
2016-01-01
Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian. This mechanism gives rise to massless Nambu–Goldstone modes and massive Anderson–Higgs modes. These modes provide a fundamental understanding of matter in the Universe and appear as collective phase or amplitude excitations of an order parameter in a many-body system. The amplitude excitation plays a crucial role in determining the critical exponents governing universal nonequilibrium dynamics in the Kibble–Zurek mechanism (KZM). Here, we characterize the amplitude excitations in a spin-1 condensate and measure the energy gap for different phases of the quantum phase transition. At the quantum critical point of the transition, finite-size effects lead to a nonzero gap. Our measurements are consistent with this prediction, and furthermore, we demonstrate an adiabatic quench through the phase transition, which is forbidden at the mean field level. This work paves the way toward generating entanglement through an adiabatic phase transition. PMID:27503886
Hoang, Thai M.; Bharath, Hebbe M.; Boguslawski, Matthew J.; Anquez, Martin; Robbins, Bryce A.; Chapman, Michael S.
2016-08-01
Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian. This mechanism gives rise to massless Nambu-Goldstone modes and massive Anderson-Higgs modes. These modes provide a fundamental understanding of matter in the Universe and appear as collective phase or amplitude excitations of an order parameter in a many-body system. The amplitude excitation plays a crucial role in determining the critical exponents governing universal nonequilibrium dynamics in the Kibble-Zurek mechanism (KZM). Here, we characterize the amplitude excitations in a spin-1 condensate and measure the energy gap for different phases of the quantum phase transition. At the quantum critical point of the transition, finite-size effects lead to a nonzero gap. Our measurements are consistent with this prediction, and furthermore, we demonstrate an adiabatic quench through the phase transition, which is forbidden at the mean field level. This work paves the way toward generating entanglement through an adiabatic phase transition.
Error suppression and error correction in adiabatic quantum computation: non-equilibrium dynamics
Sarovar, Mohan; Young, Kevin C.
2013-12-01
While adiabatic quantum computing (AQC) has some robustness to noise and decoherence, it is widely believed that encoding, error suppression and error correction will be required to scale AQC to large problem sizes. Previous works have established at least two different techniques for error suppression in AQC. In this paper we derive a model for describing the dynamics of encoded AQC and show that previous constructions for error suppression can be unified with this dynamical model. In addition, the model clarifies the mechanisms of error suppression and allows the identification of its weaknesses. In the second half of the paper, we utilize our description of non-equilibrium dynamics in encoded AQC to construct methods for error correction in AQC by cooling local degrees of freedom (qubits). While this is shown to be possible in principle, we also identify the key challenge to this approach: the requirement of high-weight Hamiltonians. Finally, we use our dynamical model to perform a simplified thermal stability analysis of concatenated-stabilizer-code encoded many-body systems for AQC or quantum memories. This work is a companion paper to ‘Error suppression and error correction in adiabatic quantum computation: techniques and challenges (2013 Phys. Rev. X 3 041013)’, which provides a quantum information perspective on the techniques and limitations of error suppression and correction in AQC. In this paper we couch the same results within a dynamical framework, which allows for a detailed analysis of the non-equilibrium dynamics of error suppression and correction in encoded AQC.
Evolving Quantum Oracles with Hybrid Quantum-inspired Evolutionary Algorithm
Ding, S; Yang, Q; Ding, Shengchao; Jin, Zhi; Yang, Qing
2006-01-01
Quantum oracles play key roles in the studies of quantum computation and quantum information. But implementing quantum oracles efficiently with universal quantum gates is a hard work. Motivated by genetic programming, this paper proposes a novel approach to evolve quantum oracles with a hybrid quantum-inspired evolutionary algorithm. The approach codes quantum circuits with numerical values and combines the cost and correctness of quantum circuits into the fitness function. To speed up the calculation of matrix multiplication in the evaluation of individuals, a fast algorithm of matrix multiplication with Kronecker product is also presented. The experiments show the validity and the effects of some parameters of the presented approach. And some characteristics of the novel approach are discussed too.
Quantum Factorization of 143 on a Dipolar-Coupling NMR system
Xu, Nanyang; Lu, Dawei; Zhou, Xianyi; Peng, Xinhua; Du, Jiangfeng
2011-01-01
Quantum algorithms could be much faster than classical ones in solving the factoring problem. Adiabatic quantum computation for this is an alternative approach other than Shor's algorithm. Here we report an improved adiabatic factoring algorithm and its experimental realization to factor the number 143 on a liquid crystal NMR quantum processor with dipole-dipole couplings. We believe this to be the largest number factored in quantum-computation realizations, which shows the practical importance of adiabatic quantum algorithms.
Quantum factorization of 143 on a dipolar-coupling nuclear magnetic resonance system.
Xu, Nanyang; Zhu, Jing; Lu, Dawei; Zhou, Xianyi; Peng, Xinhua; Du, Jiangfeng
2012-03-30
Quantum algorithms could be much faster than classical ones in solving the factoring problem. Adiabatic quantum computation for this is an alternative approach other than Shor's algorithm. Here we report an improved adiabatic factoring algorithm and its experimental realization to factor the number 143 on a liquid-crystal NMR quantum processor with dipole-dipole couplings. We believe this to be the largest number factored in quantum-computation realizations, which shows the practical importance of adiabatic quantum algorithms.
A Quantum Algorithm for Finding a Hamilton Circuit
GUO Hao; LONG Gui-Lu; SUN Yang; XIU Xiao-Lin
2001-01-01
A quantum algorithm for solving the classical NP-complete problem - the Hamilton circuit is presented. The algorithm employs the quantum SAT and the quantum search algorithms. The algorithm is square-root faster than classical algorithm, and becomes exponentially faster than classical algorithm if nonlinear quantum mechanical computer is used.
Quantum hyperparallel algorithm for matrix multiplication.
Zhang, Xin-Ding; Zhang, Xiao-Ming; Xue, Zheng-Yuan
2016-04-29
Hyperentangled states, entangled states with more than one degree of freedom, are considered as promising resource in quantum computation. Here we present a hyperparallel quantum algorithm for matrix multiplication with time complexity O(N(2)), which is better than the best known classical algorithm. In our scheme, an N dimensional vector is mapped to the state of a single source, which is separated to N paths. With the assistance of hyperentangled states, the inner product of two vectors can be calculated with a time complexity independent of dimension N. Our algorithm shows that hyperparallel quantum computation may provide a useful tool in quantum machine learning and "big data" analysis.
Quantum algorithms for solving linear differential equations
Berry, Dominic W
2010-01-01
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by homogeneous linear differential equations that produce only oscillating terms. Here we extend quantum simulation algorithms to general inhomogeneous linear differential equations, which can include exponential terms as well as oscillating terms in their solution. As with other algorithms of this type, the solution is encoded in amplitudes of the quantum state. The algorithm does not give the explicit solution, but it is possible to extract global features of the solution.
Quantum Computing and Shor`s Factoring Algorithm
Volovich, Igor V.
2001-01-01
Lectures on quantum computing. Contents: Algorithms. Quantum circuits. Quantum Fourier transform. Elements of number theory. Modular exponentiation. Shor`s algorithm for finding the order. Computational complexity of Schor`s algorithm. Factoring integers. NP-complete problems.
Quantum Genetic Algorithms for Computer Scientists
Rafael Lahoz-Beltra
2016-01-01
Genetic algorithms (GAs) are a class of evolutionary algorithms inspired by Darwinian natural selection. They are popular heuristic optimisation methods based on simulated genetic mechanisms, i.e., mutation, crossover, etc. and population dynamical processes such as reproduction, selection, etc. Over the last decade, the possibility to emulate a quantum computer (a computer using quantum-mechanical phenomena to perform operations on data) has led to a new class of GAs known as “Quantum Geneti...
Inchworm Monte Carlo for exact non-adiabatic dynamics. I. Theory and algorithms
Chen, Hsing-Ta; Cohen, Guy; Reichman, David R.
2017-02-01
In this paper, we provide a detailed description of the inchworm Monte Carlo formalism for the exact study of real-time non-adiabatic dynamics. This method optimally recycles Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. Using the example of the spin-boson model, we formulate the inchworm expansion in two distinct ways: The first with respect to an expansion in the system-bath coupling and the second as an expansion in the diabatic coupling. The latter approach motivates the development of a cumulant version of the inchworm Monte Carlo method, which has the benefit of improved scaling. This paper deals completely with methodology, while Paper II provides a comprehensive comparison of the performance of the inchworm Monte Carlo algorithms to other exact methodologies as well as a discussion of the relative advantages and disadvantages of each.
Inchworm Monte Carlo for exact non-adiabatic dynamics I. Theory and algorithms
Chen, Hsing-Ta; Reichman, David R
2016-01-01
In this paper we provide a detailed description of the inchworm Monte Carlo formalism for the exact study of real-time non-adiabatic dynamics. This method optimally recycles Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. Using the example of the spin-boson model, we formulate the inchworm expansion in two distinct ways: The first with respect to an expansion in the system-bath coupling and the second as an expansion in the diabatic coupling. The latter approach motivates the development of a cumulant version of the inchworm Monte Carlo method, which has the benefit of improved scaling. This paper deals completely with methodology, while the companion paper provides a comprehensive comparison of the performance of the inchworm Monte Carlo algorithms to other exact methodologies as well as a discussion of the relative advantages and disadvantages of each.
A quantum genetic algorithm with quantum crossover and mutation operations
SaiToh, Akira; Rahimi, Robabeh; Nakahara, Mikio
2013-11-01
In the context of evolutionary quantum computing in the literal meaning, a quantum crossover operation has not been introduced so far. Here, we introduce a novel quantum genetic algorithm that has a quantum crossover procedure performing crossovers among all chromosomes in parallel for each generation. A complexity analysis shows that a quadratic speedup is achieved over its classical counterpart in the dominant factor of the run time to handle each generation.
Jeong Ryeol Choi
2015-01-01
Full Text Available An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. At first, we derive an invariant for a simple superconducting qubit-oscillator through the introduction of its reduced Hamiltonian. Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a time-dependent strength, is evaluated using the technique of unitary transformation. The accuracy of conservation for such invariant quantities is represented in detail. Based on the results of our developments in this paper, perturbation theory is applicable to the research of quantum characteristics of more complicated qubit systems that are described by a time-dependent Hamiltonian involving nonlinear terms.
Diestler, D J
2012-03-22
The Born-Oppenheimer (BO) description of electronically adiabatic molecular processes predicts a vanishing electronic flux density (j(e)), =1/2∫dR[Δ(b) (x;R) - Δ(a) (x;R)] even though the electrons certainly move in response to the movement of the nuclei. This article, the first of a pair, proposes a quantum-mechanical "coupled-channels" (CC) theory that allows the approximate extraction of j(e) from the electronically adiabatic BO wave function . The CC theory is detailed for H(2)(+), in which case j(e) can be resolved into components associated with two channels α (=a,b), each of which corresponds to the "collision" of an "internal" atom α (proton a or b plus electron) with the other nucleus β (proton b or a). The dynamical role of the electron, which accommodates itself instantaneously to the motion of the nuclei, is submerged in effective electronic probability (population) densities, Δ(α), associated with each channel (α). The Δ(α) densities are determined by the (time-independent) BO electronic energy eigenfunction, which depends parametrically on the configuration of the nuclei, the motion of which is governed by the usual BO nuclear Schrödinger equation. Intuitively appealing formal expressions for the electronic flux density are derived for H(2)(+).
Wang, Li; Tu, Tao; Gong, Bo; Zhou, Cheng; Guo, Guang-Can
2016-01-07
High fidelity universal gates for quantum bits form an essential ingredient of quantum information processing. In particular, geometric gates have attracted attention because they have a higher intrinsic resistance to certain errors. However, their realization remains a challenge because of the need for complicated quantum control on a multi-level structure as well as meeting the adiabatic condition within a short decoherence time. Here, we demonstrate non-adiabatic quantum operations for a two-level system by applying a well-controlled geometric Landau-Zener-Stückelberg interferometry. By characterizing the gate quality, we also investigate the operation in the presence of realistic dephasing. Furthermore, the result provides an essential model suitable for understanding an interplay of geometric phase and Landau-Zener-Stückelberg process which are well explored separately.
Nie, W; Shi, X; Wei, L F
2010-01-01
In this paper, the scheme of quantum computing based on Stark chirped rapid adiabatic passage (SCRAP) technique [L. F. Wei et al., Phys. Rev. Lett. 100, 113601 (2008)] is extensively applied to implement the quantum-state manipulations in the flux-biased Josephson phase qubits. The broken-parity symmetries of bound states in flux-biased Josephson junctions are utilized to conveniently generate the desirable Stark-shifts. Then, assisted by various transition pulses universal quantum logic gates as well as arbitrary quantum-state preparations could be implemented. Compared with the usual PI-pulses operations widely used in the experiments, the adiabatic population passage proposed here is insensitive the details of the applied pulses and thus the desirable population transfers could be satisfyingly implemented. The experimental feasibility of the proposal is also discussed.
Quantum Algorithm for the Toeplitz Systems
Wan, Lin-Chun; Pan, Shi-Jie; Gao, Fei; Wen, Qiao-Yan
2016-01-01
Solving the Toeplitz systems, which is to find the vector $x$ such that $T_nx = b$ given a $n\\times n$ Toeplitz matrix $T_n$ and a vector $b$, has a variety of applications in mathematics and engineering. In this paper, we present a quantum algorithm for solving the Toeplitz systems, in which a quantum state encoding the solution with error $\\epsilon$ is generated. It is shown that our algorithm's complexity is nearly linear in the condition number, and polylog in the dimensions $n$ and in the inverse error $\\epsilon^{-1}$. This implies our algorithm is exponentially faster than the best classical algorithm for the same problem if the condition number of $T_n$ is $O(\\textrm{poly}(\\textrm{log}\\,n))$. Since no assumption on the sparseness of $T_n$ is demanded in our algorithm, the algorithm can serve as an example of quantum algorithms for solving non-sparse linear systems.
Novel quantum inspired binary neural network algorithm
OM PRAKASH PATEL; ARUNA TIWARI
2016-11-01
In this paper, a quantum based binary neural network algorithm is proposed, named as novel quantum binary neural network algorithm (NQ-BNN). It forms a neural network structure by deciding weights and separability parameter in quantum based manner. Quantum computing concept represents solution probabilistically and gives large search space to find optimal value of required parameters using Gaussian random number generator. The neural network structure forms constructively having three number of layers input layer: hidden layer and output layer. A constructive way of deciding the network eliminates the unnecessary training of neural network. A new parameter that is a quantum separability parameter (QSP) is introduced here, which finds an optimal separability plane to classify input samples. During learning, it searches for an optimal separability plane. This parameter is taken as the threshold of neuron for learning of neural network. This algorithm is tested with three benchmark datasets and produces improved results than existing quantum inspired and other classification approaches.
Quantum algorithms for testing Boolean functions
Erika Andersson
2010-06-01
Full Text Available We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2^n possible linear Boolean functions of n variables; given a linear Boolean function, the Bernstein-Vazirani quantum algorithm can deterministically identify which one of these Boolean functions we are given using just one single function query. The same quantum algorithm can also be used to learn which input variables other types of Boolean functions depend on, with a success probability that depends on the form of the Boolean function that is tested, but does not depend on the total number of input variables. We also outline a procedure to futher amplify the success probability, based on another quantum algorithm, the Grover search.
Non-adiabatic quantum evolution: The S matrix as a geometrical phase factor
Saadi, Y., E-mail: S_yahiadz@yahoo.fr [Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Université Ferhat Abbas de Sétif, Sétif 19000 (Algeria); Maamache, M. [Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Université Ferhat Abbas de Sétif, Sétif 19000 (Algeria)
2012-03-19
We present a complete derivation of the exact evolution of quantum mechanics for the case when the underlying spectrum is continuous. We base our discussion on the use of the Weyl eigendifferentials. We show that a quantum system being in an eigenstate of an invariant will remain in the subspace generated by the eigenstates of the invariant, thereby acquiring a generalized non-adiabatic or Aharonov–Anandan geometric phase linked to the diagonal element of the S matrix. The modified Pöschl–Teller potential and the time-dependent linear potential are worked out as illustrations. -- Highlights: ► In this Letter we study the exact quantum evolution for continuous spectra problems. ► We base our discussion on the use of the Weyl eigendifferentials. ► We give a generalized Lewis and Riesenfeld phase for continuous spectra. ► This generalized phase or Aharonov–Anandan geometric phase is linked to the S matrix. ► The modified Pöschl–Teller and the linear potential are worked out as illustrations.
Exciton spectrum of surface-corrugated quantum wells: the adiabatic self-consistent approach
Atenco A, N.; Perez R, F. [lnstituto de Fisica, Universidad Autonoma de Puebla, A.P. J-48, 72570 Puebla (Mexico); Makarov, N.M. [lnstituto de Ciencias, Universidad Autonoma de Puebla, Priv. 17 Norte No 3417, Col. San Miguel Hueyotlipan, 72050 Puebla (Mexico)
2005-07-01
A theory for calculating the relaxation frequency {nu} and the shift {delta} {omega} of exciton resonances in quantum wells with finite potential barriers and adiabatic surface disorder is developed. The adiabaticity implies that the correlation length R{sub C} for the well width fluctuations is much larger than the exciton radius a{sub 0} (R{sub C} >> a{sub 0}). Our theory is based on the self-consistent Green's function method, and therefore takes into account the inherent action of the exciton scattering on itself. The self-consistent approach is shown to describe quantitatively the sharp exciton resonance. It also gives the qualitatively correct resonance picture for the transition to the classical limit, as well as within the domain of the classical limit itself. We present and analyze results for h h-exciton in a GaAs quantum well with Al{sub 0.3} Ga{sub 0.7}As barriers. It is established that the self-consistency and finite height of potential barriers significantly influence on the line-shape of exciton resonances, and make the values of {nu} and {delta} {omega} be quite realistic. In particular, the relaxation frequency {nu} for the ground-state resonance has a broad, almost symmetric maximum near the resonance frequency {omega}{sub 0}, while the surface-induced resonance shift {delta} {omega} vanishes near {omega}{sub 0}, and has different signs on the sides of the exciton resonance. (Author) 43 refs., 4 figs.
A Note on Shor's Quantum Algorithm
CAO Zheng-jun; LIU Li-hua
2006-01-01
Shor proposed a polynomial time algorithm for computing the order of one element in a multiplicative group using a quantum computer. Based on Miller's randomization, he then gave a factorization algorithm. But the algorithm has two shortcomings, the order must be even and the output might be a trivial factor. Actually, these drawbacks can be overcome if the number is an RSA modulus. Applying the special structure of the RSA modulus,an algorithm is presented to overcome the two shortcomings. The new algorithm improves Shor's algorithm for factoring RSA modulus. The cost of the factorization algorithm almost depends on the calculation of the order of 2 in the multiplication group.
Power law scaling for the adiabatic algorithm for search engine ranking
Frees, Adam; Rudinger, Kenneth; Bach, Eric; Friesen, Mark; Joynt, Robert; Coppersmith, S N
2012-01-01
An important method for search engine result ranking works by finding the principal eigenvector of the "Google matrix." Recently, a quantum algorithm for this problem and evidence of an exponential speedup for some scale-free networks were presented. Here, we show that the run-time depends on features of the graphs other than the degree distribution, and can be altered sufficiently to rule out a general exponential speedup. For a sample of graphs with degree distributions that more closely resemble the Web than in previous work, the proposed algorithm does not appear to run exponentially faster than the classical case.
Power-law scaling for the adiabatic algorithm for search-engine ranking
Frees, Adam; Gamble, John King; Rudinger, Kenneth; Bach, Eric; Friesen, Mark; Joynt, Robert; Coppersmith, S. N.
2013-09-01
An important method for search engine result ranking works by finding the principal eigenvector of the “Google matrix.” Recently, a quantum algorithm for generating this eigenvector as a quantum state was presented, with evidence of an exponential speedup of this process for some scale-free networks. Here we show that the run time depends on features of the graphs other than the degree distribution, and can be altered sufficiently to rule out a general exponential speedup. According to our simulations, for a sample of graphs with degree distributions that are scale-free, with parameters thought to closely resemble the Web, the proposed algorithm for eigenvector preparation does not appear to run exponentially faster than the classical case.
Function Optimization Based on Quantum Genetic Algorithm
Ying Sun
2014-01-01
Full Text Available Optimization method is important in engineering design and application. Quantum genetic algorithm has the characteristics of good population diversity, rapid convergence and good global search capability and so on. It combines quantum algorithm with genetic algorithm. A novel quantum genetic algorithm is proposed, which is called Variable-boundary-coded Quantum Genetic Algorithm (vbQGA in which qubit chromosomes are collapsed into variable-boundary-coded chromosomes instead of binary-coded chromosomes. Therefore much shorter chromosome strings can be gained. The method of encoding and decoding of chromosome is first described before a new adaptive selection scheme for angle parameters used for rotation gate is put forward based on the core ideas and principles of quantum computation. Eight typical functions are selected to optimize to evaluate the effectiveness and performance of vbQGA against standard Genetic Algorithm (sGA and Genetic Quantum Algorithm (GQA. The simulation results show that vbQGA is significantly superior to sGA in all aspects and outperforms GQA in robustness and solving velocity, especially for multidimensional and complicated functions.
Least significant qubit algorithm for quantum images
Sang, Jianzhi; Wang, Shen; Li, Qiong
2016-11-01
To study the feasibility of the classical image least significant bit (LSB) information hiding algorithm on quantum computer, a least significant qubit (LSQb) information hiding algorithm of quantum image is proposed. In this paper, we focus on a novel quantum representation for color digital images (NCQI). Firstly, by designing the three qubits comparator and unitary operators, the reasonability and feasibility of LSQb based on NCQI are presented. Then, the concrete LSQb information hiding algorithm is proposed, which can realize the aim of embedding the secret qubits into the least significant qubits of RGB channels of quantum cover image. Quantum circuit of the LSQb information hiding algorithm is also illustrated. Furthermore, the secrets extracting algorithm and circuit are illustrated through utilizing control-swap gates. The two merits of our algorithm are: (1) it is absolutely blind and (2) when extracting secret binary qubits, it does not need any quantum measurement operation or any other help from classical computer. Finally, simulation and comparative analysis show the performance of our algorithm.
LSB Based Quantum Image Steganography Algorithm
Jiang, Nan; Zhao, Na; Wang, Luo
2016-01-01
Quantum steganography is the technique which hides a secret message into quantum covers such as quantum images. In this paper, two blind LSB steganography algorithms in the form of quantum circuits are proposed based on the novel enhanced quantum representation (NEQR) for quantum images. One algorithm is plain LSB which uses the message bits to substitute for the pixels' LSB directly. The other is block LSB which embeds a message bit into a number of pixels that belong to one image block. The extracting circuits can regain the secret message only according to the stego cover. Analysis and simulation-based experimental results demonstrate that the invisibility is good, and the balance between the capacity and the robustness can be adjusted according to the needs of applications.
Quantum heuristic algorithm for traveling salesman problem
Bang, Jeongho; Lim, James; Ryu, Junghee; Lee, Changhyoup; Lee, Jinhyoung
2010-01-01
We propose a quantum heuristic algorithm to solve a traveling salesman problem by generalizing Grover search. Sufficient conditions are derived to greatly enhance the probability of finding the tours with extremal costs, reaching almost to unity and they are shown characterized by statistical properties of tour costs. In particular for a Gaussian distribution of the tours along the cost we show that the quantum algorithm exhibits the quadratic speedup of its classical counterpart, similarly to Grover search.
Sato, Taku J.; Okuyama, Daisuke; Kimura, Hideo
2016-12-01
A tiny adiabatic-demagnetization refrigerator (T-ADR) has been developed for a commercial superconducting quantum interference device magnetometer [Magnetic Property Measurement System (MPMS) from Quantum Design]. The whole T-ADR system is fit in a cylindrical space of diameter 8.5 mm and length 250 mm, and can be inserted into the narrow sample tube of MPMS. A sorption pump is self-contained in T-ADR, and hence no complex gas handling system is necessary. With the single crystalline Gd3Ga5O12 garnet (˜2 g) used as a magnetic refrigerant, the routinely achievable lowest temperature is ˜0.56 K. The lower detection limit for a magnetization anomaly is ˜1 × 10-7 emu, estimated from fluctuation of the measured magnetization. The background level is ˜5 × 10-5 emu below 2 K at H = 100 Oe, which is largely attributable to a contaminating paramagnetic signal from the magnetic refrigerant.
Sato, Taku J; Okuyama, Daisuke; Kimura, Hideo
2016-12-01
A tiny adiabatic-demagnetization refrigerator (T-ADR) has been developed for a commercial superconducting quantum interference device magnetometer [Magnetic Property Measurement System (MPMS) from Quantum Design]. The whole T-ADR system is fit in a cylindrical space of diameter 8.5 mm and length 250 mm, and can be inserted into the narrow sample tube of MPMS. A sorption pump is self-contained in T-ADR, and hence no complex gas handling system is necessary. With the single crystalline Gd3Ga5O12 garnet (∼2 g) used as a magnetic refrigerant, the routinely achievable lowest temperature is ∼0.56 K. The lower detection limit for a magnetization anomaly is ∼1 × 10(-7) emu, estimated from fluctuation of the measured magnetization. The background level is ∼5 × 10(-5) emu below 2 K at H = 100 Oe, which is largely attributable to a contaminating paramagnetic signal from the magnetic refrigerant.
Research on palmprint identification method based on quantum algorithms.
Li, Hui; Zhang, Zhanzhan
2014-01-01
Quantum image recognition is a technology by using quantum algorithm to process the image information. It can obtain better effect than classical algorithm. In this paper, four different quantum algorithms are used in the three stages of palmprint recognition. First, quantum adaptive median filtering algorithm is presented in palmprint filtering processing. Quantum filtering algorithm can get a better filtering result than classical algorithm through the comparison. Next, quantum Fourier transform (QFT) is used to extract pattern features by only one operation due to quantum parallelism. The proposed algorithm exhibits an exponential speed-up compared with discrete Fourier transform in the feature extraction. Finally, quantum set operations and Grover algorithm are used in palmprint matching. According to the experimental results, quantum algorithm only needs to apply square of N operations to find out the target palmprint, but the traditional method needs N times of calculation. At the same time, the matching accuracy of quantum algorithm is almost 100%.
Research on Palmprint Identification Method Based on Quantum Algorithms
Hui Li
2014-01-01
Full Text Available Quantum image recognition is a technology by using quantum algorithm to process the image information. It can obtain better effect than classical algorithm. In this paper, four different quantum algorithms are used in the three stages of palmprint recognition. First, quantum adaptive median filtering algorithm is presented in palmprint filtering processing. Quantum filtering algorithm can get a better filtering result than classical algorithm through the comparison. Next, quantum Fourier transform (QFT is used to extract pattern features by only one operation due to quantum parallelism. The proposed algorithm exhibits an exponential speed-up compared with discrete Fourier transform in the feature extraction. Finally, quantum set operations and Grover algorithm are used in palmprint matching. According to the experimental results, quantum algorithm only needs to apply square of N operations to find out the target palmprint, but the traditional method needs N times of calculation. At the same time, the matching accuracy of quantum algorithm is almost 100%.
On a Nonlinear Model in Adiabatic Evolutions
Sun, Jie; Lu, Song-Feng
2016-08-01
In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully solve the problem, while the linear model can not. Also in the same setting, when the overlap between the initial state and the final stare is sufficiently large, a simple linear adiabatic evolution can achieve O(1) time efficiency, but infinite time complexity for the nonlinear model of adiabatic evolution is needed. This tells us, it is not always a wise choice to use nonlinear interpolations in adiabatic algorithms. Sometimes, simple linear adiabatic evolutions may be sufficient for using. Supported by the National Natural Science Foundation of China under Grant Nos. 61402188 and 61173050. The first author also gratefully acknowledges the support from the China Postdoctoral Science Foundation under Grant No. 2014M552041
Genetic Algorithms for Digital Quantum Simulations.
Las Heras, U; Alvarez-Rodriguez, U; Solano, E; Sanz, M
2016-06-10
We propose genetic algorithms, which are robust optimization techniques inspired by natural selection, to enhance the versatility of digital quantum simulations. In this sense, we show that genetic algorithms can be employed to increase the fidelity and optimize the resource requirements of digital quantum simulation protocols while adapting naturally to the experimental constraints. Furthermore, this method allows us to reduce not only digital errors but also experimental errors in quantum gates. Indeed, by adding ancillary qubits, we design a modular gate made out of imperfect gates, whose fidelity is larger than the fidelity of any of the constituent gates. Finally, we prove that the proposed modular gates are resilient against different gate errors.
Genetic Algorithms for Digital Quantum Simulations
Las Heras, U.; Alvarez-Rodriguez, U.; Solano, E.; Sanz, M.
2016-06-01
We propose genetic algorithms, which are robust optimization techniques inspired by natural selection, to enhance the versatility of digital quantum simulations. In this sense, we show that genetic algorithms can be employed to increase the fidelity and optimize the resource requirements of digital quantum simulation protocols while adapting naturally to the experimental constraints. Furthermore, this method allows us to reduce not only digital errors but also experimental errors in quantum gates. Indeed, by adding ancillary qubits, we design a modular gate made out of imperfect gates, whose fidelity is larger than the fidelity of any of the constituent gates. Finally, we prove that the proposed modular gates are resilient against different gate errors.
Quantum Algorithms and the Genetic Code
Patel, A D
2001-01-01
Replication of DNA and synthesis of proteins are studied from the view-pointof quantum database search. Identification of a base-pairing with a quantumquery gives a natural (and first ever!) explanation of why living organismshave 4 nucleotide bases and 20 amino acids. It is amazing that these numbersarise as solutions to an optimisation problem. Components of the DNA structurewhich implement Grover's algorithm are identified, and a physical scenario ispresented for the execution of the quantum algorithm. It is proposed thatenzymes play a crucial role in maintaining quantum coherence of the process.Experimental tests that can verify this scenario are pointed out.
PLQP & Company: Decidable Logics for Quantum Algorithms
Baltag, Alexandru; Bergfeld, Jort; Kishida, Kohei; Sack, Joshua; Smets, Sonja; Zhong, Shengyang
2014-10-01
We introduce a probabilistic modal (dynamic-epistemic) quantum logic PLQP for reasoning about quantum algorithms. We illustrate its expressivity by using it to encode the correctness of the well-known quantum search algorithm, as well as of a quantum protocol known to solve one of the paradigmatic tasks from classical distributed computing (the leader election problem). We also provide a general method (extending an idea employed in the decidability proof in Dunn et al. (J. Symb. Log. 70:353-359, 2005)) for proving the decidability of a range of quantum logics, interpreted on finite-dimensional Hilbert spaces. We give general conditions for the applicability of this method, and in particular we apply it to prove the decidability of PLQP.
Iterative quantum algorithm for distributed clock synchronization
Wang Hong-Fu; Zhang Shou
2012-01-01
Clock synchronization is a well-studied problem with many practical and scientific applications.We propose an arbitrary accuracy iterative quantum algorithm for distributed clock synchronization using only three qubits.The n bits of the time difference △ between two spatially separated clocks can be deterministically extracted by communicating only O(n) messages and executing the quantum iteration process n times based on the classical feedback and measurement operations.Finally,we also give the algorithm using only two qubits and discuss the success probability of the algorithm.
On quantum algorithms for noncommutative hidden subgroups
Ettinger, M. [Los Alamos National Lab., NM (United States); Hoeyer, P. [Odense Univ. (Denmark)
1998-12-01
Quantum algorithms for factoring and discrete logarithm have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden subgroups of noncommutative groups. The authors present a quantum algorithm for the special case of dihedral groups which determines the hidden subgroup in a linear number of calls to the input function. They also explore the difficulties of developing an algorithm to process the data to explicitly calculate a generating set for the subgroup. A general framework for the noncommutative hidden subgroup problem is discussed and they indicate future research directions.
Quantum Error Correction Protects Quantum Search Algorithms Against Decoherence.
Botsinis, Panagiotis; Babar, Zunaira; Alanis, Dimitrios; Chandra, Daryus; Nguyen, Hung; Ng, Soon Xin; Hanzo, Lajos
2016-12-07
When quantum computing becomes a wide-spread commercial reality, Quantum Search Algorithms (QSA) and especially Grover's QSA will inevitably be one of their main applications, constituting their cornerstone. Most of the literature assumes that the quantum circuits are free from decoherence. Practically, decoherence will remain unavoidable as is the Gaussian noise of classic circuits imposed by the Brownian motion of electrons, hence it may have to be mitigated. In this contribution, we investigate the effect of quantum noise on the performance of QSAs, in terms of their success probability as a function of the database size to be searched, when decoherence is modelled by depolarizing channels' deleterious effects imposed on the quantum gates. Moreover, we employ quantum error correction codes for limiting the effects of quantum noise and for correcting quantum flips. More specifically, we demonstrate that, when we search for a single solution in a database having 4096 entries using Grover's QSA at an aggressive depolarizing probability of 10(-3), the success probability of the search is 0.22 when no quantum coding is used, which is improved to 0.96 when Steane's quantum error correction code is employed. Finally, apart from Steane's code, the employment of Quantum Bose-Chaudhuri-Hocquenghem (QBCH) codes is also considered.
Quantum Error Correction Protects Quantum Search Algorithms Against Decoherence
Botsinis, Panagiotis; Babar, Zunaira; Alanis, Dimitrios; Chandra, Daryus; Nguyen, Hung; Ng, Soon Xin; Hanzo, Lajos
2016-12-01
When quantum computing becomes a wide-spread commercial reality, Quantum Search Algorithms (QSA) and especially Grover’s QSA will inevitably be one of their main applications, constituting their cornerstone. Most of the literature assumes that the quantum circuits are free from decoherence. Practically, decoherence will remain unavoidable as is the Gaussian noise of classic circuits imposed by the Brownian motion of electrons, hence it may have to be mitigated. In this contribution, we investigate the effect of quantum noise on the performance of QSAs, in terms of their success probability as a function of the database size to be searched, when decoherence is modelled by depolarizing channels’ deleterious effects imposed on the quantum gates. Moreover, we employ quantum error correction codes for limiting the effects of quantum noise and for correcting quantum flips. More specifically, we demonstrate that, when we search for a single solution in a database having 4096 entries using Grover’s QSA at an aggressive depolarizing probability of 10-3, the success probability of the search is 0.22 when no quantum coding is used, which is improved to 0.96 when Steane’s quantum error correction code is employed. Finally, apart from Steane’s code, the employment of Quantum Bose-Chaudhuri-Hocquenghem (QBCH) codes is also considered.
Power law scaling for the adiabatic algorithm for search engine ranking
Frees, Adam; King Gamble, John; Rudinger, Kenneth; Bach, Eric; Friesen, Mark; Joynt, Robert; Coppersmith, S. N.
2013-03-01
An important method for search engine result ranking works by finding the principal eigenvector of the ``Google matrix.'' Recently, a quantum algorithm for this problem and evidence of an exponential speedup for some scale-free networks were presented. Here, we show that the run-time depends on features of the graphs other than the degree distribution, and can be altered sufficiently to rule out a general exponential speedup. For a sample of graphs with degree distributions that more closely resemble the Web than in the previous work, the proposed algorithm does not appear to run exponentially faster than the classical one. This work was supported in part by ARO, DOD (W911NF-09-1-0439) and NSF (CCR-0635355, DMR 0906951). A.F. acknowledges support from the NSF REU program (PHY-PIF-1104660)
Purifying Quantum States: Quantum and Classical Algorithms
Dennis, E
2005-01-01
I give analytical estimates and numerical simulation results for the performance of Kitaev's 2d topological error-correcting codes. By providing methods for the execution of an encoded three-qubit Toffoli gate, I complete a universal gate set for these codes. I also examine the utility of Bohm's and Bohm-inspired interpretations of quantum mechanics for numerical solution of many-body dynamics and ``mechanism identification'' heuristics in discrete systems. Further, I show an unexpected quantitative correspondence between the previously known continuum of stochastic-Bohm trajectory theories on the one hand and extant path integral Monte Carlo methods on the other hand.
Maximum Information and Quantum Prediction Algorithms
McElwaine, J N
1997-01-01
This paper describes an algorithm for selecting a consistent set within the consistent histories approach to quantum mechanics and investigates its properties. The algorithm uses a maximum information principle to select from among the consistent sets formed by projections defined by the Schmidt decomposition. The algorithm unconditionally predicts the possible events in closed quantum systems and ascribes probabilities to these events. A simple spin model is described and a complete classification of all exactly consistent sets of histories formed from Schmidt projections in the model is proved. This result is used to show that for this example the algorithm selects a physically realistic set. Other tentative suggestions in the literature for set selection algorithms using ideas from information theory are discussed.
Jia, Dongming; Manz, Jörn; Paulus, Beate; Pohl, Vincent; Tremblay, Jean Christophe; Yang, Yonggang
2017-01-01
We design four linearly x- and y-polarized as well as circularly right (+) and left (-) polarized, resonant π / 2 -laser pulses that prepare the model benzene molecule in four different degenerate superposition states. These consist of equal (0.5) populations of the electronic ground state S0 (1A1g) plus one of four degenerate excited states, all of them accessible by dipole-allowed transitions. Specifically, for the molecule aligned in the xy-plane, these excited states include different complex-valued linear combinations of the 1E1u,x and 1E1u,y degenerate states. As a consequence, the laser pulses induce four different types of periodic adiabatic attosecond (as) charge migrations (AACM) in benzene, all with the same period, 504 as, but with four different types of angular fluxes. One of the characteristic differences of these fluxes are the two angles for zero fluxes, which appear as the instantaneous angular positions of the "source" and "sink" of two equivalent, or nearly equivalent branches of the fluxes which flow in pincer-type patterns from one molecular site (the "source") to the opposite one (the "sink"). These angles of zero fluxes are either fixed at the positions of two opposite carbon nuclei in the yz-symmetry plane, or at the centers of two opposite carbon-carbon bonds in the xz-symmetry plane, or the angles of zero fluxes rotate in angular forward (+) or backward (-) directions, respectively. As a resume, our quantum model simulations demonstrate quantum control of the electronic fluxes during AACM in degenerate superposition states, in the attosecond time domain, with the laser polarization as the key knob for control.
Demonstration of quantum permutation algorithm with a single photon ququart.
Wang, Feiran; Wang, Yunlong; Liu, Ruifeng; Chen, Dongxu; Zhang, Pei; Gao, Hong; Li, Fuli
2015-06-05
We report an experiment to demonstrate a quantum permutation determining algorithm with linear optical system. By employing photon's polarization and spatial mode, we realize the quantum ququart states and all the essential permutation transformations. The quantum permutation determining algorithm displays the speedup of quantum algorithm by determining the parity of the permutation in only one step of evaluation compared with two for classical algorithm. This experiment is accomplished in single photon level and the method exhibits universality in high-dimensional quantum computation.
A Quantum Algorithm Detecting Concentrated Maps.
Beichl, Isabel; Bullock, Stephen S; Song, Daegene
2007-01-01
We consider an arbitrary mapping f: {0, …, N - 1} → {0, …, N - 1} for N = 2 (n) , n some number of quantum bits. Using N calls to a classical oracle evaluating f(x) and an N-bit memory, it is possible to determine whether f(x) is one-to-one. For some radian angle 0 ≤ θ ≤ π/2, we say f(x) is θ - concentrated if and only if [Formula: see text] for some given ψ 0 and any 0 ≤ x ≤ N - 1. We present a quantum algorithm that distinguishes a θ-concentrated f(x) from a one-to-one f(x) in O(1) calls to a quantum oracle function Uf with high probability. For 0 quantum algorithm outperforms random (classical) evaluation of the function testing for dispersed values (on average). Maximal outperformance occurs at [Formula: see text] rad.
Quantum Genetic Algorithms for Computer Scientists
Rafael Lahoz-Beltra
2016-10-01
Full Text Available Genetic algorithms (GAs are a class of evolutionary algorithms inspired by Darwinian natural selection. They are popular heuristic optimisation methods based on simulated genetic mechanisms, i.e., mutation, crossover, etc. and population dynamical processes such as reproduction, selection, etc. Over the last decade, the possibility to emulate a quantum computer (a computer using quantum-mechanical phenomena to perform operations on data has led to a new class of GAs known as “Quantum Genetic Algorithms” (QGAs. In this review, we present a discussion, future potential, pros and cons of this new class of GAs. The review will be oriented towards computer scientists interested in QGAs “avoiding” the possible difficulties of quantum-mechanical phenomena.
Quantum algorithms and the genetic code
Apoorva Patel
2001-02-01
Replication of DNA and synthesis of proteins are studied from the view-point of quantum database search. Identiﬁcation of a base-pairing with a quantum query gives a natural (and ﬁrst ever!) explanation of why living organisms have 4 nucleotide bases and 20 amino acids. It is amazing that these numbers arise as solutions to an optimisation problem. Components of the DNA structure which implement Grover’s algorithm are identiﬁed, and a physical scenario is presented for the execution of the quantum algorithm. It is proposed that enzymes play a crucial role in maintaining quantum coherence of the process. Experimental tests that can verify this scenario are pointed out.
Quantum control using genetic algorithms in quantum communication: superdense coding
Domínguez-Serna, Francisco; Rojas, Fernando
2015-06-01
We present a physical example model of how Quantum Control with genetic algorithms is applied to implement the quantum superdense code protocol. We studied a model consisting of two quantum dots with an electron with spin, including spin-orbit interaction. The electron and the spin get hybridized with the site acquiring two degrees of freedom, spin and charge. The system has tunneling and site energies as time dependent control parameters that are optimized by means of genetic algorithms to prepare a hybrid Bell-like state used as a transmission channel. This state is transformed to obtain any state of the four Bell basis as required by superdense protocol to transmit two bits of classical information. The control process protocol is equivalent to implement one of the quantum gates in the charge subsystem. Fidelities larger than 99.5% are achieved for the hybrid entangled state preparation and the superdense operations.
Quantum algorithms for computational nuclear physics
Višňák Jakub
2015-01-01
Full Text Available While quantum algorithms have been studied as an efficient tool for the stationary state energy determination in the case of molecular quantum systems, no similar study for analogical problems in computational nuclear physics (computation of energy levels of nuclei from empirical nucleon-nucleon or quark-quark potentials have been realized yet. Although the difference between the above mentioned studies might seem negligible, it will be examined. First steps towards a particular simulation (on classical computer of the Iterative Phase Estimation Algorithm for deuterium and tritium nuclei energy level computation will be carried out with the aim to prove algorithm feasibility (and extensibility to heavier nuclei for its possible practical realization on a real quantum computer.
Realization of a Quantum Scheduling Algorithm Using Nuclear Magnetic Resonance
ZHANG Jing-Fu; DENG Zhi-Wei; PAN Yan-Na; LU Zhi-Heng
2004-01-01
The quantum scheduling algorithm proposed by Grover is generalized to extend its scope of applications. The generalized algorithm proposed here is realized on a nuclear magnetic resonance quantum computer. The experimental results show that the generalized algorithm can work efficiently in the case that Grover's scheduling algorithm is completely invalid, and represent the quantum advantages when qubits replace classical bits.
Algorithmic quantum simulation of memory effects
Alvarez-Rodriguez, U.; Di Candia, R.; Casanova, J.; Sanz, M.; Solano, E.
2017-02-01
We propose a method for the algorithmic quantum simulation of memory effects described by integrodifferential evolution equations. It consists in the systematic use of perturbation theory techniques and a Markovian quantum simulator. Our method aims to efficiently simulate both completely positive and nonpositive dynamics without the requirement of engineering non-Markovian environments. Finally, we find that small error bounds can be reached with polynomially scaling resources, evaluated as the time required for the simulation.
Quantum-Inspired Genetic Algorithm or Quantum Genetic Algorithm: Which Is It?
Jones, Erika
2015-04-01
Our everyday work focuses on genetic algorithms (GAs) related to quantum computing where we call ``related'' algorithms those falling into one of two classes: (1) GAs run on classical computers but making use of quantum mechanical (QM) constructs and (2) GAs run on quantum hardware. Though convention has yet to be set with respect to usage of the accepted terms quantum-inspired genetic algorithm (QIGA) and quantum genetic algorithm (QGA), we find the two terms highly suitable respectively as labels for the aforementioned classes. With these specific definitions in mind, the difference between the QIGA and QGA is greater than might first be appreciated, particularly by those coming from a perspective emphasizing GA use as a general computational tool irrespective of QM aspects (1) suggested by QIGAs and (2) inherent in QGAs. We offer a theoretical standpoint highlighting key differences-both obvious, and more significantly, subtle-to be considered in general design of a QIGA versus that of a QGA.
Algorithmic Pseudorandomness in Quantum Setups
Bendersky, Ariel; de la Torre, Gonzalo; Senno, Gabriel; Figueira, Santiago; Acín, Antonio
2016-06-01
Many experimental setups in quantum physics use pseudorandomness in places where the theory requires randomness. In this Letter we show that the use of pseudorandomness instead of proper randomness in quantum setups has potentially observable consequences. First, we present a new loophole for Bell-like experiments: if some of the parties choose their measurements pseudorandomly, then the computational resources of the local model have to be limited in order to have a proper observation of nonlocality. Second, we show that no amount of pseudorandomness is enough to produce a mixed state by computably choosing pure states from some basis.
Research on Quantum Algorithms at the Institute for Quantum Information and Matter
2016-05-29
Research on Quantum Algorithms at the Institute for Quantum Information and Matter The central goals of our project are (1) to bring large-scale... quantum algorithms , quantum complexity, fault-tolerant quantum computing REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 10. SPONSOR...Research on Quantum Algorithms at the Institute for Quantum Information and Matter Report Title The central goals of our project are (1) to bring large
Rational approximations and quantum algorithms with postselection
Mahadev, U.; de Wolf, R.
2015-01-01
We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using post-selection. We show that the minimal degree of the former equals (up to a factor of 2) the minimal query complexity of the latter. We gi
Matrix Product Operator Simulations of Quantum Algorithms
2015-02-01
Communications, pages 174–188. Springer, 1999. Bibliography 145 [21] Michelangelo Grigni, Leonard Schulman, Monica Vazirani, and Umesh Vazirani...2007. [27] Andrew M Childs, Leonard J Schulman, and Umesh V Vazirani. Quan- tum algorithms for hidden nonlinear structures. In Foundations of...and quantum in- formation. Cambridge University Press, Cambridge, 2000. [86] Charles H Bennett, Ethan Bernstein, Gilles Brassard, and Umesh Vazirani
Topology and Foundations of Quantum Algorithms
2005-07-01
9500 Gilman Drive, Mail Code 0934 La Jolla, CA 92093 -0934 Topology and Foundations of Quantum Algorithms REPORT DOCUMENTATION PAGE 18. SECURITY...Freedman, with an appendix by F. Goodman and H. Wenzl, “A magnetic model with a possible Chern-Simons phase”, Commun. Math. Phys. 234 (2003) 129–183. [9
Quantum Algorithm Processor For Finding Exact Divisors
Burger, John Robert
2005-01-01
Wiring diagrams are given for a quantum algorithm processor in CMOS to compute, in parallel, all divisors of an n-bit integer. Lines required in a wiring diagram are proportional to n. Execution time is proportional to the square of n.
Blockspin Cluster Algorithms for Quantum Spin Systems
Wiese, U J
1992-01-01
Cluster algorithms are developed for simulating quantum spin systems like the one- and two-dimensional Heisenberg ferro- and anti-ferromagnets. The corresponding two- and three-dimensional classical spin models with four-spin couplings are maped to blockspin models with two-blockspin interactions. Clusters of blockspins are updated collectively. The efficiency of the method is investigated in detail for one-dimensional spin chains. Then in most cases the new algorithms solve the problems of slowing down from which standard algorithms are suffering.
An introduction to quantum computing algorithms
Pittenger, Arthur O
2000-01-01
In 1994 Peter Shor [65] published a factoring algorithm for a quantum computer that finds the prime factors of a composite integer N more efficiently than is possible with the known algorithms for a classical com puter. Since the difficulty of the factoring problem is crucial for the se curity of a public key encryption system, interest (and funding) in quan tum computing and quantum computation suddenly blossomed. Quan tum computing had arrived. The study of the role of quantum mechanics in the theory of computa tion seems to have begun in the early 1980s with the publications of Paul Benioff [6]' [7] who considered a quantum mechanical model of computers and the computation process. A related question was discussed shortly thereafter by Richard Feynman [35] who began from a different perspec tive by asking what kind of computer should be used to simulate physics. His analysis led him to the belief that with a suitable class of "quantum machines" one could imitate any quantum system.
Novel Quantum Genetic Algorithm and Its Applications
ZHANG Ge-xiang; LI Na; JIN Wei-dong; HU Lai-zhao
2006-01-01
By introducing strong parallelism of quantum computing into evolutionary algorithm,a novel quantum genetic algorithm (NQGA) is proposed.In NQGA,a novel approach for updating the rotation angles of quantum logic gates and a strategy for enhancing search capability and avoiding premature convergence are adopted.Several typical complex continuous functions are chosen to test the performance of NQGA.Also,NQGA is applied in selecting the best feature subset from a large number of features in radar emitter signal recognition.The testing and experimental results of feature selection show that NQGA presents good search capability,rapid convergence,short computing time,and ability to avoid premature convergence effectively.
Quantum algorithms for testing properties of distributions
Bravyi, Sergey; Hassidim, Avinatan
2009-01-01
Suppose one has access to oracles generating samples from two unknown probability distributions P and Q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the L_1-norm ? This and related questions have been extensively studied during the last years in the field of property testing. In the present paper we study quantum algorithms for testing properties of distributions. It is shown that the L_1-distance between P and Q can be estimated with a constant precision using approximately N^{1/2} queries in the quantum settings, whereas classical computers need \\Omega(N) queries. We also describe quantum algorithms for testing Uniformity and Orthogonality with query complexity O(N^{1/3}). The classical query complexity of these problems is known to be \\Omega(N^{1/2}).
Improved Quantum Genetic Algorithm in Application of Scheduling Engineering Personnel
Huaixiao Wang
2014-01-01
Full Text Available To verify the availability of the improved quantum genetic algorithm in solving the scheduling engineering personnel problem, the following work has been carried out: the characteristics of the scheduling engineering personnel problem are analyzed, the quantum encoding method is proposed, and an improved quantum genetic algorithm is applied to address the issue. Taking the low efficiency and the bad performance of the conventional quantum genetic algorithm into account, a universal improved quantum genetic algorithm is introduced to solve the scheduling engineering personnel problem. Finally, the examples are applied to verify the effectiveness and superiority of the improved quantum genetic algorithm and the rationality of the encoding method.
Higher-Order Quantum-Inspired Genetic Algorithms
Nowotniak, Robert; Kucharski, Jacek
2014-01-01
This paper presents a theory and an empirical evaluation of Higher-Order Quantum-Inspired Genetic Algorithms. Fundamental notions of the theory have been introduced, and a novel Order-2 Quantum-Inspired Genetic Algorithm (QIGA2) has been presented. Contrary to all QIGA algorithms which represent quantum genes as independent qubits, in higher-order QIGAs quantum registers are used to represent genes strings which allows modelling of genes relations using quantum phenomena. Performance comparis...
A counterexample and a modification to the adiabatic approximation theorem in quantum mechanics
Gingold, H.
1991-01-01
A counterexample to the adiabatic approximation theorem is given when degeneracies are present. A formulation of an alternative version is proposed. A complete asymptotic decomposition for n dimensional self-adjoint Hamiltonian systems is restated and used.
Evolving Quantum Circuits using Genetic Algorithms
Prashant
2005-01-01
This paper describes an application of genetic algorithm for evolving quantum computing circuits. The circuits use reversible one qubit and two qubit gates which are applied on a multi-qubit system having some initial state. The genetic algorithm automatically searches the space and comes out with the appropriate circuit design, which yields desired output state. The fitness function used matches the output with desired output and the search stops when it is found. The fitness value becomes higher if the output is close to the desired output. The paper briefly discusses the operation of a quantum gate over the multi-qubit system. The paper also demonstrates some examples of the evolved circuits using the algorithm.
Semiclassical genetic algorithm with quantum crossover and mutation operations
SaiToh, Akira; Nakahara, Mikio
2012-01-01
In order for finding a good individual for a given fitness function in the context of evolutionary computing, we introduce a novel semiclassical quantum genetic algorithm. It has both of quantum crossover and quantum mutation procedures unlike conventional quantum genetic algorithms. A complexity analysis shows a certain improvement over its classical counterpart.
White Noise in Quantum Random Walk Search Algorithm
MA Lei; DU Jiang-Feng; LI Yun; LI Hui; KWEK L. C.; OH C. H.
2006-01-01
@@ The quantum random walk is a possible approach to construct new quantum search algorithms. It has been shown by Shenvi et al. [Phys. Rev. A 67 (2003)52307] that a kind of algorithm can perform an oracle search on a database of N items with O(√N) calling to the oracle, yielding a speedup similar to other quantum search algorithms.
Improved Bounds on Quantum Learning Algorithms
Atici, A; Atici, Alp; Servedio, Rocco A.
2004-01-01
In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum black-box queries which are required to exactly identify an unknown function from C is at most $O(\\frac{\\log |C|}{\\sqrt{{\\hat{\\gamma}}^{C}}})$, where $\\hat{\\gamma}^{C}$ is a combinatorial parameter of the class C. We essentially resolve this conjecture in the affirmative by giving a quantum algorithm that, for any class C, identifies any unknown function from C using at most $O(\\frac{\\log |C| \\log \\log |C|}{\\sqrt{{\\hat{\\gamma}}^{C}}})$ quantum black-box queries. We consider a range of natural problems intermediate between the exact learning problem (in which the learner must obtain all bits of information about the black-box function) and the usual problem of computing a predicate (in which the learner must obtain only one bit of information about the black-box function). ...
Ryabinkin, Ilya G; Izmaylov, Artur F
2015-01-01
We have developed a numerical differentiation scheme which eliminates evaluation of overlap determinants in calculating the time-derivative non-adiabatic couplings (TDNACs). Evaluation of these determinants was a bottleneck in previous implementations of mixed quantum-classical methods using numerical differentiation of electronic wave functions in the Slater-determinant representation. The central idea of our approach is, first, to reduce the analytic time derivatives of Slater determinants to time derivatives of molecular orbitals, and then to apply a finite-difference formula. Benchmark calculations prove the efficiency of the proposed scheme showing impressive several-order-of-magnitude speedups of the TDNAC calculation step for midsize molecules.
Adiabatic following criterion, estimation of the nonadiabatic excitation fraction and quantum jumps
Shakhmuratov, R N
2003-01-01
An accurate theory describing adiabatic following of the dark, nonabsorbing state in the three-level system is developed. An analytical solution for the wave function of the particle experiencing Raman excitation is found as an expansion in terms of the time varying nonadiabatic perturbation parameter. The solution can be presented as a sum of adiabatic and nonadiabatic parts. Both are estimated quantitatively. It is shown that the limiting value to which the amplitude of the nonadiabatic part tends is equal to the Fourier component of the nonadiabatic perturbation parameter taken at the Rabi frequency of the Raman excitation. The time scale of the variation of both parts is found. While the adiabatic part of the solution varies slowly and follows the change of the nonadiabatic perturbation parameter, the nonadiabatic part appears almost instantly, revealing a jumpwise transition between the dark and bright states. This jump happens when the nonadiabatic perturbation parameter takes its maximum value.
Identification of Hammerstein Model Based on Quantum Genetic Algorithm
Zhang Hai Li
2013-07-01
Full Text Available Nonlinear system identification is a main topic of modern identification. A new method for nonlinear system identification is presented by using Quantum Genetic Algorithm(QGA.The problems of nonlinear system identification are cast as function optimization overprameter space，and the Quantum Genetic Algorithm is adopted to solve the optimization problem. Simulation experiments show that: compared with the genetic algorithm, quantum genetic algorithm is an effective swarm intelligence algorithm, its salient features of the algorithm parameters, small population size, and the use of Quantum gate update populations, greatly improving the recognition in the optimization of speed and accuracy. Simulation results show the effectiveness of the proposed method.
Katz, Harley; McGaugh, Stacy S.; Sellwood, J. A.; de Blok, W. J. G.
We utilize Young's algorithm to model the adiabatic compression of the dark matter haloes of galaxies in the THINGS survey to determine the relationship between the halo fit to the rotation curve and the corresponding primordial halo prior to compression. Young's algorithm conserves radial action
Designing quantum gates using the genetic algorithm
Kumar, Karthikeyan S.; Paraoanu, G. S.
2012-12-01
We demonstrate the usage of Genetic Algorithm (GA) to tailor the radio frequency pulses for producing unitary transformations in qubit systems. We find that the initial population converges to the optimal solution after 10 generations, for a one segment pulse corresponding to single qubit Hadamard gate. For a two qubit CNOT gate, we see the population convergence for a two segment pulse after 150 generations. This demonstrates that the method is suitable for designing quantum gates.
Improved Quantum Genetic Algorithm in Application of Scheduling Engineering Personnel
Huaixiao Wang; Ling Li; Jianyong Liu; Yong Wang; Chengqun Fu
2014-01-01
To verify the availability of the improved quantum genetic algorithm in solving the scheduling engineering personnel problem, the following work has been carried out: the characteristics of the scheduling engineering personnel problem are analyzed, the quantum encoding method is proposed, and an improved quantum genetic algorithm is applied to address the issue. Taking the low efficiency and the bad performance of the conventional quantum genetic algorithm into account, a universal improved q...
Gammelmark, Søren; Eckardt, André
2013-01-01
We theoretically study the adiabatic preparation of an antiferromagnetic phase in a mixed Mott insulator of two bosonic atom species in a one-dimensional optical lattice. In such a system one can engineer a tunable parabolic inhomogeneity by controlling the difference of the trapping potentials...... felt by the two species. Using numerical simulations we predict that a finite parabolic potential can assist the adiabatic preparation of the antiferromagnet. The optimal strength of the parabolic inhomogeneity depends sensitively on the number imbalance between the two species. We also find...
Mineo, H.; Niu, Y. L.; Kuo, J. L.; Lin, S. H.; Fujimura, Y.
2015-08-01
The results of application of the quantum-mechanical adiabatic theory to vibrational predissociation (VPD) of water dimers, (H2O)2 and (D2O)2, are presented. We consider the VPD processes including the totally symmetric OH mode of the dimer and the bending mode of the fragment. The VPD in the adiabatic representation is induced by breakdown of the vibrational adiabatic approximation, and two types of nonadiabatic coupling matrix elements are involved: one provides the VPD induced by the low-frequency dissociation mode and the other provides the VPD through channel interactions induced by the low-frequency modes. The VPD rate constants were calculated using the Fermi golden rule expression. A closed form for the nonadiabatic transition matrix element between the discrete and continuum states was derived in the Morse potential model. All of the parameters used were obtained from the potential surfaces of the water dimers, which were calculated by the density functional theory procedures. The VPD rate constants for the two processes were calculated in the non-Condon scheme beyond the so-called Condon approximation. The channel interactions in and between the initial and final states were taken into account, and those are found to increase the VPD rates by 3(1) orders of magnitude for the VPD processes in (H2O)2 ((D2O)2). The fraction of the bending-excited donor fragments is larger than that of the bending-excited acceptor fragments. The results obtained by quantum-mechanical approach are compared with both experimental and quasi-classical trajectory calculation results.
Identification of Hammerstein Model Based on Quantum Genetic Algorithm
Zhang Hai Li
2013-01-01
Nonlinear system identification is a main topic of modern identification. A new method for nonlinear system identification is presented by using Quantum Genetic Algorithm(QGA).The problems of nonlinear system identification are cast as function optimization overprameter space，and the Quantum Genetic Algorithm is adopted to solve the optimization problem. Simulation experiments show that: compared with the genetic algorithm, quantum genetic algorithm is an effective swarm intelligence algorith...
Takeuchi, Naoki; Suzuki, Hideo; Yoshikawa, Nobuyuki
2017-05-01
Adiabatic quantum-flux-parametron (AQFP) is an energy-efficient superconductor logic. The advantage of AQFP is that the switching energy can be reduced by lowering operation frequencies or by increasing the quality factors of Josephson junctions, while keeping the energy barrier height much larger than thermal energy. In other words, both low energy dissipation and low bit error rates (BERs) can be achieved. In this paper, we report the first measurement results of the low BERs of AQFP logic. We used a superconductor voltage driver with a stack of dc superconducting-quantum-interference-devices to amplify the logic signals of AQFP gates into mV-range voltage signals for the BER measurement. Our measurement results showed 3.3 dB and 2.6 dB operation margins, in which BERs were less than 10-20, for 1 Gbps and 2 Gbps data rates, respectively. While the observed BERs were very low, the estimated switching energy for the 1-Gbps operation was only 2 zJ or 30kBT, where kB is the Boltzmann's constant and T is the temperature. Unlike conventional non-adiabatic logic, BERs are not directly associated with switching energy in AQFP.
Quantum algorithm for linear systems of equations.
Harrow, Aram W; Hassidim, Avinatan; Lloyd, Seth
2009-10-09
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b(-->), find a vector x(-->) such that Ax(-->) = b(-->). We consider the case where one does not need to know the solution x(-->) itself, but rather an approximation of the expectation value of some operator associated with x(-->), e.g., x(-->)(dagger) Mx(-->) for some matrix M. In this case, when A is sparse, N x N and has condition number kappa, the fastest known classical algorithms can find x(-->) and estimate x(-->)(dagger) Mx(-->) in time scaling roughly as N square root(kappa). Here, we exhibit a quantum algorithm for estimating x(-->)(dagger) Mx(-->) whose runtime is a polynomial of log(N) and kappa. Indeed, for small values of kappa [i.e., poly log(N)], we prove (using some common complexity-theoretic assumptions) that any classical algorithm for this problem generically requires exponentially more time than our quantum algorithm.
Quantum Algorithms for Some Well-Known NP Problems
GUO Hao; LONG Gui-Lu; LI Feng
2002-01-01
It is known that quantum computer is more powerful than classical computer.In this paper we present quantum algorithms for some famous NP problems in graph theory and combination theory,these quantum algorithms are at least quadratically faster than the classical ones.
Recursive simulation of quantum annealing
Sowa, A P; Samson, J H; Savel'ev, S E; Zagoskin, A M; Heidel, S; Zúñiga-Anaya, J C
2015-01-01
The evaluation of the performance of adiabatic annealers is hindered by lack of efficient algorithms for simulating their behaviour. We exploit the analyticity of the standard model for the adiabatic quantum process to develop an efficient recursive method for its numerical simulation in case of both unitary and non-unitary evolution. Numerical simulations show distinctly different distributions for the most important figure of merit of adiabatic quantum computing --- the success probability --- in these two cases.
Codeword stabilized quantum codes: Algorithm and structure
Chuang, Isaac; Cross, Andrew; Smith, Graeme; Smolin, John; Zeng, Bei
2009-04-01
The codeword stabilized (CWS) quantum code formalism presents a unifying approach to both additive and nonadditive quantum error-correcting codes [IEEE Trans. Inf. Theory 55, 433 (2009)]. This formalism reduces the problem of constructing such quantum codes to finding a binary classical code correcting an error pattern induced by a graph state. Finding such a classical code can be very difficult. Here, we consider an algorithm which maps the search for CWS codes to a problem of identifying maximum cliques in a graph. While solving this problem is in general very hard, we provide three structure theorems which reduce the search space, specifying certain admissible and optimal ((n,K,d)) additive codes. In particular, we find that the re does not exist any ((7,3,3)) CWS code though the linear programming bound does not rule it out. The complexity of the CWS-search algorithm is compared with the contrasting method introduced by Aggarwal and Calderbank [IEEE Trans. Inf. Theory 54, 1700 (2008)].
Discrete-query quantum algorithm for NAND trees
Childs, A M; Jordan, S P; Yeung, D; Childs, Andrew M.; Cleve, Richard; Jordan, Stephen P.; Yeung, David
2007-01-01
Recently, Farhi, Goldstone, and Gutmann gave a quantum algorithm for evaluating NAND trees that runs in time O(sqrt(N log N)) in the Hamiltonian query model. In this note, we point out that their algorithm can be converted into an algorithm using O(N^{1/2 + epsilon}) queries in the conventional quantum query model, for any fixed epsilon > 0.
A Hybrid Quantum Search Engine: A Fast Quantum Algorithm for Multiple Matches
Younes, A; Miller, J; Younes, Ahmed; Rowe, Jon; Miller, Julian
2003-01-01
In this paper we will present a quantum algorithm which works very efficiently in case of multiple matches within the search space and in the case of few matches, the algorithm performs classically. This allows us to propose a hybrid quantum search engine that integrates Grover's algorithm and the proposed algorithm here to have general performance better that any pure classical or quantum search algorithm.
Simulation of Quantum Algorithms with a Symbolic Programming Language
Nyman, Peter
2007-01-01
This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational methods. The computational language will include formulations such as quantum state, superposition and quantum operator.
2015-11-23
experience making cryogenic equipment and is at the forefront of adiabatic demagnetiza- tion cooling technology. This ADR system was delivered at the end of...Precision Devices with vacuum jackets removed, installed in Plourde research lab at Syracuse University. cuse Physics machine shop to install the system...successful initial benchmarking tests of the performance of the new refrigera- tor, the Plourde group worked to add electrical feedthroughs and experimental
Influence of parameters entanglement on the quantum algorithms
Alexey V. Kasarkin
2012-05-01
Full Text Available The article we consider the influence of parameters entanglement on the quantum algorithms, in particular influence of partial entanglement for quantum teleportation. The simulation results presented in chart form.
On the General Class of Models of Adiabatic Evolution
Sun, Jie; Lu, Songfeng; Liu, Fang
2016-10-01
The general class of models of adiabatic evolution was proposed to speed up the usual adiabatic computation in the case of quantum search problem. It was shown [8] that, by temporarily increasing the ground state energy of a time-dependent Hamiltonian to a suitable quantity, the quantum computation can perform the calculation in time complexity O(1). But it is also known that if the overlap between the initial and final states of the system is zero, then the computation based on the generalized models of adiabatic evolution can break down completely. In this paper, we find another severe limitation for this class of adiabatic evolution-based algorithms, which should be taken into account in applications. That is, it is still possible that this kind of evolution designed to deal with the quantum search problem fails completely if the interpolating paths in the system Hamiltonian are chosen inappropriately, while the usual adiabatic evolutions can do the same job relatively effectively. This implies that it is not always recommendable to use nonlinear paths in adiabatic computation. On the contrary, the usual simple adiabatic evolution may be sufficient for effective use.
Mandrà, Salvatore; Giacomo Guerreschi, Gian; Aspuru-Guzik, Alán
2016-07-01
We present an exact quantum algorithm for solving the Exact Satisfiability problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts: the first step consists in the identification and efficient characterization of a restricted subspace that contains all the valid assignments of the Exact Satisfiability; while the second part performs a quantum search in such restricted subspace. The quantum algorithm can be used either to find a valid assignment (or to certify that no solution exists) or to count the total number of valid assignments. The query complexities for the worst-case are respectively bounded by O(\\sqrt{{2}n-{M\\prime }}) and O({2}n-{M\\prime }), where n is the number of variables and {M}\\prime the number of linearly independent clauses. Remarkably, the proposed quantum algorithm results to be faster than any known exact classical algorithm to solve dense formulas of Exact Satisfiability. As a concrete application, we provide the worst-case complexity for the Hamiltonian cycle problem obtained after mapping it to a suitable Occupation problem. Specifically, we show that the time complexity for the proposed quantum algorithm is bounded by O({2}n/4) for 3-regular undirected graphs, where n is the number of nodes. The same worst-case complexity holds for (3,3)-regular bipartite graphs. As a reference, the current best classical algorithm has a (worst-case) running time bounded by O({2}31n/96). Finally, when compared to heuristic techniques for Exact Satisfiability problems, the proposed quantum algorithm is faster than the classical WalkSAT and Adiabatic Quantum Optimization for random instances with a density of constraints close to the satisfiability threshold, the regime in which instances are typically the hardest to solve. The proposed quantum algorithm can be straightforwardly extended to the generalized version of the Exact Satisfiability known as Occupation
Quantum Computation: Particle and Wave Aspects of Algorithms
Patel, Apoorva
2011-01-01
The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen. Clever quantum algorithms have been discovered in recent years, although not systematically, and the field remains under active investigation. Richard Feynman was one of the pioneers who foresaw the power of quantum computers. In this issue dedicated to him, I give an introduction to how particle and wave aspects contribute to the power of quantum computers. Shor's and Grover's algorithms are analysed as examples.
Classical computing, quantum computing, and Shor's factoring algorithm
Manin, Yu I
1999-01-01
This is an expository talk written for the Bourbaki Seminar. After a brief introduction, Section 1 discusses in the categorical language the structure of the classical deterministic computations. Basic notions of complexity icluding the P/NP problem are reviewed. Section 2 introduces the notion of quantum parallelism and explains the main issues of quantum computing. Section 3 is devoted to four quantum subroutines: initialization, quantum computing of classical Boolean functions, quantum Fourier transform, and Grover's search algorithm. The central Section 4 explains Shor's factoring algorithm. Section 5 relates Kolmogorov's complexity to the spectral properties of computable function. Appendix contributes to the prehistory of quantum computing.
Geometry of the Adiabatic Theorem
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
Peilin Zhang
2015-01-01
Full Text Available We present an algorithm of quantum restricted Boltzmann machine network based on quantum gates. The algorithm is used to initialize the procedure that adjusts the qubit and weights. After adjusting, the network forms an unsupervised generative model that gives better classification performance than other discriminative models. In addition, we show how the algorithm can be constructed with quantum circuit for quantum computer.
Algorithmic Complexity in Cosmology and Quantum Gravity
D. Singleton
2002-01-01
Full Text Available Abstract: In this article we use the idea of algorithmic complexity (AC to study various cosmological scenarios, and as a means of quantizing the ravitational interaction. We look at 5D and 7D cosmological models where the Universe begins as a higher dimensional Planck size spacetime which fluctuates between Euclidean and Lorentzian signatures. These fluctuations are overned by the AC of the two different signatures. At some point a transition to a 4D Lorentzian signature Universe occurs, with the extra dimensions becoming "frozen" or non-dynamical. We also apply the idea of algorithmic complexity to study composite wormholes, the entropy of black holes, and the path integral for quantum gravity. Some of the physical consequences of the idea presented here are:the birth of the Universe with a fluctuating metric signature; the transition from a fluctuating metric signature to Lorentzian one; "frozen" extra dimensions as a consequence of this transition; quantum handles in the spacetime foam as regions with multidimensional gravity.
Takeuchi, Naoki; Nagasawa, Shuichi; China, Fumihiro; Ando, Takumi; Hidaka, Mutsuo; Yamanashi, Yuki; Yoshikawa, Nobuyuki
2017-03-01
Adiabatic quantum-flux-parametron (AQFP) logic is an energy-efficient superconductor logic with zero static power consumption and very small switching energy. In this paper, we report a new AQFP cell library designed using the AIST 10 kA cm-2 Nb high-speed standard process (HSTP), which is a high-critical-current-density version of the AIST 2.5 kA cm-2 Nb standard process (STP2). Since the intrinsic damping of the Josephson junction (JJ) of HSTP is relatively strong, shunt resistors for JJs were removed and the energy efficiency improved significantly. Also, excitation transformers in the new cells were redesigned so that the cells can operate in a four-phase excitation mode. We described the detail of HSTP and the AQFP cell library designed using HSTP, and showed experimental results of cell test circuits.
Diestler, D J; Kenfack, A; Manz, J; Paulus, B
2012-03-22
This article presents the results of the first quantum simulations of the electronic flux density (j(e)) by the "coupled-channels" (CC) theory, the fundamentals of which are presented in the previous article [Diestler, D. J. J. Phys. Chem. A 2012, DOI: 10.1021/jp207843z]. The principal advantage of the CC scheme is that it employs exclusively standard methods of quantum chemistry and quantum dynamics within the framework of the Born-Oppenheimer approximation (BOA). The CC theory goes beyond the BOA in that it yields a nonzero j(e) for electronically adiabatic processes, in contradistinction to the BOA itself, which always gives j(e) = 0. The CC is applied to oriented H(2)(+) vibrating in the electronic ground state ((2)Σ(g)(+)), for which the nuclear and electronic flux densities evolve on a common time scale of about 22 fs per vibrational period. The system is chosen as a touchstone for the CC theory, because it is the only one for which highly accurate flux densities have been calculated numerically without invoking the BOA [Barth et al, Chem. Phys. Lett. 2009, 481, 118]. Good agreement between CC and accurate results supports the CC approach, another advantage of which is that it allows a transparent interpretation of the temporal and spatial properties of j(e).
Gammelmark, Søren; Eckardt, André
2013-01-01
We theoretically study the adiabatic preparation of an antiferromagnetic phase in a mixed Mott insulator of two bosonic atom species in a one-dimensional optical lattice. In such a system one can engineer a tunable parabolic inhomogeneity by controlling the difference of the trapping potentials f...... that during the preparation finite size effects will play a crucial role for a system of realistic size. The experiment that we propose can be realized, for example, using atomic mixtures of rubidium 87 with potassium 41, or ytterbium 168 with ytterbium 174....
One-step generation of qutrit entanglement via adiabatic passage in cavity quantum electrodynamics
Ma Song-She; Chen Mei-Feng; Jiang Xia-Ping
2011-01-01
A scheme is proposed for generating a three-dimensional entangled state for two atoms trapped in a cavity by one step via adiabatic passage.In the scheme,the two atoms are always in ground states and the field mode of the cavity excited is negligible under a certain condition.Therefore,the scheme is very robust against decoherence.Furthermore,it needs neither the exact control of all parameters nor the accurate control of the interaction time.It is shown that qutrit entanglement can be generated with a high fidelity.
Pure spin current induced by adiabatic quantum pumping in zigzag-edged graphene nanoribbons
Souma, Satofumi, E-mail: ssouma@harbor.kobe-u.ac.jp; Ogawa, Matsuto [Department of Electrical and Electronic Engineering, Kobe University, 1-1 Rokkodai, Nada, Kobe 657-8501 (Japan)
2014-05-05
We show theoretically that pure spin current can be generated in zigzag edged graphene nanoribbons through the adiabatic pumping by edge selective pumping potentials. The origin of such pure spin current is the spin splitting of the edge localized states, which are oppositely spin polarized at opposite edges. In the proposed device, each edge of the ribbon is covered by two independent time-periodic local gate potentials with a definite phase difference, inducing the edge spin polarized current. When the pumping phase difference is opposite in sign between two edges, the total charge currents is zero and the pure edge spin current is generated.
Quantum Monte Carlo methods algorithms for lattice models
Gubernatis, James; Werner, Philipp
2016-01-01
Featuring detailed explanations of the major algorithms used in quantum Monte Carlo simulations, this is the first textbook of its kind to provide a pedagogical overview of the field and its applications. The book provides a comprehensive introduction to the Monte Carlo method, its use, and its foundations, and examines algorithms for the simulation of quantum many-body lattice problems at finite and zero temperature. These algorithms include continuous-time loop and cluster algorithms for quantum spins, determinant methods for simulating fermions, power methods for computing ground and excited states, and the variational Monte Carlo method. Also discussed are continuous-time algorithms for quantum impurity models and their use within dynamical mean-field theory, along with algorithms for analytically continuing imaginary-time quantum Monte Carlo data. The parallelization of Monte Carlo simulations is also addressed. This is an essential resource for graduate students, teachers, and researchers interested in ...
Comment on `Do we have a consistent non-adiabatic quantum-classical mechanics?'
Kisil, Vladimir V.
2009-01-01
We argue with claims of the paper [Agostini F., Caprara S. and Ciccotti G., Europhys. Lett. EPL, 78 (2007) Art. 30001, 6] that the quantum-classic bracket introduced in [arXiv:quant-ph/0506122] produces "artificial coupling" and has "genuinely classical nature". Keywords: p-mechanics, quantum, classic, commutator, Poisson bracket, mixing, coupling, semi-classical
Renaud, N.; Grozema, F.C.
2014-01-01
We report numerical simulations of biexciton generation in coupled quantum dots (CQDs) placed in a static electric field and excited by a chirped laser pulse. Our simulations explicitly account for exciton-phonon interactions at finite temperature using a non-Markovian quantum jump approach to solve
Quantum algorithms for biomolecular solutions of the satisfiability problem on a quantum machine.
Chang, Weng-Long; Ren, Ting-Ting; Luo, Jun; Feng, Mang; Guo, Minyi; Weicheng Lin, Kawuu
2008-09-01
In this paper, we demonstrate that the logic computation performed by the DNA-based algorithm for solving general cases of the satisfiability problem can be implemented more efficiently by our proposed quantum algorithm on the quantum machine proposed by Deutsch. To test our theory, we carry out a three-quantum bit nuclear magnetic resonance experiment for solving the simplest satisfiability problem.
Billeter, S R
1998-01-01
This thesis describes the methodology of quantum dynamical (QD) simulation of proton transfers in aqueous solutions, its implementation in the simulation program QDGROMOS and its application to protonated water and aqueous solutions of acetic acid. QDGROMOS is based on the GROMOS96 molecular dynamics (MD) program package. Many of the solutions to partial problems such as the representation of the quantum state, the solution of the time-dependent Schrodinger equation, the forces from the quantum subsystem, the time-ordering of the propagations and the correlations between the subsystems, are complementary. In chapter 1, various numerical propagation algorithms for solving the time-dependent Schrodinger equation under the influence of a constant Hamilton operator are compared against each other, mainly in one dimension. A Chebysheff series expansion and the expansion in terms of eigenstates of the Hamilton operator were found to be most stable. Chapter 2 describes the theory, the methods and the algorithms of Q...
A Quantum Algorithm for the Hamiltonian NAND Tree
Farhi, E; Gutmann, S
2007-01-01
We give a quantum algorithm for the NAND tree problem in the Hamiltonian oracle model. The algorithm uses a continuous time quantum walk with a run time proportional to sqrt(N)*sqrt(logN). We also show a lower bound of sqrt(N) for the NAND tree problem in the Hamiltonian oracle model.
A Study of Quantum Algorithms and Quantum Cryptography
小柴, 健史
2007-01-01
This report describes properties of basic cryptographic primitives (quantum public-key cryptosystmes and quantum one-way functions) in the quantum world where quantum computers are available. Some quantum public-key cryptosystems have already proposed. However, the security requirements for quantum public-key cryptosystems are not studied well. We propose several security notions for quantum public-key cryptosystems and discuss relation among them. In the classical setting, the notion of one-...
NOVEL QUANTUM-INSPIRED GENETIC ALGORITHM BASED ON IMMUNITY
Li Ying; Zhao Rongchun; Zhang Yanning; Jiao Licheng
2005-01-01
A novel algorithm, the Immune Quantum-inspired Genetic Algorithm (IQGA), is proposed by introducing immune concepts and methods into Quantum-inspired Genetic Algorithm (QGA). With the condition of preserving QGA's advantages, IQGA utilizes the characteristics and knowledge in the pending problems for restraining the repeated and ineffective operations during evolution, so as to improve the algorithm efficiency. The experimental results of the knapsack problem show that the performance of IQGA is superior to the Conventional Genetic Algorithm (CGA), the Immune Genetic Algorithm (IGA) and QGA.
QUANTUM MONTE-CARLO SIMULATIONS - ALGORITHMS, LIMITATIONS AND APPLICATIONS
DERAEDT, H
1992-01-01
A survey is given of Quantum Monte Carlo methods currently used to simulate quantum lattice models. The formalisms employed to construct the simulation algorithms are sketched. The origin of fundamental (minus sign) problems which limit the applicability of the Quantum Monte Carlo approach is shown
Quantum Monte Carlo Simulations : Algorithms, Limitations and Applications
Raedt, H. De
1992-01-01
A survey is given of Quantum Monte Carlo methods currently used to simulate quantum lattice models. The formalisms employed to construct the simulation algorithms are sketched. The origin of fundamental (minus sign) problems which limit the applicability of the Quantum Monte Carlo approach is shown
Quantum state specific reactant preparation in a molecular beam by rapid adiabatic passage
Chadwick, Helen, E-mail: helen.chadwick@epfl.ch; Hundt, P. Morten; Reijzen, Maarten E. van; Yoder, Bruce L.; Beck, Rainer D. [Laboratoire de Chimie Physique Moléculaire, Ecole Polytechnique Fédérale de Lausanne, Lausanne (Switzerland)
2014-01-21
Highly efficient preparation of molecules in a specific rovibrationally excited state for gas/surface reactivity measurements is achieved in a molecular beam using tunable infrared (IR) radiation from a single mode continuous wave optical parametric oscillator (cw-OPO). We demonstrate that with appropriate focusing of the IR radiation, molecules in the molecular beam crossing the fixed frequency IR field experience a Doppler tuning that can be adjusted to achieve complete population inversion of a two-level system by rapid adiabatic passage (RAP). A room temperature pyroelectric detector is used to monitor the excited fraction in the molecular beam and the population inversion is detected and quantified using IR bleaching by a second IR-OPO. The second OPO is also used for complete population transfer to an overtone or combination vibration via double resonance excitation using two spatially separated RAP processes.
Quantum discord and entanglement in grover search algorithm
Ye, Bin; Zhang, Tingzhong; Qiu, Liang; Wang, Xuesong
2016-06-01
Imperfections and noise in realistic quantum computers may seriously affect the accuracy of quantum algorithms. In this article we explore the impact of static imperfections on quantum entanglement as well as non-entangled quantum correlations in Grover's search algorithm. Using the metrics of concurrence and geometric quantum discord, we show that both the evolution of entanglement and quantum discord in Grover algorithm can be restrained with the increasing strength of static imperfections. For very weak imperfections, the quantum entanglement and discord exhibit periodic behavior, while the periodicity will most certainly be destroyed with stronger imperfections. Moreover, entanglement sudden death may occur when the strength of static imperfections is greater than a certain threshold.
Linear-scaling and parallelizable algorithms for stochastic quantum chemistry
Booth, George H; Alavi, Ali
2013-01-01
For many decades, quantum chemical method development has been dominated by algorithms which involve increasingly complex series of tensor contractions over one-electron orbital spaces. Procedures for their derivation and implementation have evolved to require the minimum amount of logic and rely heavily on computationally efficient library-based matrix algebra and optimized paging schemes. In this regard, the recent development of exact stochastic quantum chemical algorithms to reduce computational scaling and memory overhead requires a contrasting algorithmic philosophy, but one which when implemented efficiently can often achieve higher accuracy/cost ratios with small random errors. Additionally, they can exploit the continuing trend for massive parallelization which hinders the progress of deterministic high-level quantum chemical algorithms. In the Quantum Monte Carlo community, stochastic algorithms are ubiquitous but the discrete Fock space of quantum chemical methods is often unfamiliar, and the metho...
Lisi, A D; Illuminati, F; Vitali, D; Lisi, Antonio Di; Siena, Silvio De; Illuminati, Fabrizio; Vitali, David
2004-01-01
We introduce an efficient and robust scheme to generate maximally entangled states of two atomic ensembles. The scheme is based on quantum non-demolition measurements of total atomic populations and on quantum feedback conditioned by the measurements outputs. The high efficiency of the scheme is tested and confirmed numerically for photo-detection with ideal efficiency as well as in the presence of losses.
del Campo, Adolfo; Rams, Marek M; Zurek, Wojciech H
2012-09-14
The dynamics of a quantum phase transition is inextricably woven with the formation of excitations, as a result of critical slowing down in the neighborhood of the critical point. We design a transitionless quantum driving through a quantum critical point, allowing one to access the ground state of the broken-symmetry phase by a finite-rate quench of the control parameter. The method is illustrated in the one-dimensional quantum Ising model in a transverse field. Driving through the critical point is assisted by an auxiliary Hamiltonian, for which the interplay between the range of the interaction and the modes where excitations are suppressed is elucidated.
Building Blocks Propagation in Quantum-Inspired Genetic Algorithm
Nowotniak, Robert; Kucharski, Jacek
2010-01-01
This paper presents an analysis of building blocks propagation in Quantum-Inspired Genetic Algorithm, which belongs to a new class of metaheuristics drawing their inspiration from both biological evolution and unitary evolution of quantum systems. The expected number of quantum chromosomes matching a schema has been analyzed and a random variable corresponding to this issue has been introduced. The results have been compared with Simple Genetic Algorithm. Also, it has been presented how selec...
Grover quantum searching algorithm based on weighted targets
Li Panchi; Li Shiyong
2008-01-01
The current Grover quantum searching algorithm cannot identify the difference in importance of the search targets when it is applied to an unsorted quantum database, and the probability for each search target is equal. To solve this problem, a Grover searching algorithm based on weighted targets is proposed. First, each target is endowed a weight coefficient according to its importance. Applying these different weight coefficients, the targets are represented as quantum superposition states. Second, the novel Grover searching algorithm based on the quantum superposition of the weighted targets is constructed. Using this algorithm, the probability of getting each target can be approximated to the corresponding weight coefficient, which shows the flexibility of this algorithm.Finally, the validity of the algorithm is proved by a simple searching example.
A linear time quantum algorithm for 3SAT
Walters, Zachary B
2015-01-01
A quantum algorithm for the NP complete problem of satisfying boolean formulas with three variables per clause (3SAT) is presented. Departing from traditional models of quantum computation, this algorithm makes extensive use of irreversible operations to incoherently transfer population from states which do not solve some problem of interest to states which do. Provided that a solution exists, the algorithm yields exponential decay of nonsolution probability, at a rate controlled by the user.
Quantum lattice gas algorithm for the telegraph equation.
Coffey, Mark W; Colburn, Gabriel G
2009-06-01
The telegraph equation combines features of both the diffusion and wave equations and has many applications to heat propagation, transport in disordered media, and elsewhere. We describe a quantum lattice gas algorithm (QLGA) for this partial differential equation with one spatial dimension. This algorithm generalizes one previously known for the diffusion equation. We present an analysis of the algorithm and accompanying simulation results. The QLGA is suitable for simulation on combined classical-quantum computers.
Efficient algorithms for the laboratory discovery of optimal quantum controls.
Turinici, Gabriel; Le Bris, Claude; Rabitz, Herschel
2004-01-01
The laboratory closed-loop optimal control of quantum phenomena, expressed as minimizing a suitable cost functional, is currently implemented through an optimization algorithm coupled to the experimental apparatus. In practice, the most commonly used search algorithms are variants of genetic algorithms. As an alternative choice, a direct search deterministic algorithm is proposed in this paper. For the simple simulations studied here, it outperforms the existing approaches. An additional algorithm is introduced in order to reveal some properties of the cost functional landscape.
An N/4 fixed-point duality quantum search algorithm
无
2010-01-01
Here a fixed-point duality quantum search algorithm is proposed.This algorithm uses iteratively non-unitary operations and measurements to search an unsorted database.Once the marked item is found,the algorithm stops automatically.This algorithm uses a constant non-unitary operator,and requires N/4 steps on average(N is the number of data from the database) to locate the marked state.The implementation of this algorithm in a usual quantum computer is also demonstrated.
Influences of Gate Operation Errors in the Quantum Counting Algorithm
Qing Ai; Yan-Song Li; Gui-Lu Long
2006-01-01
In this article, the error analysis in the quantum counting algorithm is investigated. It has been found that the random error plays as important a role as the systematic error does in the phase inversion operations. Both systematic and random errors are important in the Hadamard transformation. This is quite different from the Grover algorithm and the Shor algorithm.
Possible universal quantum algorithms for generalized Turaev-Viro invariants
Vélez, Mario; Ospina, Juan
2011-05-01
An emergent trend in quantum computation is the topological quantum computation (TQC). Briefly, TQC results from the application of quantum computation with the aim to solve the problems of quantum topology such as topological invariants for knots and links (Jones polynomials, HOMFLY polynomials, Khovanov polynomials); topological invariants for graphs (Tutte polynomial and Bollobás-Riordan polynomial); topological invariants for 3-manifolds (Reshetiskin-Turaev, Turaev-Viro and Turaer-Viro-Ocneanu invariants) and topological invariants for 4-manifolds( Crane-Yetter invariants). In a few words, TQC is concerned with the formulation of quantum algorithms for the computation of these topological invariants in quantum topology. Given that one of the fundamental achievements of quantum topology was the discovery of strong connections between monoidal categories and 3-dimensional manifolds, in TQC is possible and necessary to exploit such connections with the purpose to formulate universal quantum algorithms for topological invariants of 3-manifolds. In the present work we make an exploration of such possibilities. Specifically we search for universal quantum algorithms for generalized Turaev-Viro invariants of 3-manifolds such as the Turaev-Viro-Ocneanu invariants, the Kashaev-Baseilhac-Benedetti invariants of 3-manifolds with links and the Geer-Kashaev-Turaev invariants of 3-manifolds with a link and a principal bundle. We also look for physical systems (three dimensional topological insulators and three-dimensional gravity) over which implement the resulting universal topological quantum algorithms.
Building Blocks Propagation in Quantum-Inspired Genetic Algorithm
Nowotniak, Robert
2010-01-01
This paper presents an analysis of building blocks propagation in Quantum-Inspired Genetic Algorithm, which belongs to a new class of metaheuristics drawing their inspiration from both biological evolution and unitary evolution of quantum systems. The expected number of quantum chromosomes matching a schema has been analyzed and a random variable corresponding to this issue has been introduced. The results have been compared with Simple Genetic Algorithm. Also, it has been presented how selected binary quantum chromosomes cover a domain of one-dimensional fitness function.
Oreshkov, Ognyan; Calsamiglia, John
2010-07-30
We propose a theory of adiabaticity in quantum markovian dynamics based on a decomposition of the Hilbert space induced by the asymptotic behavior of the Lindblad semigroup. A central idea of our approach is that the natural generalization of the concept of eigenspace of the Hamiltonian in the case of markovian dynamics is a noiseless subsystem with a minimal noisy cofactor. Unlike previous attempts to define adiabaticity for open systems, our approach deals exclusively with physical entities and provides a simple, intuitive picture at the Hilbert-space level, linking the notion of adiabaticity to the theory of noiseless subsystems. As two applications of our theory, we propose a general framework for decoherence-assisted computation in noiseless codes and a dissipation-driven approach to holonomic computation based on adiabatic dragging of subsystems that is generally not achievable by nondissipative means.
Decoherence in optimized quantum random-walk search algorithm
Zhang, Yu-Chao; Bao, Wan-Su; Wang, Xiang; Fu, Xiang-Qun
2015-08-01
This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the optimized quantum random-walk search algorithm with decoherence is depicted through defining the shift operator which includes the possibility of broken links. For a given database size, we obtain the maximum success rate of the algorithm and the required number of iterations through numerical simulations and analysis when the algorithm is in the presence of decoherence. Then the computational complexity of the algorithm with decoherence is obtained. The results show that the ultimate effect of broken-link-type decoherence on the optimized quantum random-walk search algorithm is negative. Project supported by the National Basic Research Program of China (Grant No. 2013CB338002).
Effects of decoherence and imperfections for quantum algorithms
Pomeransky, A A; Shepelyansky, D L
2004-01-01
We study effects of static inter-qubit interactions and random errors in quantum gates on the stability of various quantum algorithms including the Grover quantum search algorithm and the quantum chaos maps. For the Grover algorithm our numerical and analytical results show existence of regular and chaotic phases depending on the static imperfection strength $\\epsilon$. The critical border $\\epsilon_c$ between two phases drops polynomially with the number of qubits $n_q$ as $\\epsilon_c \\sim n_q^{-3/2}$. In the regular phase $(\\epsilon 2^{-n_q/2}$. In the chaotic phase $(\\epsilon > \\epsilon_c)$ the algorithm is completely destroyed. The results for the Grover algorithm are compared with the imperfection effects for quantum algorithms of quantum chaos maps where the universal law for the fidelity decay is given by the Random Matrix Theory (RMT). We also discuss a new gyroscopic quantum error correction method which allows to reduce the effect of static imperfections. In spite of this decay GYQEC allows to obta...
Childs, A M; Farhi, E; Goldstone, J; Gutmann, S; Landahl, A J; Childs, Andrew M.; Deotto, Enrico; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam; Landahl, Andrew J.
2002-01-01
We propose a quantum algorithm for solving combinatorial search problems that uses only a sequence of measurements. The algorithm is similar in spirit to quantum computation by adiabatic evolution, in that the goal is to remain in the ground state of a time-varying Hamiltonian. Indeed, we show that the running times of the two algorithms are closely related. We also show how to achieve the quadratic speedup for Grover's unstructured search problem with only two measurements. Finally, we discuss some similarities and differences between the adiabatic and measurement algorithms.
Practical and algorithmical manifestations of quantum chaos
Li, B; Li, Baowen; Robnik, Marko
1995-01-01
Quantum chaos manifests itself also in algorithmical complexity of methods, including the numerical ones, in solving the Schr\\"odinger equation. In this contribution we address the problem of calculating the eigenenergies and the eigenstates by various numerical methods applied to 2-dim generic billiard systems. In particular we analyze the dependence of the accuracy (errors) on the density of discretization of the given numerical method. We do this for several different billiard shapes, especially for the Robnik billiard. We study the numerical error of the boundary integral method and the plane wave decomposition method as a function of the discretization parameter b which by definition is the number of discretization nodes on the boundary per one de Broglie wavelength (arclength) interval. For boundary integral method, we discover that at each \\lambda the error scales as a power law = A b^{-\\alpha}, where \\alpha is a strong function of \\lambda: In the KAM-like regime 0\\le \\lambda\\le 1/4 it is large and cl...
Quantum Teleportation and Grover's Algorithm Without the Wavefunction
Niestegge, Gerd
2017-01-01
In the same way as the quantum no-cloning theorem and quantum key distribution in two preceding papers, entanglement-assisted quantum teleportation and Grover's search algorithm are generalized by transferring them to an abstract setting, including usual quantum mechanics as a special case. This again shows that a much more general and abstract access to these quantum mechanical features is possible than commonly thought. A non-classical extension of conditional probability and, particularly, a very special type of state-independent conditional probability are used instead of Hilbert spaces and wavefunctions.
Quantum Teleportation and Grover's Algorithm Without the Wavefunction
Niestegge, Gerd
2017-02-01
In the same way as the quantum no-cloning theorem and quantum key distribution in two preceding papers, entanglement-assisted quantum teleportation and Grover's search algorithm are generalized by transferring them to an abstract setting, including usual quantum mechanics as a special case. This again shows that a much more general and abstract access to these quantum mechanical features is possible than commonly thought. A non-classical extension of conditional probability and, particularly, a very special type of state-independent conditional probability are used instead of Hilbert spaces and wavefunctions.
Krajewski, Florian R.; Müser, Martin H.
2005-07-01
The spectral density of quantum mechanical Frenkel Kontorova chains moving in disordered, external potentials is investigated by means of path-integral molecular dynamics. If the second moment of the embedding potential is well defined (roughness exponent H=0), there is one regime in which the chain is pinned (large masses m of chain particles) and one in which it is unpinned (small m). If the embedding potential can be classified as a random walk on large length scales ( H=1/2), then the chain is always pinned irrespective of the value of m. For H=1/2, two phonon-like branches appear in the spectra.
Design of Quantum Algorithms Using Physics Tools
2014-06-02
spin chains, the development of a novel quantum money scheme, a study of quantum interactive proof systems , research on Hamiltonians on graphs...in the Hamiltonians . The states of a quantum spin chain are naturally represented in the Matrix Product States (MPS) framework. Using imaginary time...worked on a wide range of topics with some common themes related by the study of quantum Hamiltonians . Ground state properties of Hamiltonians and the
Quantum Dynamical Entropies and Gács Algorithmic Entropy
Fabio Benatti
2012-07-01
Full Text Available Several quantum dynamical entropies have been proposed that extend the classical Kolmogorov–Sinai (dynamical entropy. The same scenario appears in relation to the extension of algorithmic complexity theory to the quantum realm. A theorem of Brudno establishes that the complexity per unit time step along typical trajectories of a classical ergodic system equals the KS-entropy. In the following, we establish a similar relation between the Connes–Narnhofer–Thirring quantum dynamical entropy for the shift on quantum spin chains and the Gács algorithmic entropy. We further provide, for the same system, a weaker linkage between the latter algorithmic complexity and a different quantum dynamical entropy proposed by Alicki and Fannes.
Topology control based on quantum genetic algorithm in sensor networks
SUN Lijuan; GUO Jian; LU Kai; WANG Ruchuan
2007-01-01
Nowadays,two trends appear in the application of sensor networks in which both multi-service and quality of service (QoS)are supported.In terms of the goal of low energy consumption and high connectivity,the control on topology is crucial.The algorithm of topology control based on quantum genetic algorithm in sensor networks is proposed.An advantage of the quantum genetic algorithm over the conventional genetic algorithm is demonstrated in simulation experiments.The goals of high connectivity and low consumption of energy are reached.
Realization of Shor's algorithm on an optical quantum computer
无
2008-01-01
@@ A research team led by Prof. PAN Jianwei with the University of Science and Technology of China (USTC), CAS has been successful in performing Shor's algorithm, a quantum algorithm for factorization, in an optical quantum computer. The feat is also independently made by another team led by Andrew White from the University of Queensland in Brisbane, Australia. Both results were published in the 19 December, 2007 issue of Physics Review Newsletters.
PEA: Polymorphic Encryption Algorithm based on quantum computation
Komninos, N.; Mantas, G.
2011-01-01
In this paper, a polymorphic encryption algorithm (PEA), based on basic quantum computations, is proposed for the encryption of binary bits. PEA is a symmetric key encryption algorithm that applies different combinations of quantum gates to encrypt binary bits. PEA is also polymorphic since the states of the shared secret key control the different combinations of the ciphertext. It is shown that PEA achieves perfect secrecy and is resilient to eavesdropping and Trojan horse attacks. A securit...
Quantum Algorithms for Finding Claws, Collisions and Triangles
Buhrman, H; Hoyer, P; Magniez, F; Santha, M; De Wolf, R; Buhrman, Harry; Durr, Christoph; Hoyer, Peter; Magniez, Frederic; Santha, Miklos; Wolf, Ronald de
2000-01-01
We present several applications of quantum amplitude amplification to finding claws and collisions in ordered or unordered functions. Our algorithms generalize those of Brassard, Hoyer, and Tapp, and imply an N^{3/4} log(N) quantum upper bound for the element distinctness problem (contrasting with N\\log(N) classical complexity). We also give an algorithm to finding a triangle in a graph more efficiently than classically.
Quantum Behaved Particle Swarm Optimization Algorithm Based on Artificial Fish Swarm
Dong Yumin; Zhao Li
2014-01-01
Quantum behaved particle swarm algorithm is a new intelligent optimization algorithm; the algorithm has less parameters and is easily implemented. In view of the existing quantum behaved particle swarm optimization algorithm for the premature convergence problem, put forward a quantum particle swarm optimization algorithm based on artificial fish swarm. The new algorithm based on quantum behaved particle swarm algorithm, introducing the swarm and following activities, meanwhile using the a...
Noise effects in the quantum search algorithm from the computational complexity point of view
Gawron, Piotr; Klamka, Jerzy; Winiarczyk, Ryszard
2011-01-01
We analyse the resilience of the quantum search algorithm in the presence of quantum noise modelled as trace preserving completely positive maps. We study the influence of noise on computational complexity of the quantum search algorithm. We show that only for small amounts of noise the quantum search algorithm is still more efficient than any classical algorithm.
Quantum Algorithms for Tree Isomorphism and State Symmetrization
Rosenbaum, David
2010-01-01
The graph isomorphism problem is theoretically interesting and also has many practical applications. The best known classical algorithms for graph isomorphism all run in time super-polynomial in the size of the graph in the worst case. An interesting open problem is whether quantum computers can solve the graph isomorphism problem in polynomial time. In this paper, an algorithm is shown which can decide if two rooted trees are isomorphic in polynomial time. Although this problem is easy to solve efficiently on a classical computer, the techniques developed may be useful as a basis for quantum algorithms for deciding isomorphism of more interesting types of graphs. The related problem of quantum state symmetrization is also studied. A polynomial time algorithm for the problem of symmetrizing a set of orthonormal states over an arbitrary permutation group is shown. This algorithm is then generalized to allow symmetrization over a set of representatives of the cosets of a normal subgroup.
Quantum Algorithms with Fixed Points: The Case of Database Search
Grover, L K; Tulsi, T; Grover, Lov K.; Patel, Apoorva; Tulsi, Tathagat
2006-01-01
The standard quantum search algorithm lacks a feature, enjoyed by many classical algorithms, of having a fixed-point, i.e. a monotonic convergence towards the solution. Here we present two variations of the quantum search algorithm, which get around this limitation. The first replaces selective inversions in the algorithm by selective phase shifts of $\\frac{\\pi}{3}$. The second controls the selective inversion operations using two ancilla qubits, and irreversible measurement operations on the ancilla qubits drive the starting state towards the target state. Using $q$ oracle queries, these variations reduce the probability of finding a non-target state from $\\epsilon$ to $\\epsilon^{2q+1}$, which is asymptotically optimal. Similar ideas can lead to robust quantum algorithms, and provide conceptually new schemes for error correction.
A secure quantum key distribution scheme based on variable quantum encoding algorithms
Zhiwen Zhao; Yi Luo; Zhangji Zhao; Haiming Long
2011-01-01
The security of the quantum secret key plays a critical role in quantum communications. Thus far, one problem that still exists in existing protocols is the leakage of the length of the secret key. In this letter, based on variable quantum encoding algorithms, we propose a secure quantum key distribution scheme, which can overcome the security problem involving the leakage of the secret key. Security analysis shows that the proposed scheme is both secure and effective.%@@ The security of the quantum secret key plays a critical role in quantum communications.Thus far, one problem that still exists in existing protocols is the leakage of the length of the secret key.In this letter,based on variable quantum encoding algorithms, we propose a secure quantum key distribution scheme,which can overcome the security problem involving the leakage of the secret key.Security analysis shows that the proposed scheme is both secure and effective.
Quantum computation with classical light: The Deutsch Algorithm
Perez-Garcia, Benjamin [Photonics and Mathematical Optics Group, Tecnológico de Monterrey, Monterrey 64849 (Mexico); University of the Witwatersrand, Private Bag 3, Johannesburg 2050 (South Africa); Francis, Jason [School of Chemistry and Physics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000 (South Africa); McLaren, Melanie [University of the Witwatersrand, Private Bag 3, Johannesburg 2050 (South Africa); Hernandez-Aranda, Raul I. [Photonics and Mathematical Optics Group, Tecnológico de Monterrey, Monterrey 64849 (Mexico); Forbes, Andrew [University of the Witwatersrand, Private Bag 3, Johannesburg 2050 (South Africa); Konrad, Thomas, E-mail: konradt@ukzn.ac.za [School of Chemistry and Physics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000 (South Africa); National Institute of Theoretical Physics, Durban Node, Private Bag X54001, Durban 4000 (South Africa)
2015-08-28
We present an implementation of the Deutsch Algorithm using linear optical elements and laser light. We encoded two quantum bits in form of superpositions of electromagnetic fields in two degrees of freedom of the beam: its polarisation and orbital angular momentum. Our approach, based on a Sagnac interferometer, offers outstanding stability and demonstrates that optical quantum computation is possible using classical states of light. - Highlights: • We implement the Deutsh Algorithm using linear optical elements and classical light. • Our qubits are encoded in the polarisation and orbital angular momentum of the beam. • We show that it is possible to achieve quantum computation with two qubits in the classical domain of light.
Algorithms for Quantum Branching Programs Based on Fingerprinting
Ablayev, Farid; 10.4204/EPTCS.9.1
2009-01-01
In the paper we develop a method for constructing quantum algorithms for computing Boolean functions by quantum ordered read-once branching programs (quantum OBDDs). Our method is based on fingerprinting technique and representation of Boolean functions by their characteristic polynomials. We use circuit notation for branching programs for desired algorithms presentation. For several known functions our approach provides optimal QOBDDs. Namely we consider such functions as Equality, Palindrome, and Permutation Matrix Test. We also propose a generalization of our method and apply it to the Boolean variant of the Hidden Subgroup Problem.
Reasoning about Grover's quantum search algorithm using probabilistic wp
Butler, M.J.; Hartel, P.H.
1999-01-01
Grover's search algorithm is designed to be executed on a quantum-mechanical computer. In this article, the probabilistic wp-calculus is used to model and reason about Grover's algorithm. It is demonstrated that the calculus provides a rigorous programming notation for modeling this and other quantu
Invariant Quantum Algorithms for Insertion into an Ordered List
Farhi, E; Gutmann, S; Sipser, M; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam; Sipser, Michael
1999-01-01
We consider the problem of inserting one item into a list of N-1 ordered items. We previously showed that no quantum algorithm could solve this problem in fewer than log N/(2 log log N) queries, for N large. We transform the problem into a "translationally invariant" problem and restrict attention to invariant algorithms. We construct the "greedy" invariant algorithm and show numerically that it outperforms the best classical algorithm for various N. We also find invariant algorithms that succeed exactly in fewer queries than is classically possible, and iterating one of them shows that the insertion problem can be solved in fewer than 0.53 log N quantum queries for large N (where log N is the classical lower bound). We don't know whether a o(log N) algorithm exists.
A quantum heuristic algorithm for the traveling salesman problem
Bang, Jeongho; Ryu, Junghee; Lee, Changhyoup; Yoo, Seokwon; Lim, James; Lee, Jinhyoung
2012-12-01
We propose a quantum heuristic algorithm to solve the traveling salesman problem by generalizing the Grover search. Sufficient conditions are derived to greatly enhance the probability of finding the tours with the cheapest costs reaching almost to unity. These conditions are characterized by the statistical properties of tour costs and are shown to be automatically satisfied in the large-number limit of cities. In particular for a continuous distribution of the tours along the cost, we show that the quantum heuristic algorithm exhibits a quadratic speedup compared to its classical heuristic algorithm.
Numerical Simulations of a Possible Hypercomputational Quantum Algorithm
Sicard, Andrés; Ospina, Juan; Vélez, Mario
2005-01-01
The hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. Several numerical simulations of a possible hypercomputational algorithm based on quantum computations previously constructed by the authors are presented. The hypercomputability of our algorithm is based on the fact that this algorithm could solve a classically non-computable decision problem, Hilbert's tenth problem. The numerical simul...
Relaxation of the EM Algorithm via Quantum Annealing
Miyahara, Hideyuki
2016-01-01
The EM algorithm is a novel numerical method to obtain maximum likelihood estimates and is often used for practical calculations. However, many of maximum likelihood estimation problems are nonconvex, and it is known that the EM algorithm fails to give the optimal estimate by being trapped by local optima. In order to deal with this difficulty, we propose a deterministic quantum annealing EM algorithm by introducing the mathematical mechanism of quantum fluctuations into the conventional EM algorithm because quantum fluctuations induce the tunnel effect and are expected to relax the difficulty of nonconvex optimization problems in the maximum likelihood estimation problems. We show a theorem that guarantees its convergence and give numerical experiments to verify its efficiency.
Universality of Entanglement and Quantum Computation Complexity
Orus, R; Orus, Roman; Latorre, Jose I.
2004-01-01
We study the universality of scaling of entanglement in Shor's factoring algorithm and in adiabatic quantum algorithms across a quantum phase transition for both the NP-complete Exact Cover problem as well as the Grover's problem. The analytic result for Shor's algorithm shows a linear scaling of the entropy in terms of the number of qubits, therefore difficulting the possibility of an efficient classical simulation protocol. A similar result is obtained numerically for the quantum adiabatic evolution Exact Cover algorithm, which also shows universality of the quantum phase transition the system evolves nearby. On the other hand, entanglement in Grover's adiabatic algorithm remains a bounded quantity even at the critical point. A classification of scaling of entanglement appears as a natural grading of the computational complexity of simulating quantum phase transitions.
Wu, Jin-Lei; Song, Chong; Xu, Jing; Yu, Lin; Ji, Xin; Zhang, Shou
2016-09-01
An efficient scheme is proposed for generating n-qubit Greenberger-Horne-Zeilinger states of n superconducting qubits separated by (n-1) coplanar waveguide resonators capacitively via adiabatic passage with the help of quantum Zeno dynamics in one step. In the scheme, it is not necessary to precisely control the time of the whole operation and the Rabi frequencies of classical fields because of the introduction of adiabatic passage. The numerical simulations for three-qubit Greenberger-Horne-Zeilinger state show that the scheme is insensitive to the dissipation of the resonators and the energy relaxation of the superconducting qubits. The three-qubit Greenberger-Horne-Zeilinger state can be deterministically generated with comparatively high fidelity in the current experimental conditions, though the scheme is somewhat sensitive to the dephasing of superconducting qubits.
Quantum-inspired immune clonal algorithm for global optimization.
Jiao, Licheng; Li, Yangyang; Gong, Maoguo; Zhang, Xiangrong
2008-10-01
Based on the concepts and principles of quantum computing, a novel immune clonal algorithm, called a quantum-inspired immune clonal algorithm (QICA), is proposed to deal with the problem of global optimization. In QICA, the antibody is proliferated and divided into a set of subpopulation groups. The antibodies in a subpopulation group are represented by multistate gene quantum bits. In the antibody's updating, the general quantum rotation gate strategy and the dynamic adjusting angle mechanism are applied to accelerate convergence. The quantum not gate is used to realize quantum mutation to avoid premature convergences. The proposed quantum recombination realizes the information communication between subpopulation groups to improve the search efficiency. Theoretical analysis proves that QICA converges to the global optimum. In the first part of the experiments, 10 unconstrained and 13 constrained benchmark functions are used to test the performance of QICA. The results show that QICA performs much better than the other improved genetic algorithms in terms of the quality of solution and computational cost. In the second part of the experiments, QICA is applied to a practical problem (i.e., multiuser detection in direct-sequence code-division multiple-access systems) with a satisfying result.
Generalized quantum counting algorithm for non-uniform amplitude distribution
Tan, Jianing; Ruan, Yue; Li, Xi; Chen, Hanwu
2017-03-01
We give generalized quantum counting algorithm to increase universality of quantum counting algorithm. Non-uniform initial amplitude distribution is possible due to the diversity of situations on counting problems or external noise in the amplitude initialization procedure. We give the reason why quantum counting algorithm is invalid on this situation. By modeling in three-dimensional space spanned by unmarked state, marked state and free state to the entire Hilbert space of n qubits, we find Grover iteration can be regarded as improper rotation in the space. This allows us to give formula to solve counting problem. Furthermore, we express initial amplitude distribution in the eigenvector basis of improper rotation matrix. This is necessary to obtain mathematical analysis of counting problem on various situations. Finally, we design four simulation experiments, the results of which show that compared with original quantum counting algorithm, generalized quantum counting algorithm wins great satisfaction from three aspects: (1) Whether initial amplitude distribution is uniform; (2) the diversity of situations on counting problems; and (3) whether phase estimation technique can get phase exactly.
A quantum–quantum Metropolis algorithm
Yung, Man-Hong; Aspuru-Guzik, Alan
2012-01-01
The classical Metropolis sampling method is a cornerstone of many statistical modeling applications that range from physics, chemistry, and biology to economics. This method is particularly suitable for sampling the thermal distributions of classical systems. The challenge of extending this method to the simulation of arbitrary quantum systems is that, in general, eigenstates of quantum Hamiltonians cannot be obtained efficiently with a classical computer. However, this challenge can be overc...
Research on Quantum Algorithms at the Institute for Quantum Information
2009-10-17
algorithm. Monte Carlo results for the five-qubit and seven-qubit codes demonstrate that the message passing algorithm has a significantly higher...states and observables of an arbitrary process are linearly isomorphic to a matrix algebra, which unifies the Schrodinger and Heisenberg pictures and
Improved Quantum-Inspired Evolutionary Algorithm for Engineering Design Optimization
Jinn-Tsong Tsai
2012-01-01
Full Text Available An improved quantum-inspired evolutionary algorithm is proposed for solving mixed discrete-continuous nonlinear problems in engineering design. The proposed Latin square quantum-inspired evolutionary algorithm (LSQEA combines Latin squares and quantum-inspired genetic algorithm (QGA. The novel contribution of the proposed LSQEA is the use of a QGA to explore the optimal feasible region in macrospace and the use of a systematic reasoning mechanism of the Latin square to exploit the better solution in microspace. By combining the advantages of exploration and exploitation, the LSQEA provides higher computational efficiency and robustness compared to QGA and real-coded GA when solving global numerical optimization problems with continuous variables. Additionally, the proposed LSQEA approach effectively solves mixed discrete-continuous nonlinear design optimization problems in which the design variables are integers, discrete values, and continuous values. The computational experiments show that the proposed LSQEA approach obtains better results compared to existing methods reported in the literature.
Compiling quantum algorithms for architectures with multi-qubit gates
Martinez, Esteban A.; Monz, Thomas; Nigg, Daniel; Schindler, Philipp; Blatt, Rainer
2016-06-01
In recent years, small-scale quantum information processors have been realized in multiple physical architectures. These systems provide a universal set of gates that allow one to implement any given unitary operation. The decomposition of a particular algorithm into a sequence of these available gates is not unique. Thus, the fidelity of the implementation of an algorithm can be increased by choosing an optimized decomposition into available gates. Here, we present a method to find such a decomposition, where a small-scale ion trap quantum information processor is used as an example. We demonstrate a numerical optimization protocol that minimizes the number of required multi-qubit entangling gates by design. Furthermore, we adapt the method for state preparation, and quantum algorithms including in-sequence measurements.
Enhanced Precedence Scheduling Algorithm with Dynamic Time Quantum (EPSADTQ
G. Siva Nageswara Rao
2015-07-01
Full Text Available This study proposes a new algorithm which is a logical extension of the popular Round Robin CPU scheduling algorithm. The Round Robin algorithm can be effective only if the time quantum is chosen accurately. Even by taking mean average of burst times as time quantum, the performance of the RR cannot be improved beyond a certain point. However, the novel method proposed here, suggests that a priority be assigned to each process based on balanced precedence factor. The novel method also uses mean average as a time quantum. Experiments are conducted in order to measure the effectiveness of this novel method. The results clearly showed that EPSADTQ is superior to RR and PSMTQ and its variants. EPSADTQ resulted in a significant reduction of the no. of context switches, average waiting time and average turnaround time.
Quantum Computing - A new Implementation of Simon Algorithm for 3-Dimensional Registers
Adina Bărîlă
2015-03-01
Full Text Available Quantum computing is a new field of science aiming to use quantum phenomena in order to perform operations on data. The Simon algorithm is one of the quantum algorithms which solves a certain problem exponentially faster than any classical algorithm solving the same problem. Simulating of quantum algorithms is very important since quantum hardware is not available outside of the research labs. QCL (Quantum Computation Language is the most advanced implemented quantum computer simulator and was conceived by Bernhard Ömer. The paper presents an implementation in QCL of the Simon algorithm in the case of 3-dimensional registers.
Zheng, An-Shou; Cheng, Yong-Jin; Liu, Ji-Bing; Li, Tie-Ping
We propose an alternative scheme to prepare the Greenberg-Horne-Zeilinger (GHZ) state and realize a SWAP gate by using Superconducting Quantum-interference devices (SQUIDs) coupled to a cavity. The present scheme, based on the adiabatic evolution of dark state, constitutes a decoherence-free method in the sense that spontaneous emission and cavity damping are avoided. Besides, the standard GHZ state can be directly obtained without measurement or any auxiliary SQUIDs and the construction of the SWAP gate does not require a composition of elementary gates from a universal set. Thus the procedure is simplified and decoherence is greatly suppressed.
Valence-bond quantum Monte Carlo algorithms defined on trees.
Deschner, Andreas; Sørensen, Erik S
2014-09-01
We present a class of algorithms for performing valence-bond quantum Monte Carlo of quantum spin models. Valence-bond quantum Monte Carlo is a projective T=0 Monte Carlo method based on sampling of a set of operator strings that can be viewed as forming a treelike structure. The algorithms presented here utilize the notion of a worm that moves up and down this tree and changes the associated operator string. In quite general terms, we derive a set of equations whose solutions correspond to a whole class of algorithms. As specific examples of this class of algorithms, we focus on two cases. The bouncing worm algorithm, for which updates are always accepted by allowing the worm to bounce up and down the tree, and the driven worm algorithm, where a single parameter controls how far up the tree the worm reaches before turning around. The latter algorithm involves only a single bounce where the worm turns from going up the tree to going down. The presence of the control parameter necessitates the introduction of an acceptance probability for the update.
Adiabatic Evolution in XXX Spin Chain is Fast
Korepin, V
2004-01-01
Adiabatic theorem of quantum mechanics was used by E. Farhi, J. Goldstone, S. Gutmann and M. Sipser to design quantum algorithms of a new kind. A quantum computer evolves slowly enough, so that it remains in its instantaneous ground state, which tells the solution. We consider XXX Heisenberg spin chain. We rotate magnetic field and change its magnitude. The ground state evolves from a ferromagnetic one into a nontrivial ground state of XXX anti-ferromagnet. This adiabatic evolution goes very gently. Because of SU(2) symmetry and integrability only one mode get exited. We prove that the time of the evolution scales as a square root of number of qubits. This is faster then other known examples.
Cencek, Wojciech; Przybytek, Michał; Komasa, Jacek; Mehl, James B; Jeziorski, Bogumił; Szalewicz, Krzysztof
2012-06-14
The adiabatic, relativistic, and quantum electrodynamics (QED) contributions to the pair potential of helium were computed, fitted separately, and applied, together with the nonrelativistic Born-Oppenheimer (BO) potential, in calculations of thermophysical properties of helium and of the properties of the helium dimer. An analysis of the convergence patterns of the calculations with increasing basis set sizes allowed us to estimate the uncertainties of the total interaction energy to be below 50 ppm for interatomic separations R smaller than 4 bohrs and for the distance R = 5.6 bohrs. For other separations, the relative uncertainties are up to an order of magnitude larger (and obviously still larger near R = 4.8 bohrs where the potential crosses zero) and are dominated by the uncertainties of the nonrelativistic BO component. These estimates also include the contributions from the neglected relativistic and QED terms proportional to the fourth and higher powers of the fine-structure constant α. To obtain such high accuracy, it was necessary to employ explicitly correlated Gaussian expansions containing up to 2400 terms for smaller R (all R in the case of a QED component) and optimized orbital bases up to the cardinal number X = 7 for larger R. Near-exact asymptotic constants were used to describe the large-R behavior of all components. The fitted potential, exhibiting the minimum of -10.996 ± 0.004 K at R = 5.608 0 ± 0.000 1 bohr, was used to determine properties of the very weakly bound (4)He(2) dimer and thermophysical properties of gaseous helium. It is shown that the Casimir-Polder retardation effect, increasing the dimer size by about 2 Å relative to the nonrelativistic BO value, is almost completely accounted for by the inclusion of the Breit-interaction and the Araki-Sucher contributions to the potential, of the order α(2) and α(3), respectively. The remaining retardation effect, of the order of α(4) and higher, is practically negligible for the bound
Basis for a neuronal version of Grover's quantum algorithm.
Clark, Kevin B
2014-01-01
Grover's quantum (search) algorithm exploits principles of quantum information theory and computation to surpass the strong Church-Turing limit governing classical computers. The algorithm initializes a search field into superposed N (eigen)states to later execute nonclassical "subroutines" involving unitary phase shifts of measured states and to produce root-rate or quadratic gain in the algorithmic time (O(N (1/2))) needed to find some "target" solution m. Akin to this fast technological search algorithm, single eukaryotic cells, such as differentiated neurons, perform natural quadratic speed-up in the search for appropriate store-operated Ca(2+) response regulation of, among other processes, protein and lipid biosynthesis, cell energetics, stress responses, cell fate and death, synaptic plasticity, and immunoprotection. Such speed-up in cellular decision making results from spatiotemporal dynamics of networked intracellular Ca(2+)-induced Ca(2+) release and the search (or signaling) velocity of Ca(2+) wave propagation. As chemical processes, such as the duration of Ca(2+) mobilization, become rate-limiting over interstore distances, Ca(2+) waves quadratically decrease interstore-travel time from slow saltatory to fast continuous gradients proportional to the square-root of the classical Ca(2+) diffusion coefficient, D (1/2), matching the computing efficiency of Grover's quantum algorithm. In this Hypothesis and Theory article, I elaborate on these traits using a fire-diffuse-fire model of store-operated cytosolic Ca(2+) signaling valid for glutamatergic neurons. Salient model features corresponding to Grover's quantum algorithm are parameterized to meet requirements for the Oracle Hadamard transform and Grover's iteration. A neuronal version of Grover's quantum algorithm figures to benefit signal coincidence detection and integration, bidirectional synaptic plasticity, and other vital cell functions by rapidly selecting, ordering, and/or counting optional
Orbital excitation blockade and algorithmic cooling in quantum gases.
Bakr, Waseem S; Preiss, Philipp M; Tai, M Eric; Ma, Ruichao; Simon, Jonathan; Greiner, Markus
2011-12-21
Interaction blockade occurs when strong interactions in a confined, few-body system prevent a particle from occupying an otherwise accessible quantum state. Blockade phenomena reveal the underlying granular nature of quantum systems and allow for the detection and manipulation of the constituent particles, be they electrons, spins, atoms or photons. Applications include single-electron transistors based on electronic Coulomb blockade and quantum logic gates in Rydberg atoms. Here we report a form of interaction blockade that occurs when transferring ultracold atoms between orbitals in an optical lattice. We call this orbital excitation blockade (OEB). In this system, atoms at the same lattice site undergo coherent collisions described by a contact interaction whose strength depends strongly on the orbital wavefunctions of the atoms. We induce coherent orbital excitations by modulating the lattice depth, and observe staircase-like excitation behaviour as we cross the interaction-split resonances by tuning the modulation frequency. As an application of OEB, we demonstrate algorithmic cooling of quantum gases: a sequence of reversible OEB-based quantum operations isolates the entropy in one part of the system and then an irreversible step removes the entropy from the gas. This technique may make it possible to cool quantum gases to have the ultralow entropies required for quantum simulation of strongly correlated electron systems. In addition, the close analogy between OEB and dipole blockade in Rydberg atoms provides a plan for the implementation of two-quantum-bit gates in a quantum computing architecture with natural scalability.
A Fast Measurement based fixed-point Quantum Search Algorithm
Mani, Ashish
2011-01-01
Generic quantum search algorithm searches for target entity in an unsorted database by repeatedly applying canonical Grover's quantum rotation transform to reach near the vicinity of the target entity represented by a basis state in the Hilbert space associated with the qubits. Thus, when qubits are measured, there is a high probability of finding the target entity. However, the number of times quantum rotation transform is to be applied for reaching near the vicinity of the target is a function of the number of target entities present in the unsorted database, which is generally unknown. A wrong estimate of the number of target entities can lead to overshooting or undershooting the targets, thus reducing the success probability. Some proposals have been made to overcome this limitation. These proposals either employ quantum counting to estimate the number of solutions or fixed point schemes. This paper proposes a new scheme for stopping the application of quantum rotation transformation on reaching near the ...
High-Fidelity Entangled Bell States via Shortcuts to Adiabaticity
Paul, Koushik
2016-01-01
We present a couple of protocols based on shortcut to adiabaticity techniques for rapid generation of robust entangled Bell states in a system of two two-state systems. Our protocols rely on the so-called transitionless quantum driving (TQD) algorithm and Lewis-Riesenfeld invariant (LRI) method. Both TQD and LRI methods result in high fidelity in population transfer.Our study shows that it is possible to prepare an entangled state in infinitely short time without losing robustness and efficiency.
Research on Quantum Searching Algorithms Based on Phase Shifts
ZHONG Pu-Cha; BAO Wan-Su
2008-01-01
@@ One iterative in Grover's original quantum search algorithm consists of two Hadamard-Walsh transformations, a selective amplitude inversion and a diffusion amplitude inversion. We concentrate on the relation among the probability of success of the algorithm, the phase shifts, the number of target items and the number of iterations via replacing the two amplitude inversions by phase shifts of an arbitrary φ = ψ(0 ≤φ, ψ≤ 2π). Then, according to the relation we find out the optimal phase shifts when the number of iterations is given. We present a new quantum search algorithm based on the optimal phase shifts of 1.018 after 0.5π /√M/N iterations. The new algorithm can obtain either a single target item or multiple target items in the search space with the probability of success at least 93.43%.
Scale invariance of entanglement dynamics in Grover's quantum search algorithm
Rossi, M; Macchiavello, C
2012-01-01
We calculate the amount of entanglement of the multiqubit quantum states employed in the Grover algorithm, by following its dynamics at each step of the computation. We show that genuine multipartite entanglement is always present. Remarkably, the dynamics of any type of entanglement as well as of genuine multipartite entanglement is independent of the number $n$ of qubits for large $n$, thus exhibiting a scale invariance property. We also investigate criteria for efficient simulatability in the context of Grover's algorithm.
The variational-relaxation algorithm for finding quantum bound states
Schroeder, Daniel V.
2017-09-01
I describe a simple algorithm for numerically finding the ground state and low-lying excited states of a quantum system. The algorithm is an adaptation of the relaxation method for solving Poisson's equation, and is fundamentally based on the variational principle. It is especially useful for two-dimensional systems with nonseparable potentials, for which simpler techniques are inapplicable yet the computation time is minimal.
Adiabatic superconducting cells for ultra-low-power artificial neural networks.
Schegolev, Andrey E; Klenov, Nikolay V; Soloviev, Igor I; Tereshonok, Maxim V
2016-01-01
We propose the concept of using superconducting quantum interferometers for the implementation of neural network algorithms with extremely low power dissipation. These adiabatic elements are Josephson cells with sigmoid- and Gaussian-like activation functions. We optimize their parameters for application in three-layer perceptron and radial basis function networks.
Adiabatic superconducting cells for ultra-low-power artificial neural networks
Andrey E. Schegolev
2016-10-01
Full Text Available We propose the concept of using superconducting quantum interferometers for the implementation of neural network algorithms with extremely low power dissipation. These adiabatic elements are Josephson cells with sigmoid- and Gaussian-like activation functions. We optimize their parameters for application in three-layer perceptron and radial basis function networks.
Quantum algorithms for virtual Jones polynomials via Thistlethwaite theorems
Vélez, Mario; Ospina, Juan
2010-04-01
Recently a quantum algorithm for the Jones polynomial of virtual links was proposed by Kauffman and Dye via the implementation of the virtual braid group in anyonic topological quantum computation when the virtual crossings are considered as generalized swap gates. Also recently, a mathematical method for the computation of the Jones polynomial of a given virtual link in terms of the relative Tuttle polynomial of its face (Tait) graph with some suitable variable substitutions was proposed by Diao and Hetyei. The method of Diao and Hetyei is offered as an alternative to the ribbon graph approach according to which the Tutte polynomial of a given virtual link is computed in terms of the Bollobás- Riordan polynomial of the corresponding ribbon graph. The method of Diao and Hetyei can be considered as an extension of the celebrated Thistlethwaite theorem according to which invariant polynomials for knots and links are derived from invariant polynomials for graphs. Starting from these ideas we propose a quantum algorithm for the Jones polynomial of a given virtual link in terms of the generalized Tutte polynomials by exploiting the Thistlethwaite theorem and the Kauffman algorithm . Our method is claimed as the quantum version of the Diao-Hetyei method. Possible supersymmetric implementations of our algortihm are discussed jointly with its formulations using topological quantum lambda calculus.
Preparation of GHZ States via Grover's Quantum Searching Algorithm
ZENG Hao-Sheng; KUANG Le-Man
2000-01-01
We propose an approach to prepare GHZ(Greenberger, Horne, Zeilinger) states of an arbitrary multi-particle system in terms of Grover's fast quantum searching algorithm. The approach can be used to produce other entangled states with variou degrees of entanglement.
Fast Quantum Algorithms for Numerical Integrals and Stochastic Processes
Abrams, D.; Williams, C.
1999-01-01
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known classical deterministic algotithms and a quadratic speed increase incomparison to classical Monte Carlo methods.
A quantum algorithm for Viterbi decoding of classical convolutional codes
Grice, Jon R.; Meyer, David A.
2015-07-01
We present a quantum Viterbi algorithm (QVA) with better than classical performance under certain conditions. In this paper, the proposed algorithm is applied to decoding classical convolutional codes, for instance, large constraint length and short decode frames . Other applications of the classical Viterbi algorithm where is large (e.g., speech processing) could experience significant speedup with the QVA. The QVA exploits the fact that the decoding trellis is similar to the butterfly diagram of the fast Fourier transform, with its corresponding fast quantum algorithm. The tensor-product structure of the butterfly diagram corresponds to a quantum superposition that we show can be efficiently prepared. The quantum speedup is possible because the performance of the QVA depends on the fanout (number of possible transitions from any given state in the hidden Markov model) which is in general much less than . The QVA constructs a superposition of states which correspond to all legal paths through the decoding lattice, with phase as a function of the probability of the path being taken given received data. A specialized amplitude amplification procedure is applied one or more times to recover a superposition where the most probable path has a high probability of being measured.
Blockspin Scheme and Cluster Algorithm for Quantum Spin Systems
Ying, H P; Ying, He-Ping; Wiese, Uwe-Jens
1992-01-01
We present a numerical study using a cluster algorithm for the 1-d $S=1/2$ quantum Heisenberg models. The dynamical critical exponent for anti-ferromagnetic chains is $z=0.0(1)$ such that critical slowing down is eliminated.
Quantum algorithms for topological and geometric analysis of data.
Lloyd, Seth; Garnerone, Silvano; Zanardi, Paolo
2016-01-25
Extracting useful information from large data sets can be a daunting task. Topological methods for analysing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying topological features and for determining how such features persist as the data is viewed at different scales. Here we present quantum machine learning algorithms for calculating Betti numbers--the numbers of connected components, holes and voids--in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian. The algorithms provide an exponential speed-up over the best currently known classical algorithms for topological data analysis.
Numerical Simulations of a Possible Hypercomputational Quantum Algorithm
Sicard, A; Vélez, M; Sicard, Andr\\'es; Ospina, Juan; V\\'elez, Mario
2005-01-01
The hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. Several numerical simulations of a possible hypercomputational algorithm based on quantum computations previously constructed by the authors are presented. The hypercomputability of our algorithm is based on the fact that this algorithm could solve a classically non-computable decision problem, Hilbert's tenth problem. The numerical simulations were realized for three types of Diophantine equations: with and without solutions in non-negative integers, and without solutions by way of various traditional mathematical packages.
Quantum algorithms for topological and geometric analysis of data
Lloyd, Seth; Garnerone, Silvano; Zanardi, Paolo
2016-01-01
Extracting useful information from large data sets can be a daunting task. Topological methods for analysing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying topological features and for determining how such features persist as the data is viewed at different scales. Here we present quantum machine learning algorithms for calculating Betti numbers—the numbers of connected components, holes and voids—in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian. The algorithms provide an exponential speed-up over the best currently known classical algorithms for topological data analysis. PMID:26806491
Quantum Cryptography Based on the Deutsch-Jozsa Algorithm
Nagata, Koji; Nakamura, Tadao; Farouk, Ahmed
2017-09-01
Recently, secure quantum key distribution based on Deutsch's algorithm using the Bell state is reported (Nagata and Nakamura, Int. J. Theor. Phys. doi: 10.1007/s10773-017-3352-4, 2017). Our aim is of extending the result to a multipartite system. In this paper, we propose a highly speedy key distribution protocol. We present sequre quantum key distribution based on a special Deutsch-Jozsa algorithm using Greenberger-Horne-Zeilinger states. Bob has promised to use a function f which is of one of two kinds; either the value of f( x) is constant for all values of x, or else the value of f( x) is balanced, that is, equal to 1 for exactly half of the possible x, and 0 for the other half. Here, we introduce an additional condition to the function when it is balanced. Our quantum key distribution overcomes a classical counterpart by a factor O(2 N ).
Li, Dafa
2016-05-01
The adiabatic theorem was proposed about 90 years ago and has played an important role in quantum physics. The quantitative adiabatic condition constructed from eigenstates and eigenvalues of a Hamiltonian is a traditional tool to estimate adiabaticity and has proven to be the necessary and sufficient condition for adiabaticity. However, recently the condition has become a controversial subject. In this paper, we list some expressions to estimate the validity of the adiabatic approximation. We show that the quantitative adiabatic condition is invalid for the adiabatic approximation via the Euclidean distance between the adiabatic state and the evolution state. Furthermore, we deduce general necessary and sufficient conditions for the validity of the adiabatic approximation by different definitions.
Quantum-based algorithm for optimizing artificial neural networks.
Tzyy-Chyang Lu; Gwo-Ruey Yu; Jyh-Ching Juang
2013-08-01
This paper presents a quantum-based algorithm for evolving artificial neural networks (ANNs). The aim is to design an ANN with few connections and high classification performance by simultaneously optimizing the network structure and the connection weights. Unlike most previous studies, the proposed algorithm uses quantum bit representation to codify the network. As a result, the connectivity bits do not indicate the actual links but the probability of the existence of the connections, thus alleviating mapping problems and reducing the risk of throwing away a potential candidate. In addition, in the proposed model, each weight space is decomposed into subspaces in terms of quantum bits. Thus, the algorithm performs a region by region exploration, and evolves gradually to find promising subspaces for further exploitation. This is helpful to provide a set of appropriate weights when evolving the network structure and to alleviate the noisy fitness evaluation problem. The proposed model is tested on four benchmark problems, namely breast cancer and iris, heart, and diabetes problems. The experimental results show that the proposed algorithm can produce compact ANN structures with good generalization ability compared to other algorithms.
A search algorithm for quantum state engineering and metrology
Knott, P. A.
2016-07-01
In this paper we present a search algorithm that finds useful optical quantum states which can be created with current technology. We apply the algorithm to the field of quantum metrology with the goal of finding states that can measure a phase shift to a high precision. Our algorithm efficiently produces a number of novel solutions: we find experimentally ready schemes to produce states that show significant improvements over the state-of-the-art, and can measure with a precision that beats the shot noise limit by over a factor of 4. Furthermore, these states demonstrate a robustness to moderate/high photon losses, and we present a conceptually simple measurement scheme that saturates the Cramér-Rao bound.
Effect of qubit losses on Grover's quantum search algorithm
Dasari, Durga; Mølmer, Klaus
2012-01-01
We investigate the performance of Grover's quantum search algorithm on a register that is subject to a loss of particles that carry qubit information. Under the assumption that the basic steps of the algorithm are applied correctly on the correspondingly shrinking register, we show...... that the algorithm converges to mixed states with 50% overlap with the target state in the bit positions still present. As an alternative to error correction, we present a procedure that combines the outcome of different trials of the algorithm to determine the solution to the full search problem. The procedure may...... be relevant for experiments where the algorithm is adapted as the loss of particles is registered and for experiments with Rydberg blockade interactions among neutral atoms, where monitoring of atom losses is not even necessary....
A fast quantum algorithm for the affine Boolean function identification
Younes, Ahmed
2015-02-01
Bernstein-Vazirani algorithm (the one-query algorithm) can identify a completely specified linear Boolean function using a single query to the oracle with certainty. The first aim of the paper is to show that if the provided Boolean function is affine, then one more query to the oracle (the two-query algorithm) is required to identify the affinity of the function with certainty. The second aim of the paper is to show that if the provided Boolean function is incompletely defined, then the one-query and the two-query algorithms can be used as bounded-error quantum polynomial algorithms to identify certain classes of incompletely defined linear and affine Boolean functions respectively with probability of success at least 2/3.
A subexponential-time algorithm for the quantum separability problem
Brandao, Fernando G S L; Yard, Jon
2010-01-01
We present a subexponential-time algorithm solving the weak membership problem for the convex set of separable, i.e. non-entangled, bipartite density matrices. The algorithm decides whether a density matrix is separable or eps-away from the set of the separable states in time exp(O(eps^(-2) log|A| log|B|)), where |A| and |B| are the local dimensions, and the distance is measured with either the Euclidean norm, or with the so-called LOCC norm. The latter is an operationally motivated norm giving the optimal probability of distinguishing two bipartite quantum states, each shared by two parties, using any protocol formed by quantum local operations and classical communication (LOCC) between the parties. We also obtain improved algorithms for optimizing over the set of separable states, for estimating the minimal output entropy of quantum channels and for computing the ground-state energy of mean-field Hamiltonians. The techniques we develop are also applied to quantum Merlin-Arthur games, where we show that mult...
Center for Quantum Algorithms and Complexity
2014-05-12
2014 Received Paper 1.00 3.00 2.00 7.00 5.00 Dorit Aharonov, Itai Arad, Sandy Irani. Efficient algorithm for approximating one-dimensional ground states...Property testing of unitary operators, Physical Review A, (11 2011): 0. doi: 10.1103/PhysRevA.84.052328 Dorit Aharonov, Itai Arad, Umesh Vazirani...1367-2630/13/11/113043 Itai Arad, Zeph Landau, Umesh Vazirani. Improved one-dimensional area law for frustration-free systems, Physical Review B
Unitary Quantum Lattice Algorithms for Turbulence
2016-05-23
collision operator, based on the 3D relativistic Dirac particle dynamics theory of Yepez, ĈD = cosθ x( ) −i sinθ x( ) −i sinθ x( ) cosθ x... based algorithm it will result in a finite difference representation of the GP Eq. (24) provided the parameters are so chosen to yield diffusion-like...Fluid Dynamics, ed. H. W. Oh, ( InTech Publishers, Croatia, 2012) [20] “Unitary qubit lattice simulations of complex vortex structures
Real-Coded Quantum-Inspired Genetic Algorithm-Based BP Neural Network Algorithm
Jianyong Liu
2015-01-01
Full Text Available The method that the real-coded quantum-inspired genetic algorithm (RQGA used to optimize the weights and threshold of BP neural network is proposed to overcome the defect that the gradient descent method makes the algorithm easily fall into local optimal value in the learning process. Quantum genetic algorithm (QGA is with good directional global optimization ability, but the conventional QGA is based on binary coding; the speed of calculation is reduced by the coding and decoding processes. So, RQGA is introduced to explore the search space, and the improved varied learning rate is adopted to train the BP neural network. Simulation test shows that the proposed algorithm is effective to rapidly converge to the solution conformed to constraint conditions.
Hypercomputation based on quantum computing
Sicard, A; Ospina, J; Sicard, Andr\\'es; V\\'elez, Mario; Ospina, Juan
2004-01-01
We present a quantum algorithm for a (classically) incomputable decision problem: the Hilbert's tenth problem; namely, we present a hypercomputation model based on quantum computation. The model is inspired by the one proposed by Tien D. Kieu. Our model exploits the quantum adiabatic process and the characteristics of the representation of the dynamical algebra su(1,1) associated to the infinite square well. Furthermore, it is demonstrated that the model proposed is a universal quantum computation model.
Data detection algorithms for multiplexed quantum dot encoding.
Goss, Kelly C; Messier, Geoff G; Potter, Mike E
2012-02-27
A group of quantum dots can be designed to have a unique spectral emission by varying the size of the quantum dots (wavelength) and number of quantum dots (intensity). This technique has been previously proposed for biological tags and object identification. The potential of this system lies in the ability to have a large number of distinguishable wavelengths and intensity levels. This paper presents a communications system model for MxQDs including the interference between neighbouring QD colours and detector noise. An analytical model of the signal-to-noise ratio of a Charge-Coupled Device (CCD) spectrometer is presented and confirmed with experimental results. We then apply a communications system perspective and propose data detection algorithms that increase the readability of the quantum dots tags. It is demonstrated that multiplexed quantum dot barcodes can be read with 99.7% accuracy using the proposed data detection algorithms in a system with 6 colours and 6 intensity values resulting in 46,655 unique spectral codes.
Quantum-statistical equation-of-state models of dense plasmas: high-pressure Hugoniot shock adiabats
Pain, Jean-Christophe
2007-01-01
We present a detailed comparison of two self-consistent equation-of-state models which differ from their electronic contribution: the atom in a spherical cell and the atom in a jellium of charges. It is shown that both models are well suited for the calculation of Hugoniot shock adiabats in the high pressure range (1 Mbar-10 Gbar), and that the atom-in-a-jellium model provides a better treatment of pressure ionization. Comparisons with experimental data are also presented. Shell effects on shock adiabats are reviewed in the light of these models. They lead to additional features not only in the variations of pressure versus density, but also in the variations of shock velocity versus particle velocity. Moreover, such effects are found to be responsible for enhancement of the electronic specific heat.
Tan, Ru-Chao; Lei, Tong; Zhao, Qing-Min; Gong, Li-Hua; Zhou, Zhi-Hong
2016-12-01
To improve the slow processing speed of the classical image encryption algorithms and enhance the security of the private color images, a new quantum color image encryption algorithm based on a hyper-chaotic system is proposed, in which the sequences generated by the Chen's hyper-chaotic system are scrambled and diffused with three components of the original color image. Sequentially, the quantum Fourier transform is exploited to fulfill the encryption. Numerical simulations show that the presented quantum color image encryption algorithm possesses large key space to resist illegal attacks, sensitive dependence on initial keys, uniform distribution of gray values for the encrypted image and weak correlation between two adjacent pixels in the cipher-image.
Suppressing decoherence of quantum algorithms by jump codes
Kern, O; Kern, Oliver; Alber, Gernot
2005-01-01
The stabilizing properties of one-error correcting jump codes are explored under realistic non-ideal conditions. For this purpose the quantum algorithm of the tent-map is decomposed into a universal set of Hamiltonian quantum gates which ensure perfect correction of spontaneous decay processes under ideal circumstances even if they occur during a gate operation. An entanglement gate is presented which is capable of entangling any two logical qubits of different one-error correcting code spaces. With the help of this gate simultaneous spontaneous decay processes affecting physical qubits of different code spaces can be corrected and decoherence can be suppressed significantly.
Efficient quantum algorithm for computing n-time correlation functions.
Pedernales, J S; Di Candia, R; Egusquiza, I L; Casanova, J; Solano, E
2014-07-11
We propose a method for computing n-time correlation functions of arbitrary spinorial, fermionic, and bosonic operators, consisting of an efficient quantum algorithm that encodes these correlations in an initially added ancillary qubit for probe and control tasks. For spinorial and fermionic systems, the reconstruction of arbitrary n-time correlation functions requires the measurement of two ancilla observables, while for bosonic variables time derivatives of the same observables are needed. Finally, we provide examples applicable to different quantum platforms in the frame of the linear response theory.
Implementing a Quantum Algorithm with Exchange-Coupled Quantum Dots: a Feasibility study
Myrgren, E S
2003-01-01
We present Monte Carlo wavefunction simulations for quantum computations employing an exchange-coupled array of quantum dots. Employing a combination of experimentally and theoretically available parameters, we find that gate fidelities greater than 98 % may be obtained with current experimental and technological capabilities. Application to an encoded 3 qubit (nine physical qubits) Deutsch-Josza computation indicates that the algorithmic fidelity is more a question of the total time to implement the gates than of the physical complexity of those gates.
Learning algorithm and application of quantum BP neural networks based on universal quantum gates
无
2008-01-01
A quantum BP neural networks model with learning algorithm is proposed.First,based on the universality of single qubit rotation gate and two-qubit controlled-NOT gate,a quantum neuron model is constructed,which is composed of input,phase rotation,aggregation,reversal rotation and output.In this model,the input is described by qubits,and the output is given by the probability of the state in which |1＞ is observed.The phase rotation and the reversal rotation are performed by the universal quantum gates.Secondly,the quantum BP neural networks model is constructed,in which the output layer and the hide layer are quantum neurons.With the application of the gradient descent algorithm,a learning algorithm of the model is proposed,and the continuity of the model is proved.It is shown that this model and algorithm are superior to the conventional BP networks in three aspects: convergence speed,convergence rate and robustness,by two application examples of pattern recognition and function approximation.
Scheme for Implementing Quantum Search Algorithm in a Cluster State Quantum Computer
ZHANG Da-Li; WANG Yan-Hui; ZHANG Yong
2008-01-01
Using cluster state and single qubit measurement one can perform the one-way quantum computation. Here we give a detailed scheme for realizing a modified Grover search algorithm using measurements on cluster state. We give the measurement pattern for the duster-state realization of the algorithm and estimated the number of measurement needed for its implementation. It is found that O(23n/2n2) number of single qubit measurements is required for its realization in a cluster-state quantum computer.
An improved robust ADMM algorithm for quantum state tomography
Li, Kezhi; Zhang, Hui; Kuang, Sen; Meng, Fangfang; Cong, Shuang
2016-06-01
In this paper, an improved adaptive weights alternating direction method of multipliers algorithm is developed to implement the optimization scheme for recovering the quantum state in nearly pure states. The proposed approach is superior to many existing methods because it exploits the low-rank property of density matrices, and it can deal with unexpected sparse outliers as well. The numerical experiments are provided to verify our statements by comparing the results to three different optimization algorithms, using both adaptive and fixed weights in the algorithm, in the cases of with and without external noise, respectively. The results indicate that the improved algorithm has better performances in both estimation accuracy and robustness to external noise. The further simulation results show that the successful recovery rate increases when more qubits are estimated, which in fact satisfies the compressive sensing theory and makes the proposed approach more promising.
Quantum Algorithm for Computing the Period Lattice of an Infrastructure
Fontein, Felix
2011-01-01
We present a quantum algorithm for computing the period lattice of infrastructures of fixed dimension. The algorithm applies to infrastructures that satisfy certain conditions. The latter are always fulfilled for infrastructures obtained from global fields, i.e., algebraic number fields and function fields with finite constant fields, as described in [Fon11]. The first of our main contributions is a rigorous and complete proof that the running time of the algorithm is polynomial in the logarithm of the determinant of the period lattice and exponential in the dimension n. The second main contribution is the determination of an explicit lower bound on the success probability of our algorithm which improves on the bounds given in the works of Hallgren and Schmidt and Vollmer. The exponential scaling seems inevitable because the best currently known methods for carrying out fundamental arithmetic operations in infrastructures obtained from algebraic number fields take exponential time. In contrast, the problem of...
Semiconductor adiabatic qubits
Carroll, Malcolm S.; Witzel, Wayne; Jacobson, Noah Tobias; Ganti, Anand; Landahl, Andrew J.; Lilly, Michael; Nguyen, Khoi Thi; Bishop, Nathaniel; Carr, Stephen M.; Bussmann, Ezra; Nielsen, Erik; Levy, James Ewers; Blume-Kohout, Robin J.; Rahman, Rajib
2016-12-27
A quantum computing device that includes a plurality of semiconductor adiabatic qubits is described herein. The qubits are programmed with local biases and coupling terms between qubits that represent a problem of interest. The qubits are initialized by way of a tuneable parameter, a local tunnel coupling within each qubit, such that the qubits remain in a ground energy state, and that initial state is represented by the qubits being in a superposition of |0> and |1> states. The parameter is altered over time adiabatically or such that relaxation mechanisms maintain a large fraction of ground state occupation through decreasing the tunnel coupling barrier within each qubit with the appropriate schedule. The final state when tunnel coupling is effectively zero represents the solution state to the problem represented in the |0> and |1> basis, which can be accurately read at each qubit location.
Quantum Google Algorithm: Construction and Application to Complex Networks
Paparo, G D; Comellas, F; Martin-Delgado, M A
2014-01-01
We review the main findings on the ranking capabilities of the recently proposed Quantum PageRank algorithm (G.D. Paparo et al., Sci. Rep. 2, 444 (2012) and G.D. Paparo et al., Sci. Rep. 3, 2773 (2013)) applied to large complex networks. The algorithm has been shown to identify unambiguously the underlying topology of the network and to be capable of clearly highlighting the structure of secondary hubs of networks. Furthermore, it can resolve the degeneracy in importance of the low-lying part of the list of rankings. Examples of applications include real-world instances from the WWW, which typically display a scale-free network structure and models of hierarchical networks. The quantum algorithm has been shown to display an increased stability with respect to a variation of the damping parameter, present in the Google algorithm, and a more clearly pronounced power-law behaviour in the distribution of importance among the nodes, as compared to the classical algorithm.
Acceleration of quantum optimal control theory algorithms with mixing strategies.
Castro, Alberto; Gross, E K U
2009-05-01
We propose the use of mixing strategies to accelerate the convergence of the common iterative algorithms utilized in quantum optimal control theory (QOCT). We show how the nonlinear equations of QOCT can be viewed as a "fixed-point" nonlinear problem. The iterative algorithms for this class of problems may benefit from mixing strategies, as it happens, e.g., in the quest for the ground-state density in Kohn-Sham density-functional theory. We demonstrate, with some numerical examples, how the same mixing schemes utilized in this latter nonlinear problem may significantly accelerate the QOCT iterative procedures.
Quantum Multiplexer Designing and Optimization applying Genetic Algorithm
Debarka Mukhopadhyay
2010-09-01
Full Text Available This paper shows how to design efficient quantum multiplexer circuit borrowed from classical computer design. The design will show that it is composed of some Toffole gates or C2NOT gate and some two input CNOT gates. Every C2NOT gate is synthesized and optimized by applying the genetic algorithm to get the best possible combination for the design of these gate circuits.
Quantum algorithms for topological and geometric analysis of data
2014-01-01
Extracting useful information from large data sets can be a daunting task. Topological methods for analysing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying topological features and for determining how such features persist as the data is viewed at different scales. Here we present quantum machine learning algorithms for calculating Betti numbers—the numbers of connected components, holes and voids—in persiste...
Quantum Algorithmic Integrability The Metaphor of Polygonal Billiards
Mantica, G
1999-01-01
An elementary application of Algorithmic Complexity Theory to the polygonal approximations of curved billiards-integrable and chaotic-unveils the equivalence of this problem to the procedure of quantization of classical systems: the scaling relations for the average complexity of symbolic trajectories are formally the same as those governing the semi-classical limit of quantum systems. Two cases-the circle, and the stadium-are examined in detail, and are presented as paradigms.
Coherence depletion in the Grover quantum search algorithm
Shi, Hai-Long; Liu, Si-Yuan; Wang, Xiao-Hui; Yang, Wen-Li; Yang, Zhan-Ying; Fan, Heng
2017-03-01
We investigate the role of quantum coherence depletion (QCD) in the Grover search algorithm (GA) by using several typical measures of quantum coherence and quantum correlations. By using the relative entropy of coherence measure (Cr), we show that the success probability depends on the QCD. The same phenomenon is also found by using the l1 norm of coherence measure (Cl1).In the limit case, the cost performance is defined to characterize the behavior about QCD in enhancing the success probability of GA, which is only related to the number of searcher items and the scale of the database, regardless of using Cr or Cl 1. In the generalized Grover search algorithm (GGA), the QCD for a class of states increases with the required optimal measurement time. In comparison, the quantification of other quantum correlations in GA, such as pairwise entanglement, multipartite entanglement, pairwise discord, and genuine multipartite discord, cannot be directly related to the success probability or the optimal measurement time. Additionally, we do not detect pairwise nonlocality or genuine tripartite nonlocality in GA since Clauser-Horne-Shimony-Holt inequality and Svetlichny's inequality are not violated.
Measuring peptide mass spectrum correlation using the quantum Grover algorithm.
Choo, Keng Wah
2007-03-01
We investigated the use of the quantum Grover algorithm in the mass-spectrometry-based protein identification process. The approach coded the mass spectra on a quantum register and uses the Grover search algorithm for searching multiple solutions to find matches from a database. Measurement of the fidelity between the input and final states was used to quantify the similarity between the experimental and theoretical spectra. The optimal number of iteration is proven to be pi/4sqrt[N/k] , where k refers to the number of marked states. We found that one iteration is sufficient for the search if we let more that 62% of the N states be marked states. By measuring the fidelity after only one iteration of Grover search, we discovered that it resembles that of the correlation-based measurement used in the existing protein identification software. We concluded that the quantum Grover algorithm can be adapted for a correlation-based mass spectra database search, provided that decoherence can be kept to a minimum.
An Efficient Exact Quantum Algorithm for the Integer Square-free Decomposition Problem
Jun Li; Xinhua Peng; Jiangfeng Du; Dieter Suter
2012-01-01
Quantum computers are known to be qualitatively more powerful than classical computers, but so far only a small number of different algorithms have been discovered that actually use this potential. It would therefore be highly desirable to develop other types of quantum algorithms that widen the range of possible applications. Here we propose an efficient and exact quantum algorithm for finding the square-free part of a large integer - a problem for which no efficient classical algorithm exis...
Experimental implementation of Hogg's algorithm on a three-quantum-bit NMR quantum computer
Peng, Xinhua; Zhu, Xiwen; Fang, Ximing; Feng, Mang; Liu, Maili; Gao, Kelin
2002-04-01
Using nuclear magnetic resonance (NMR) techniques with a three-qubit sample, we have experimentally implemented the highly structured algorithm for the satisfiability problem with one variable in each clause proposed by Hogg. A simplified temporal averaging procedure was employed to prepare the three-qubit pseudopure state. The algorithm was completed with only a single evaluation of the structure of the problem and the solutions were found theoretically with probability 100%, results that outperform both unstructured quantum and the best classical search algorithms. However, about 90% of the corresponding experimental fidelities can be attributed to the imperfections of manipulations.
Bhole, Gaurav; Anjusha, V. S.; Mahesh, T. S.
2016-04-01
A robust control over quantum dynamics is of paramount importance for quantum technologies. Many of the existing control techniques are based on smooth Hamiltonian modulations involving repeated calculations of basic unitaries resulting in time complexities scaling rapidly with the length of the control sequence. Here we show that bang-bang controls need one-time calculation of basic unitaries and hence scale much more efficiently. By employing a global optimization routine such as the genetic algorithm, it is possible to synthesize not only highly intricate unitaries, but also certain nonunitary operations. We demonstrate the unitary control through the implementation of the optimal fixed-point quantum search algorithm in a three-qubit nuclear magnetic resonance (NMR) system. Moreover, by combining the bang-bang pulses with the crusher gradients, we also demonstrate nonunitary transformations of thermal equilibrium states into effective pure states in three- as well as five-qubit NMR systems.
A pure-sampling quantum Monte Carlo algorithm.
Ospadov, Egor; Rothstein, Stuart M
2015-01-14
The objective of pure-sampling quantum Monte Carlo is to calculate physical properties that are independent of the importance sampling function being employed in the calculation, save for the mismatch of its nodal hypersurface with that of the exact wave function. To achieve this objective, we report a pure-sampling algorithm that combines features of forward walking methods of pure-sampling and reptation quantum Monte Carlo (RQMC). The new algorithm accurately samples properties from the mixed and pure distributions simultaneously in runs performed at a single set of time-steps, over which extrapolation to zero time-step is performed. In a detailed comparison, we found RQMC to be less efficient. It requires different sets of time-steps to accurately determine the energy and other properties, such as the dipole moment. We implement our algorithm by systematically increasing an algorithmic parameter until the properties converge to statistically equivalent values. As a proof in principle, we calculated the fixed-node energy, static α polarizability, and other one-electron expectation values for the ground-states of LiH and water molecules. These quantities are free from importance sampling bias, population control bias, time-step bias, extrapolation-model bias, and the finite-field approximation. We found excellent agreement with the accepted values for the energy and a variety of other properties for those systems.
Concise quantum associative memories with nonlinear search algorithm
Tchapet Njafa, J.P.; Nana Engo, S.G. [Laboratory of Photonics, Department of Physics, University of Ngaoundere (Cameroon)
2016-02-15
The model of Quantum Associative Memories (QAM) we propose here consists in simplifying and generalizing that of Rigui Zhou et al. [1] which uses the quantum matrix with the binary decision diagram put forth by David Rosenbaum [2] and the Abrams and Lloyd's nonlinear search algorithm [3]. Our model gives the possibility to retrieve one of the sought states in multi-values retrieving scheme when a measurement is done on the first register in O(c-r) time complexity. It is better than Grover's algorithm and its modified form which need O(√((2{sup n})/(m))) steps when they are used as the retrieval algorithm. n is the number of qubits of the first register and m the number of x values for which f(x) = 1. As the nonlinearity makes the system highly susceptible to the noise, an analysis of the influence of the single qubit noise channels on the Nonlinear Search Algorithm of our model of QAM shows a fidelity of about 0.7 whatever the number of qubits existing in the first register, thus demonstrating the robustness of our model. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Implementation of Period-Finding Algorithm by Means of Simulating Quantum Fourier Transform
Zohreh Moghareh Abed
2010-01-01
Full Text Available In this paper, we introduce quantum fourier transform as a key ingredient for many useful algorithms. These algorithms make a solution for problems which is considered to be intractable problems on a classical computer. Quantum Fourier transform is propounded as a key for quantum phase estimation algorithm. In this paper our aim is the implementation of period-finding algorithm.Quantum computer solves this problem, exponentially faster than classical one. Quantum phase estimation algorithm is the key for the period-finding problem .Therefore, by means of simulating quantum Fourier transform, we are able to implement the period-finding algorithm. In this paper, the simulation of quantum Fourier transform is carried out by Matlab software.
The Improvement of Quantum Genetic Algorithm and Its Application on Function Optimization
Huaixiao Wang
2013-01-01
Full Text Available To accelerate the evolutionary process and increase the probability to find the optimal solution, the following methods are proposed to improve the conventional quantum genetic algorithm: an improved method to determine the rotating angle, the self-adaptive rotating angle strategy, adding the quantum mutation operation and quantum disaster operation. The efficiency and accuracy to search the optimal solution of the algorithm are greatly improved. Simulation test shows that the improved quantum genetic algorithm is more effective than the conventional quantum genetic algorithm to solve some optimization problems.
Application of quantum algorithms to direct measurement of concurrence of a two-qubit pure state
Wang Hong-Fu; Zhang Shou
2009-01-01
This paper proposes a method to measure directly the concurrence of an arbitrary two-qubit pure state based on a generalized Grover quantum iteration algorithm and a phase estimation algorithm. The concurrence can be calculated by applying quantum algorithms to two available copies of the bipartite system, and a final measurement on the auxiliary working qubits gives a better estimation of the concurrence. This method opens new prospects of entanglement measure by the application of quantum algorithms. The implementation of the protocol would be an important step toward quantum information processing and more complex entanglement measure of the finite-dimensional quantum system with an arbitrary number of qubits.
Exact quantum algorithm to distinguish Boolean functions of different weights
Braunstein, Samuel L [Computer Science, University of York, York YO10 5DD (United Kingdom); Choi, Byung-Soo [Computer Science, University of York, York YO10 5DD (United Kingdom); Ghosh, Subhroshekhar [Indian Statistical Institute, Kolkata 700 108 (India); Maitra, Subhamoy [Applied Statistics Unit, Indian Statistical Institute, Kolkata 700 108 (India)
2007-07-20
In this work, we exploit the Grover operator for the weight analysis of a Boolean function, specifically to solve the weight-decision problem. The weight w is the fraction of all possible inputs for which the output is 1. The goal of the weight-decision problem is to find the exact weight w from the given two weights w{sub 1} and w{sub 2} satisfying a general weight condition as w{sub 1} + w{sub 2} = 1 and 0 < w{sub 1} < w{sub 2} < 1. First, we propose a limited weight-decision algorithm where the function has another constraint: a weight is in {l_brace} W{sub 1} = sin{sup 2}(k/(2k+1) {pi}/2), w{sub 2} = cos{sup 2}(k/(2k+1) {pi}/2){r_brace} for integer k. Second, by changing the phases in the last two Grover iterations, we propose a general weight-decision algorithm which is free from the above constraint. Finally, we show that when our algorithm requires O(k) queries to find w with a unit success probability, any classical algorithm requires at least {omega}(k{sup 2}) queries for a unit success probability. In addition, we show that our algorithm requires fewer queries to solve this problem compared with the quantum counting algorithm.
Du, Tingsong; Hu, Yang; Ke, Xianting
2015-01-01
An improved quantum artificial fish swarm algorithm (IQAFSA) for solving distributed network programming considering distributed generation is proposed in this work. The IQAFSA based on quantum computing which has exponential acceleration for heuristic algorithm uses quantum bits to code artificial fish and quantum revolving gate, preying behavior, and following behavior and variation of quantum artificial fish to update the artificial fish for searching for optimal value. Then, we apply the proposed new algorithm, the quantum artificial fish swarm algorithm (QAFSA), the basic artificial fish swarm algorithm (BAFSA), and the global edition artificial fish swarm algorithm (GAFSA) to the simulation experiments for some typical test functions, respectively. The simulation results demonstrate that the proposed algorithm can escape from the local extremum effectively and has higher convergence speed and better accuracy. Finally, applying IQAFSA to distributed network problems and the simulation results for 33-bus radial distribution network system show that IQAFSA can get the minimum power loss after comparing with BAFSA, GAFSA, and QAFSA.
An Efficient Exact Quantum Algorithm for the Integer Square-free Decomposition Problem.
Li, Jun; Peng, Xinhua; Du, Jiangfeng; Suter, Dieter
2012-01-01
Quantum computers are known to be qualitatively more powerful than classical computers, but so far only a small number of different algorithms have been discovered that actually use this potential. It would therefore be highly desirable to develop other types of quantum algorithms that widen the range of possible applications. Here we propose an efficient and exact quantum algorithm for finding the square-free part of a large integer - a problem for which no efficient classical algorithm exists. The algorithm relies on properties of Gauss sums and uses the quantum Fourier transform. We give an explicit quantum network for the algorithm. Our algorithm introduces new concepts and methods that have not been used in quantum information processing so far and may be applicable to a wider class of problems.
An Efficient Deterministic Quantum Algorithm for the Integer Square-free Decomposition Problem
Li, Jun; Du, Jiangfeng; Suter, Dieter
2011-01-01
Quantum computers are known to be qualitatively more powerful than classical computers, but so far only a small number of different algorithms have been discovered that actually use this potential. It would therefore be highly desirable to develop other types of quantum algorithms that widen the range of possible applications. Here we propose an efficient and deterministic quantum algorithm for finding the square-free part of a large integer - a problem for which no efficient classical algorithm exists. The algorithm relies on properties of Gauss sums and uses the quantum Fourier transform. We give an explicit quantum network for the algorithm. Our algorithm introduces new concepts and methods that have not been used in quantum information processing so far and may be applicable to a wider class of problems.
A hybrid quantum encoding algorithm of vector quantization for image compression
Pang Chao-Yang; Zhou Zheng-Wei; Guo Guang-Can
2006-01-01
Many classical encoding algorithms of vector quantization (VQ) of image compression that can obtain global optimal solution have computational complexity O(N). A pure quantum VQ encoding algorithm with probability of success near 100% has been proposed, that performs operations 45√N times approximately. In this paper, a hybrid quantum VQ encoding algorithm between the classical method and the quantum algorithm is presented. The number of its operations is less than √N for most images, and it is more efficient than the pure quantum algorithm.
Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes
Williams Colin P.
1999-01-01
Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.
Gustin, Chris; Hughes, Stephen
2017-08-01
We study the role of electron-phonon scattering for a pulse-triggered quantum dot single-photon source which utilizes a modified version of stimulated Raman adiabatic passage and cavity coupling. This on-demand source is coherently pumped with an optical pulse in the presence of a continuous-wave laser drive, allowing for efficient generation of indistinguishable single photons with polarizations orthogonal to the applied fields. In contrast to previous studies, we explore the role of electron-phonon scattering on this semiconductor system by using a polaron master equation approach to model the biexciton-exciton cascade and cavity mode coupling. In addition to background zero-phonon-line decoherence processes, microscopic electron-acoustic-phonon coupling, which usually degrades the indistinguishability and efficiency of semiconductor photon sources, is rigorously taken into account. We study how different system parameters (including cavity and laser detunings, cavity spectral width, temperature) affect the device performance and contrast the relative influence of intrinsic phonon coupling with other dephasing mechanisms. We describe how this biexciton-exciton cascade scheme allows for true single photons to be generated with over 90% quantum indistinguishability and efficiency simultaneously using realistic experimental parameters. We also show how the double-field dressing can be probed through the cavity-emitted spectrum.
Algebraic and algorithmic frameworks for optimized quantum measurements
Laghaout, Amine; Andersen, Ulrik Lund
2015-01-01
von Neumann projections are the main operations by which information can be extracted from the quantum to the classical realm. They are, however, static processes that do not adapt to the states they measure. Advances in the field of adaptive measurement have shown that this limitation can...... for designing optimized measurements. Our approach is twofold: The first is algebraic and formulates the problem of measurement as a simple matrix diagonalization problem. The second is algorithmic and models the optimal interaction between measurement outcomes and measurement settings as a cascaded network...... of conditional probabilities. Finally, we demonstrate that several figures of merit, such as Bell factors, can be improved by optimized measurements. This leads us to the promising observation that measurement detectors which - taken individually - have a low quantum efficiency can be arranged into circuits...
The implementation of Grover's algorithm in optically driven quantum dots
Yin, W.; Liang, J. Q.; Yan, Q. W.
2006-11-01
In this paper, we study the implementation of Grover's algorithm using the system of three identical quantum dots (QDs) coupled by a multi-frequency optical field. Our result shows that increasing the electric field strength A speeds up the oscillations of the occupations of the excited states rather than increasing the occupation probabilities of those states. The larger the detuning of the field from resonance, the fewer the states which can be used as qubits. Compared with a multi-frequency external field, a single-frequency external field will generate much lower amplitudes of the excited states under the same coupling strength A and interdot Coulomb interaction V. However, when the three quantum dots are coupled with a single-frequency external field, these amplitudes increase on increasing the coupling strength A or decreasing the interdot Coulomb interaction V.
Quantum algorithm for universal implementation of the projective measurement of energy.
Nakayama, Shojun; Soeda, Akihito; Murao, Mio
2015-05-15
A projective measurement of energy (PME) on a quantum system is a quantum measurement determined by the Hamiltonian of the system. PME protocols exist when the Hamiltonian is given in advance. Unknown Hamiltonians can be identified by quantum tomography, but the time cost to achieve a given accuracy increases exponentially with the size of the quantum system. In this Letter, we improve the time cost by adapting quantum phase estimation, an algorithm designed for computational problems, to measurements on physical systems. We present a PME protocol without quantum tomography for Hamiltonians whose dimension and energy scale are given but which are otherwise unknown. Our protocol implements a PME to arbitrary accuracy without any dimension dependence on its time cost. We also show that another computational quantum algorithm may be used for efficient estimation of the energy scale. These algorithms show that computational quantum algorithms, with suitable modifications, have applications beyond their original context.
Subotnik, Joseph E; Ouyang, Wenjun; Landry, Brian R
2013-12-07
In this article, we demonstrate that Tully's fewest-switches surface hopping (FSSH) algorithm approximately obeys the mixed quantum-classical Liouville equation (QCLE), provided that several conditions are satisfied--some major conditions, and some minor. The major conditions are: (1) nuclei must be moving quickly with large momenta; (2) there cannot be explicit recoherences or interference effects between nuclear wave packets; (3) force-based decoherence must be added to the FSSH algorithm, and the trajectories can no longer rigorously be independent (though approximations for independent trajectories are possible). We furthermore expect that FSSH (with decoherence) will be most robust when nonadiabatic transitions in an adiabatic basis are dictated primarily by derivative couplings that are presumably localized to crossing regions, rather than by small but pervasive off-diagonal force matrix elements. In the end, our results emphasize the strengths of and possibilities for the FSSH algorithm when decoherence is included, while also demonstrating the limitations of the FSSH algorithm and its inherent inability to follow the QCLE exactly.
Abstract structure of unitary oracles for quantum algorithms
William Zeng
2014-12-01
Full Text Available We show that a pair of complementary dagger-Frobenius algebras, equipped with a self-conjugate comonoid homomorphism onto one of the algebras, produce a nontrivial unitary morphism on the product of the algebras. This gives an abstract understanding of the structure of an oracle in a quantum computation, and we apply this understanding to develop a new algorithm for the deterministic identification of group homomorphisms into abelian groups. We also discuss an application to the categorical theory of signal-flow networks.
Multi-objective quantum genetic algorithm in WSNs distribution optimization
Wen, Hao; Ren, Hong-liang
2013-03-01
To achieve lower energy and higher detection coverage simultaneously in scattering distribution wireless sensor networks (WSNs), a multi-objective optimization function combined with area coverage and node-communication energy is constructed. Based on the multi-objective quantum genetic algorithm (Mo-QGA) proposed by Li Bin and Zhuang-zhen Quan et al, we have obtained optimum solutions close to Pareto front. Experimental results indicate that the Mo-QGA has advantages both on efficiency and coverage, as well as low energy.
Mesoscopi Detailed Balance Algorithms for Quantum and Classical Turbulence
2013-02-01
the one-dimensional Magnetohydrodynamics-Burgers equations, KdV and nonlinear Schrodinger equations. Generalizing to three dimensions, quantum...with C4 = I (5) (Here I is the identity matrix). On the otherhand, to recover the KdV equation ∂ψ ∂t + ψ ∂ψ ∂x + ∂ 3ψ ∂x3...derivative, the unitary collide-stream algorithm interwines the streaming on the two probability amplitudes KdV : ψ t + Δt( ) = S1CT S2TC
Quantum algorithmic integrability: The metaphor of classical polygonal billiards
Mantica, Giorgio
2000-06-01
We study the algorithmic complexity of motions in classical polygonal billiards, which, as the number of sides increases, tend to curved billiards, both regular and chaotic. This study unveils the equivalence of this problem to the procedure of quantization: the average complexity of symbolic trajectories in polygonal billiards features the same scaling relations (with respect to the number of sides) that govern quantum systems when a semiclassical parameter is varied. Two cases, the polygonal approximations of the circle and of the stadium, are examined in detail and are presented as paradigms of quantization of integrable and chaotic systems.
An Efficient Deterministic Quantum Algorithm for the Integer Square-free Decomposition Problem
Li, Jun; Peng, Xinhua; Du, Jiangfeng; Suter, Dieter
2011-01-01
Quantum computers are known to be qualitatively more powerful than classical computers, but so far only a small number of different algorithms have been discovered that actually use this potential. It would therefore be highly desirable to develop other types of quantum algorithms that widen the range of possible applications. Here we propose an efficient and deterministic quantum algorithm for finding the square-free part of a large integer - a problem for which no efficient classical algori...
Efficient algorithms for large-scale quantum transport calculations
Brück, Sascha; Calderara, Mauro; Bani-Hashemian, Mohammad Hossein; VandeVondele, Joost; Luisier, Mathieu
2017-08-01
Massively parallel algorithms are presented in this paper to reduce the computational burden associated with quantum transport simulations from first-principles. The power of modern hybrid computer architectures is harvested in order to determine the open boundary conditions that connect the simulation domain with its environment and to solve the resulting Schrödinger equation. While the former operation takes the form of an eigenvalue problem that is solved by a contour integration technique on the available central processing units (CPUs), the latter can be cast into a linear system of equations that is simultaneously processed by SplitSolve, a two-step algorithm, on general-purpose graphics processing units (GPUs). A significant decrease of the computational time by up to two orders of magnitude is obtained as compared to standard solution methods.
Adiabatic theorems for generators of contracting evolutions
Avron, J E; Graf, G M; Grech, P
2011-01-01
We develop an adiabatic theory for generators of contracting evolution on Banach spaces. This provides a uniform framework for a host of adiabatic theorems ranging from unitary quantum evolutions through quantum evolutions of open systems generated by Lindbladians all the way to classically driven stochastic systems. In all these cases the adiabatic evolution approximates, to lowest order, the natural notion of parallel transport in the manifold of instantaneous stationary states. The dynamics in the manifold of instantaneous stationary states and transversal to it have distinct characteristics: The former is irreversible and the latter is transient in a sense that we explain. Both the gapped and gapless cases are considered. Some applications are discussed.
A quantum-inspired genetic algorithm based on probabilistic coding for multiple sequence alignment.
Huo, Hong-Wei; Stojkovic, Vojislav; Xie, Qiao-Luan
2010-02-01
Quantum parallelism arises from the ability of a quantum memory register to exist in a superposition of base states. Since the number of possible base states is 2(n), where n is the number of qubits in the quantum memory register, one operation on a quantum computer performs what an exponential number of operations on a classical computer performs. The power of quantum algorithms comes from taking advantages of quantum parallelism. Quantum algorithms are exponentially faster than classical algorithms. Genetic optimization algorithms are stochastic search algorithms which are used to search large, nonlinear spaces where expert knowledge is lacking or difficult to encode. QGMALIGN--a probabilistic coding based quantum-inspired genetic algorithm for multiple sequence alignment is presented. A quantum rotation gate as a mutation operator is used to guide the quantum state evolution. Six genetic operators are designed on the coding basis to improve the solution during the evolutionary process. The experimental results show that QGMALIGN can compete with the popular methods, such as CLUSTALX and SAGA, and performs well on the presenting biological data. Moreover, the addition of genetic operators to the quantum-inspired algorithm lowers the cost of overall running time.
A. AL-Salhi, Yahya E.; Lu, Songfeng
2016-08-01
Quantum steganography can solve some problems that are considered inefficient in image information concealing. It researches on Quantum image information concealing to have been widely exploited in recent years. Quantum image information concealing can be categorized into quantum image digital blocking, quantum image stereography, anonymity and other branches. Least significant bit (LSB) information concealing plays vital roles in the classical world because many image information concealing algorithms are designed based on it. Firstly, based on the novel enhanced quantum representation (NEQR), image uniform blocks clustering around the concrete the least significant Qu-block (LSQB) information concealing algorithm for quantum image steganography is presented. Secondly, a clustering algorithm is proposed to optimize the concealment of important data. Finally, we used Con-Steg algorithm to conceal the clustered image blocks. Information concealing located on the Fourier domain of an image can achieve the security of image information, thus we further discuss the Fourier domain LSQu-block information concealing algorithm for quantum image based on Quantum Fourier Transforms. In our algorithms, the corresponding unitary Transformations are designed to realize the aim of concealing the secret information to the least significant Qu-block representing color of the quantum cover image. Finally, the procedures of extracting the secret information are illustrated. Quantum image LSQu-block image information concealing algorithm can be applied in many fields according to different needs.
Quantum searching application in search based software engineering
Wu, Nan; Song, FangMin; Li, Xiangdong
2013-05-01
The Search Based Software Engineering (SBSE) is widely used in software engineering for identifying optimal solutions. However, there is no polynomial-time complexity solution used in the traditional algorithms for SBSE, and that causes the cost very high. In this paper, we analyze and compare several quantum search algorithms that could be applied for SBSE: quantum adiabatic evolution searching algorithm, fixed-point quantum search (FPQS), quantum walks, and a rapid modified Grover quantum searching method. The Grover's algorithm is thought as the best choice for a large-scaled unstructured data searching and theoretically it can be applicable to any search-space structure and any type of searching problems.
Pang Chao-Yang; Zhou Zheng-Wei; Chen Ping-Xing; Guo Guang-Can
2006-01-01
Vector quantization (VQ) is an important data compression method. The key of the encoding of VQ is to find the closest vector among N vectors for a feature vector. Many classical linear search algorithms take O(N) steps of distance computing between two vectors. The quantum VQ iteration and corresponding quantum VQ encoding algorithm that takes O(√V) steps are presented in this paper. The unitary operation of distance computing can be performed on a number of vectors simultaneously because the quantum state exists in a superposition of states. The quantum VQ iteration comprises three oracles, by contrast many quantum algorithms have only one oracle, such as Shor's factorization algorithm and Grover's algorithm. Entanglement state is generated and used, by contrast the state in Grover's algorithm is not an entanglement state. The quantum VQ iteration is a rotation over subspace, by contrast the Grover iteration is a rotation over global space. The quantum VQ iteration extends the Grover iteration to the more complex search that requires more oracles. The method of the quantum VQ iteration is universal.
The Jones polynomial: quantum algorithms and applications in quantum complexity theory
Yard, J; Yard, Jon; Wocjan, Pawel
2006-01-01
We analyze relationships between the Jones polynomial and quantum computation. Our first result is a polynomial-time quantum algorithm which gives an additive approximation of the Jones polynomial, in the sense of Bordewich, Freedman, Lovasz and Welsh, of any link obtained from a certain general family of closures of braids, evaluated at any primitive root of unity. This family encompasses the well-known plat and trace closures, generalizing results recently obtained by Aharonov, Jones and Landau. We base our algorithm on a local qubit implementation of the unitary Jones-Wenzl representations of the braid group which makes the underlying representation theory apparent, allowing us to provide an algorithm for approximating the HOMFLYPT two-variable polynomial of the trace closure of a braid at certain pairs of values as well. Next, we provide a self-contained proof that any quantum computation can be replaced by an additive approximation of the Jones polynomial, evaluated at almost any primitive root of unity....
One-qubit quantum gates in a circular graphene quantum dot: genetic algorithm approach.
Amparán, Gibrán; Rojas, Fernando; Pérez-Garrido, Antonio
2013-05-16
The aim of this work was to design and control, using genetic algorithm (GA) for parameter optimization, one-charge-qubit quantum logic gates σx, σy, and σz, using two bound states as a qubit space, of circular graphene quantum dots in a homogeneous magnetic field. The method employed for the proposed gate implementation is through the quantum dynamic control of the qubit subspace with an oscillating electric field and an onsite (inside the quantum dot) gate voltage pulse with amplitude and time width modulation which introduce relative phases and transitions between states. Our results show that we can obtain values of fitness or gate fidelity close to 1, avoiding the leakage probability to higher states. The system evolution, for the gate operation, is presented with the dynamics of the probability density, as well as a visualization of the current of the pseudospin, characteristic of a graphene structure. Therefore, we conclude that is possible to use the states of the graphene quantum dot (selecting the dot size and magnetic field) to design and control the qubit subspace, with these two time-dependent interactions, to obtain the optimal parameters for a good gate fidelity using GA.
One-qubit quantum gates in a circular graphene quantum dot: genetic algorithm approach
Amparán, Gibrán; Rojas, Fernando; Pérez-Garrido, Antonio
2013-05-01
The aim of this work was to design and control, using genetic algorithm (GA) for parameter optimization, one-charge-qubit quantum logic gates σ x, σ y, and σ z, using two bound states as a qubit space, of circular graphene quantum dots in a homogeneous magnetic field. The method employed for the proposed gate implementation is through the quantum dynamic control of the qubit subspace with an oscillating electric field and an onsite (inside the quantum dot) gate voltage pulse with amplitude and time width modulation which introduce relative phases and transitions between states. Our results show that we can obtain values of fitness or gate fidelity close to 1, avoiding the leakage probability to higher states. The system evolution, for the gate operation, is presented with the dynamics of the probability density, as well as a visualization of the current of the pseudospin, characteristic of a graphene structure. Therefore, we conclude that is possible to use the states of the graphene quantum dot (selecting the dot size and magnetic field) to design and control the qubit subspace, with these two time-dependent interactions, to obtain the optimal parameters for a good gate fidelity using GA.
A Novel Exact Fixed-node Quantum Monte Carlo Algorithm
Hong Xin HUANG
2004-01-01
In this paper we proposed a novel exact fixed-node quantum Monte Carlo (EFNQMC) algorithm, which is a self-optimizing and self-improving procedure. In contrast to the previous EFNQMC method, the trial function is optimized synchronistically in the diffusion procedure, but not before the beginning of EFNQMC computation. In order to optimize the trial function, the improved steepest descent technique is used, in which the step size is automatically adjustable. The procedure is quasi-Newton and converges super linearly. We also use a novel trial function, which has correct electron-electron and electron-nucleus cusp conditions. The novel EFNQMC algorithm and the novel trial function are employed to calculate the energies of 11A1 state of CH2, 1Ag state of C8 and the ground-states of H2, LiH, Li2, H2O, respectively. The test results show that both the novel algorithm and the trial function proposed in the present paper are very excellent.
An Allele Real-Coded Quantum Evolutionary Algorithm Based on Hybrid Updating Strategy.
Zhang, Yu-Xian; Qian, Xiao-Yi; Peng, Hui-Deng; Wang, Jian-Hui
2016-01-01
For improving convergence rate and preventing prematurity in quantum evolutionary algorithm, an allele real-coded quantum evolutionary algorithm based on hybrid updating strategy is presented. The real variables are coded with probability superposition of allele. A hybrid updating strategy balancing the global search and local search is presented in which the superior allele is defined. On the basis of superior allele and inferior allele, a guided evolutionary process as well as updating allele with variable scale contraction is adopted. And H ε gate is introduced to prevent prematurity. Furthermore, the global convergence of proposed algorithm is proved by Markov chain. Finally, the proposed algorithm is compared with genetic algorithm, quantum evolutionary algorithm, and double chains quantum genetic algorithm in solving continuous optimization problem, and the experimental results verify the advantages on convergence rate and search accuracy.
An Allele Real-Coded Quantum Evolutionary Algorithm Based on Hybrid Updating Strategy
Yu-Xian Zhang
2016-01-01
Full Text Available For improving convergence rate and preventing prematurity in quantum evolutionary algorithm, an allele real-coded quantum evolutionary algorithm based on hybrid updating strategy is presented. The real variables are coded with probability superposition of allele. A hybrid updating strategy balancing the global search and local search is presented in which the superior allele is defined. On the basis of superior allele and inferior allele, a guided evolutionary process as well as updating allele with variable scale contraction is adopted. And Hε gate is introduced to prevent prematurity. Furthermore, the global convergence of proposed algorithm is proved by Markov chain. Finally, the proposed algorithm is compared with genetic algorithm, quantum evolutionary algorithm, and double chains quantum genetic algorithm in solving continuous optimization problem, and the experimental results verify the advantages on convergence rate and search accuracy.
Arik, Metin; Yarman, Tolga; Kholmetskii, Alexander L.
2009-01-01
Previously, we established a connection between the macroscopic classical laws of gases and the quantum mechanical description of molecules of an ideal gas (T. Yarman et al. arXiv:0805.4494). In such a gas, the motion of each molecule can be considered independently on all other molecules, and thus the macroscopic parameters of the ideal gas, like pressure P and temperature T, can be introduced as a result of simple averaging over all individual motions of the molecules. It was shown that for...
A scheme for implementing quantum clock synchronization algorithm in cavity QED
Wu Qin-Qin; Kuang Le-Man
2006-01-01
In this paper, we propose a scheme for implementing the quantum clock synchronization (QCS) algorithm in cavity quantum electrodynamic (QED) formalism. Our method is based on three-level ladder-type atoms interacting with classical and quantized cavity fields. Atom-qubit realizations of three-qubit and four-qubit QCS algorithms are explicitly presented.
Chernyavskiy, A. Yu.
2013-01-01
The simple and universal global optimization method based on simplified multipopulation genetic algorithm is presented. The method is applied to quantum information problems. It is compared to the genetic algorithm on standard test functions, and also tested on the calculation of quantum discord and minimal entanglement entropy, which is an entanglement measure for pure multipartite states.
A novel quantum-inspired immune clonal algorithm with the evolutionary game approach
Qiuyi Wu; Licheng Jiao; Yangyang Li; Xiaozheng Deng
2009-01-01
The quantum-inspired immune clonal algorithm (QICA) is a rising intelligence algorithm. Based on evolutionary game theory and QICA, a quantum-inspired immune algorithm embedded with evolutionary game (EGQICA) is proposed to solve combination optimi-zation problems. In this paper, we map the quantum antibody's finding the optimal solution to player's pursuing maximum utility by choosing strategies in evolutionary games. Replicator dynamics is used to model the behavior of the quantum antibody and the memory mechanism is also introduced in this work. Experimental results indicate that the proposed approach maintains a good diversity and achieves superior performance.
Observation of Majorization Principle for quantum algorithms via 3-D integrated photonic circuits
Flamini, Fulvio; Giordani, Taira; Bentivegna, Marco; Spagnolo, Nicoló; Crespi, Andrea; Corrielli, Giacomo; Osellame, Roberto; Martin-Delgado, Miguel Angel; Sciarrino, Fabio
2016-01-01
The Majorization Principle is a fundamental statement governing the dynamics of information processing in optimal and efficient quantum algorithms. While quantum computation can be modeled to be reversible, due to the unitary evolution undergone by the system, these quantum algorithms are conjectured to obey a quantum arrow of time dictated by the Majorization Principle: the probability distribution associated to the outcomes gets ordered step-by-step until achieving the result of the computation. Here we report on the experimental observation of the effects of the Majorization Principle for two quantum algorithms, namely the quantum fast Fourier transform and a recently introduced validation protocol for the certification of genuine many-boson interference. The demonstration has been performed by employing integrated 3-D photonic circuits fabricated via femtosecond laser writing technique, which allows to monitor unambiguously the effects of majorization along the execution of the algorithms. The measured ob...
A Novel Algorithm of Quantum Random Walk in Server Traffic Control and Task Scheduling
Dong Yumin
2014-01-01
Full Text Available A quantum random walk optimization model and algorithm in network cluster server traffic control and task scheduling is proposed. In order to solve the problem of server load balancing, we research and discuss the distribution theory of energy field in quantum mechanics and apply it to data clustering. We introduce the method of random walk and illuminate what the quantum random walk is. Here, we mainly research the standard model of one-dimensional quantum random walk. For the data clustering problem of high dimensional space, we can decompose one m-dimensional quantum random walk into m one-dimensional quantum random walk. In the end of the paper, we compare the quantum random walk optimization method with GA (genetic algorithm, ACO (ant colony optimization, and SAA (simulated annealing algorithm. In the same time, we prove its validity and rationality by the experiment of analog and simulation.
The Improvement of Quantum Genetic Algorithm and Its Application on Function Optimization
Huaixiao Wang; Jianyong Liu; Jun Zhi; Chengqun Fu
2013-01-01
To accelerate the evolutionary process and increase the probability to find the optimal solution, the following methods are proposed to improve the conventional quantum genetic algorithm: an improved method to determine the rotating angle, the self-adaptive rotating angle strategy, adding the quantum mutation operation and quantum disaster operation. The efficiency and accuracy to search the optimal solution of the algorithm are greatly improved. Simulation test shows that the improved quantu...
Dong Yumin
2014-01-01
Full Text Available A quantum optimization scheme in network cluster server task scheduling is proposed. We explore and research the distribution theory of energy field in quantum mechanics; specially, we apply it to data clustering. We compare the quantum optimization method with genetic algorithm (GA, ant colony optimization (ACO, simulated annealing algorithm (SAA. At the same time, we prove its validity and rationality by analog simulation and experiment.
Quantum Algorithm for Commutativity Testing of a Matrix Set
Itakura, Y K
2005-01-01
Suppose we have k matrices of size n by n. We are given an oracle that knows all the entries of k matrices, that is, we can query the oracle an (i,j) entry of the l-th matrix. The goal is to test if each pair of k matrices commute with each other or not with as few queries to the oracle as possible. In order to solve this problem, we use a theorem of Mario Szegedy (quant-ph/0401053) that relates a hitting time of a classical random walk to that of a quantum walk. We also take a look at another method of quantum walk by Andris Ambainis (quant-ph/0311001). We apply both walks into triangle finding problem (quant-ph/0310134) and matrix verification problem (quant-ph/0409035) to compare the powers of the two different walks. We also present Ambainis's method of lower bounding technique (quant-ph/0002066) to obtain a lower bound for this problem. It turns out Szegedy's algorithm can be generalized to solve similar problems. Therefore we use Szegedy's theorem to analyze the problem of matrix set commutativity. We g...
Adaptive double chain quantum genetic algorithm for constrained optimization problems
Kong Haipeng
2015-02-01
Full Text Available Optimization problems are often highly constrained and evolutionary algorithms (EAs are effective methods to tackle this kind of problems. To further improve search efficiency and convergence rate of EAs, this paper presents an adaptive double chain quantum genetic algorithm (ADCQGA for solving constrained optimization problems. ADCQGA makes use of double-individuals to represent solutions that are classified as feasible and infeasible solutions. Fitness (or evaluation functions are defined for both types of solutions. Based on the fitness function, three types of step evolution (SE are defined and utilized for judging evolutionary individuals. An adaptive rotation is proposed and used to facilitate updating individuals in different solutions. To further improve the search capability and convergence rate, ADCQGA utilizes an adaptive evolution process (AEP, adaptive mutation and replacement techniques. ADCQGA was first tested on a widely used benchmark function to illustrate the relationship between initial parameter values and the convergence rate/search capability. Then the proposed ADCQGA is successfully applied to solve other twelve benchmark functions and five well-known constrained engineering design problems. Multi-aircraft cooperative target allocation problem is a typical constrained optimization problem and requires efficient methods to tackle. Finally, ADCQGA is successfully applied to solving the target allocation problem.
Adaptive double chain quantum genetic algorithm for constrained optimization problems
Kong Haipeng; Li Ni; Shen Yuzhong
2015-01-01
Optimization problems are often highly constrained and evolutionary algorithms (EAs) are effective methods to tackle this kind of problems. To further improve search efficiency and con-vergence rate of EAs, this paper presents an adaptive double chain quantum genetic algorithm (ADCQGA) for solving constrained optimization problems. ADCQGA makes use of double-individuals to represent solutions that are classified as feasible and infeasible solutions. Fitness (or evaluation) functions are defined for both types of solutions. Based on the fitness function, three types of step evolution (SE) are defined and utilized for judging evolutionary individuals. An adaptive rotation is proposed and used to facilitate updating individuals in different solutions. To further improve the search capability and convergence rate, ADCQGA utilizes an adaptive evolution process (AEP), adaptive mutation and replacement techniques. ADCQGA was first tested on a widely used benchmark function to illustrate the relationship between initial parameter values and the convergence rate/search capability. Then the proposed ADCQGA is successfully applied to solve other twelve benchmark functions and five well-known constrained engineering design problems. Multi-aircraft cooperative target allocation problem is a typical constrained optimization problem and requires efficient methods to tackle. Finally, ADCQGA is successfully applied to solving the target allocation problem.
Wanneng Shu
2009-01-01
Quantum-inspired genetic algorithm (QGA) is applied to simulated annealing (SA) to develop a class of quantum-inspired simulated annealing genetic algorithm (QSAGA) for combinatorial optimization. With the condition of preserving QGA advantages, QSAGA takes advantage of the SA algorithm so as to avoid premature convergence. To demonstrate its effectiveness and applicability, experiments are carried out on the knapsack problem. The results show that QSAGA performs well, without premature conve...
A genetic algorithm for finding pulse sequences for NMR quantum computing
Rethinam, M J; Behrman, E C; Steck, J E; Skinner, S R
2004-01-01
We present a genetic algorithm for finding a set of pulse sequences, or rotations, for a given quantum logic gate, as implemented by NMR. We demonstrate the utility of the method by showing that shorter sequences than have been previously published can be found for both a CNOT and for the central part of Shor's algorithm (for N=15.) Artificial intelligence techniques like the genetic algorithm here presented have an enormous potential for simplifying the implementation of working quantum computers.
Wu, Guorong [National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6 (Canada); State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, Liaoning 116023 (China); Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China); Neville, Simon P. [Department of Chemistry, University of Ottawa, 10 Marie Curie, Ottawa, Ontario K1N 6N5 (Canada); Schalk, Oliver [National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6 (Canada); Department of Physics, AlbaNova University Center, Stockholm University, Roslagstullsbacken 21, 106 91 Stockholm (Sweden); Sekikawa, Taro [Department of Applied Physics, Hokkaido University, Kita-13 Nishi-8, Kita-ku, Sapporo 060-8628 (Japan); Ashfold, Michael N. R. [School of Chemistry, University of Bristol, Bristol BS8 1TS (United Kingdom); Worth, Graham A. [School of Chemistry, University of Birmingham, Edgbaston, Birmingham B15 2TT (United Kingdom); Stolow, Albert, E-mail: astolow@uottawa.ca [National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6 (Canada); Department of Chemistry, University of Ottawa, 10 Marie Curie, Ottawa, Ontario K1N 6N5 (Canada); Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5 (Canada)
2016-01-07
The dynamics of N-methylpyrrole following excitation at wavelengths in the range 241.5-217.0 nm were studied using a combination of time-resolved photoelectron spectroscopy (TRPES), ab initio quantum dynamics calculations using the multi-layer multi-configurational time-dependent Hartree method, as well as high-level photoionization cross section calculations. Excitation at 241.5 and 236.2 nm results in population of the A{sub 2}(πσ{sup ∗}) state, in agreement with previous studies. Excitation at 217.0 nm prepares the previously neglected B{sub 1}(π3p{sub y}) Rydberg state, followed by prompt internal conversion to the A{sub 2}(πσ{sup ∗}) state. In contrast with the photoinduced dynamics of pyrrole, the lifetime of the wavepacket in the A{sub 2}(πσ{sup ∗}) state was found to vary with excitation wavelength, decreasing by one order of magnitude upon tuning from 241.5 nm to 236.2 nm and by more than three orders of magnitude when excited at 217.0 nm. The order of magnitude difference in lifetimes measured at the longer excitation wavelengths is attributed to vibrational excitation in the A{sub 2}(πσ{sup ∗}) state, facilitating wavepacket motion around the potential barrier in the N–CH{sub 3} dissociation coordinate.
量子遗传算法研究现状%Actuality of Research on Quantum Genetic Algorithm
杨俊安; 庄镇泉
2003-01-01
Quantum Genetic Algorithm (QGA)is the combination of quantum computation and genetic algorithm. In this paper, actuality of research on QGA is summarized. QGA and Multi-universe Parallel Quantum Genetic Algorithm (MPQGA)are discussed in detail. Application progenies in respective regions are introduced. The subsequent research on QGA is also prospected.
Luo Zhi-Hua; Cao Xi-Jin; Yu Chao-Fan
2011-01-01
Based on the Holstein model Hamiltonian of one-dimensional molecular crystals, by making use of the expansion approach of the correlated squeezed-coherent states of phonon instead of the two-phonon coherent state expansion scheme, the properties of the ground state and the anomalous quantum fluctuations are investigated in a strongly coupled electron-phonon system with special consideration of the electron-two-phonon interaction. The effective renormalization ((～α)i) of the displacement of the squeezed phonons with the effect of the squeezed-coherent states of phonon and both the electron-displaced phonon and the polaron-squeezed phonon correlations have been combined to obtain the anomalous quantum fluctuations for the corrections of the coherent state. Due to these non-adiabatic correlations, the effective displacement parameter (～α)i is larger than the ordinary parameter αi(0). In comparison with the electron-one-phonon interaction (g) corrected as (～α)ig, we have found the electron-two-phonon interaction (g1) corrected as (～α)2ig1 is enhanced significantly. For this reason, the ground state energy (EO(2)) contributed by the electron-two-phonon interaction is more negative than the single-phonon case (EO(1)) and the soliton solution is more stable. At the same time, the effects of the electron-two-phonon interaction greatly increase the polaron energy and the quantum fluctuations. Furthermore,in a deeper level, we have considered the effect of the polaron-squeezed phonon correlation (f-correlation). Since this correlation parameter f ＞ 1, this effect will strengthen the electron-one and two-phonon interactions by f(～α)ig and f2( ～α)2i1, respectively. The final results show that the ground state energy and the polaron energy will appear more negative further and the quantum fluctuations will gain further improvement.
Reactive power and voltage control based on general quantum genetic algorithms
Vlachogiannis, Ioannis (John); Østergaard, Jacob
2009-01-01
This paper presents an improved evolutionary algorithm based on quantum computing for optima l steady-state performance of power systems. However, the proposed general quantum genetic algorithm (GQ-GA) can be applied in various combinatorial optimization problems. In this study the GQ-GA determines...... techniques such as enhanced GA, multi-objective evolutionary algorithm and particle swarm optimization algorithms, as well as the classical primal-dual interior-point optimal power flow algorithm. The comparison demonstrates the ability of the GQ-GA in reaching more optimal solutions....
A Novel Color Image Encryption Algorithm Based on Quantum Chaos Sequence
Liu, Hui; Jin, Cong
2017-03-01
In this paper, a novel algorithm of image encryption based on quantum chaotic is proposed. The keystreams are generated by the two-dimensional logistic map as initial conditions and parameters. And then general Arnold scrambling algorithm with keys is exploited to permute the pixels of color components. In diffusion process, a novel encryption algorithm, folding algorithm, is proposed to modify the value of diffused pixels. In order to get the high randomness and complexity, the two-dimensional logistic map and quantum chaotic map are coupled with nearest-neighboring coupled-map lattices. Theoretical analyses and computer simulations confirm that the proposed algorithm has high level of security.
Wu, Guorong [National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6 (Canada); State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, Liaoning 116023 (China); Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China); Neville, Simon P.; Worth, Graham A., E-mail: g.a.worth@bham.ac.uk [School of Chemistry, University of Birmingham, Edgbaston, Birmingham B15 2TT (United Kingdom); Schalk, Oliver [National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6 (Canada); Department of Physics, AlbaNova University Center, Stockholm University, Roslagstullsbacken 21, 109 61 Stockholm (Sweden); Sekikawa, Taro [National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6 (Canada); Department of Applied Physics, Hokkaido University, Kita-13 Nishi-8, Kita-ku, Sapporo 060-8628 (Japan); Ashfold, Michael N. R. [School of Chemistry, University of Bristol, Bristol BS8 1TS (United Kingdom); Stolow, Albert, E-mail: astolow@uottawa.ca [National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6 (Canada); Departments of Chemistry and Physics, University of Ottawa, 10 Marie Curie, Ottawa, Ontario K1N 6N5 (Canada)
2015-02-21
The dynamics of pyrrole excited at wavelengths in the range 242-217 nm are studied using a combination of time-resolved photoelectron spectroscopy and wavepacket propagations performed using the multi-configurational time-dependent Hartree method. Excitation close to the origin of pyrrole’s electronic spectrum, at 242 and 236 nm, is found to result in an ultrafast decay of the system from the ionization window on a single timescale of less than 20 fs. This behaviour is explained fully by assuming the system to be excited to the A{sub 2}(πσ{sup ∗}) state, in accord with previous experimental and theoretical studies. Excitation at shorter wavelengths has previously been assumed to result predominantly in population of the bright A{sub 1}(ππ{sup ∗}) and B{sub 2}(ππ{sup ∗}) states. We here present time-resolved photoelectron spectra at a pump wavelength of 217 nm alongside detailed quantum dynamics calculations that, together with a recent reinterpretation of pyrrole’s electronic spectrum [S. P. Neville and G. A. Worth, J. Chem. Phys. 140, 034317 (2014)], suggest that population of the B{sub 1}(πσ{sup ∗}) state (hitherto assumed to be optically dark) may occur directly when pyrrole is excited at energies in the near UV part of its electronic spectrum. The B{sub 1}(πσ{sup ∗}) state is found to decay on a timescale of less than 20 fs by both N-H dissociation and internal conversion to the A{sub 2}(πσ{sup ∗}) state.
Huang, Yu; Guo, Feng; Li, Yongling; Liu, Yufeng
2015-01-01
Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO) is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm.
Yu Huang
Full Text Available Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm.
Noon, Abbas; Kadry, Seifedine
2011-01-01
Round Robin, considered as the most widely adopted CPU scheduling algorithm, undergoes severe problems directly related to quantum size. If time quantum chosen is too large, the response time of the processes is considered too high. On the other hand, if this quantum is too small, it increases the overhead of the CPU. In this paper, we propose a new algorithm, called AN, based on a new approach called dynamic-time-quantum; the idea of this approach is to make the operating systems adjusts the time quantum according to the burst time of the set of waiting processes in the ready queue. Based on the simulations and experiments, we show that the new proposed algorithm solves the fixed time quantum problem and increases the performance of Round Robin.
Dupuy, Nicolas; Bouaouli, Samira; Mauri, Francesco; Sorella, Sandro; Casula, Michele
2015-06-01
We study the ionization energy, electron affinity, and the π → π∗ (1La) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the 1La excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral 1La excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account.
Dupuy, Nicolas; Bouaouli, Samira; Mauri, Francesco; Sorella, Sandro; Casula, Michele
2015-06-07
We study the ionization energy, electron affinity, and the π → π(∗) ((1)La) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the (1)La excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral (1)La excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account.
Dupuy, Nicolas, E-mail: nicolas.dupuy@impmc.upmc.fr [Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, case 115, 4 place Jussieu, 75252 Paris Cedex 05 (France); Bouaouli, Samira, E-mail: samira.bouaouli@lct.jussieu.fr [Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, case 115, 4 place Jussieu, 75252 Paris Cedex 05 (France); Mauri, Francesco, E-mail: francesco.mauri@impmc.upmc.fr; Casula, Michele, E-mail: michele.casula@impmc.upmc.fr [CNRS and Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, case 115, 4 place Jussieu, 75252 Paris Cedex 05 (France); Sorella, Sandro, E-mail: sorella@sissa.it [International School for Advanced Studies (SISSA), Via Beirut 2-4, 34014 Trieste, Italy and INFM Democritos National Simulation Center, Trieste (Italy)
2015-06-07
We study the ionization energy, electron affinity, and the π → π{sup ∗} ({sup 1}L{sub a}) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the {sup 1}L{sub a} excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral {sup 1}L{sub a} excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account.
Tesch, Carmen M; de Vivie-Riedle, Regina
2004-12-22
The phase of quantum gates is one key issue for the implementation of quantum algorithms. In this paper we first investigate the phase evolution of global molecular quantum gates, which are realized by optimally shaped femtosecond laser pulses. The specific laser fields are calculated using the multitarget optimal control algorithm, our modification of the optimal control theory relevant for application in quantum computing. As qubit system we use vibrational modes of polyatomic molecules, here the two IR-active modes of acetylene. Exemplarily, we present our results for a Pi gate, which shows a strong dependence on the phase, leading to a significant decrease in quantum yield. To correct for this unwanted behavior we include pressure on the quantum phase in our multitarget approach. In addition the accuracy of these phase corrected global quantum gates is enhanced. Furthermore we could show that in our molecular approach phase corrected quantum gates and basis set independence are directly linked. Basis set independence is also another property highly required for the performance of quantum algorithms. By realizing the Deutsch-Jozsa algorithm in our two qubit molecular model system, we demonstrate the good performance of our phase corrected and basis set independent quantum gates.
Sugisaki, Kenji; Yamamoto, Satoru; Nakazawa, Shigeaki; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Takui, Takeji
2016-08-18
Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum. The proposed quantum algorithm enables us to prepare the wave function consisting of an exponential number of Slater determinants only by a polynomial number of quantum operations.
Q-Learning-Based Adjustable Fixed-Phase Quantum Grover Search Algorithm
Guo, Ying; Shi, Wensha; Wang, Yijun; Hu, Jiankun
2017-02-01
We demonstrate that the rotation phase can be suitably chosen to increase the efficiency of the phase-based quantum search algorithm, leading to a dynamic balance between iterations and success probabilities of the fixed-phase quantum Grover search algorithm with Q-learning for a given number of solutions. In this search algorithm, the proposed Q-learning algorithm, which is a model-free reinforcement learning strategy in essence, is used for performing a matching algorithm based on the fraction of marked items λ and the rotation phase α. After establishing the policy function α = π(λ), we complete the fixed-phase Grover algorithm, where the phase parameter is selected via the learned policy. Simulation results show that the Q-learning-based Grover search algorithm (QLGA) enables fewer iterations and gives birth to higher success probabilities. Compared with the conventional Grover algorithms, it avoids the optimal local situations, thereby enabling success probabilities to approach one.
Simulated Quantum Computation of Molecular Energies
Aspuru-Guzik, A; Love, P J; Head-Gordon, M; Aspuru-Guzik, Al\\'an; Dutoi, Anthony D.; Love, Peter J.; Head-Gordon, Martin
2005-01-01
The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical interest using modest numbers of quantum bits. Calculations of the water and lithium hydride molecular ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estimation algorithm. The recursive algorithm reduces the number of quantum bits required for the readout register from about 20 to 4. Mappings of the molecular wave function to the quantum bits are described. An adiabatic method for the preparation of a good approximate ground-state wave function is described and demonstrated for a stretched hydrogen molecule. The number of quantum bits required scales linearly with the number of basis functions, and the number of gates required grows polynomially with the number of quantum bits.
Optimization of Microgrid Using Quantum Inspired Evolutionary Algorithm
Ebrahim Zare juybari
2014-08-01
Full Text Available This paper presents a generalized formulation for determining the optimal operating strategy and cost optimization scheme as well as reducing the emissions of a MicroGrid (MG. In this article a microgrid including a wind turbine, pv array and a CHP system consisting of fuel cells and a microturbine is studied and then the modeling of various DERs is conducted and the objective functions and constraints are developed. The model takes into consideration the operation and maintenance costs as well as the reduction in emissions of NOx, SO2, and CO2 In the end the Quantum-Inspired Evolutionary Algorithm is employed to solved the optimal model and an operation scheme is achieved while meeting various constraints on the basis of tariff details, equipment performance, weather conditions and forecasts, load details and forecasts and other necessary information and then the economic costs and environmental impacts are analyzed and a conclusion that the QEA can achieve high environmental benefits and spend as low operation cost as possible. according to power Output functions and cost function of the various units , can be achieve to minimize cost.
Ab initio multiple cloning algorithm for quantum nonadiabatic molecular dynamics.
Makhov, Dmitry V; Glover, William J; Martinez, Todd J; Shalashilin, Dmitrii V
2014-08-07
We present a new algorithm for ab initio quantum nonadiabatic molecular dynamics that combines the best features of ab initio Multiple Spawning (AIMS) and Multiconfigurational Ehrenfest (MCE) methods. In this new method, ab initio multiple cloning (AIMC), the individual trajectory basis functions (TBFs) follow Ehrenfest equations of motion (as in MCE). However, the basis set is expanded (as in AIMS) when these TBFs become sufficiently mixed, preventing prolonged evolution on an averaged potential energy surface. We refer to the expansion of the basis set as "cloning," in analogy to the "spawning" procedure in AIMS. This synthesis of AIMS and MCE allows us to leverage the benefits of mean-field evolution during periods of strong nonadiabatic coupling while simultaneously avoiding mean-field artifacts in Ehrenfest dynamics. We explore the use of time-displaced basis sets, "trains," as a means of expanding the basis set for little cost. We also introduce a new bra-ket averaged Taylor expansion (BAT) to approximate the necessary potential energy and nonadiabatic coupling matrix elements. The BAT approximation avoids the necessity of computing electronic structure information at intermediate points between TBFs, as is usually done in saddle-point approximations used in AIMS. The efficiency of AIMC is demonstrated on the nonradiative decay of the first excited state of ethylene. The AIMC method has been implemented within the AIMS-MOLPRO package, which was extended to include Ehrenfest basis functions.
Ab initio multiple cloning algorithm for quantum nonadiabatic molecular dynamics
Makhov, Dmitry V.; Shalashilin, Dmitrii V. [Department of Chemistry, University of Leeds, Leeds LS2 9JT (United Kingdom); Glover, William J.; Martinez, Todd J. [Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA and SLAC National Accelerator Laboratory, Menlo Park, California 94025 (United States)
2014-08-07
We present a new algorithm for ab initio quantum nonadiabatic molecular dynamics that combines the best features of ab initio Multiple Spawning (AIMS) and Multiconfigurational Ehrenfest (MCE) methods. In this new method, ab initio multiple cloning (AIMC), the individual trajectory basis functions (TBFs) follow Ehrenfest equations of motion (as in MCE). However, the basis set is expanded (as in AIMS) when these TBFs become sufficiently mixed, preventing prolonged evolution on an averaged potential energy surface. We refer to the expansion of the basis set as “cloning,” in analogy to the “spawning” procedure in AIMS. This synthesis of AIMS and MCE allows us to leverage the benefits of mean-field evolution during periods of strong nonadiabatic coupling while simultaneously avoiding mean-field artifacts in Ehrenfest dynamics. We explore the use of time-displaced basis sets, “trains,” as a means of expanding the basis set for little cost. We also introduce a new bra-ket averaged Taylor expansion (BAT) to approximate the necessary potential energy and nonadiabatic coupling matrix elements. The BAT approximation avoids the necessity of computing electronic structure information at intermediate points between TBFs, as is usually done in saddle-point approximations used in AIMS. The efficiency of AIMC is demonstrated on the nonradiative decay of the first excited state of ethylene. The AIMC method has been implemented within the AIMS-MOLPRO package, which was extended to include Ehrenfest basis functions.
Tingsong Du
2015-01-01
Full Text Available An improved quantum artificial fish swarm algorithm (IQAFSA for solving distributed network programming considering distributed generation is proposed in this work. The IQAFSA based on quantum computing which has exponential acceleration for heuristic algorithm uses quantum bits to code artificial fish and quantum revolving gate, preying behavior, and following behavior and variation of quantum artificial fish to update the artificial fish for searching for optimal value. Then, we apply the proposed new algorithm, the quantum artificial fish swarm algorithm (QAFSA, the basic artificial fish swarm algorithm (BAFSA, and the global edition artificial fish swarm algorithm (GAFSA to the simulation experiments for some typical test functions, respectively. The simulation results demonstrate that the proposed algorithm can escape from the local extremum effectively and has higher convergence speed and better accuracy. Finally, applying IQAFSA to distributed network problems and the simulation results for 33-bus radial distribution network system show that IQAFSA can get the minimum power loss after comparing with BAFSA, GAFSA, and QAFSA.
Experimental Realization of a One-way Quantum Computer Algorithm Solving Simon's Problem
Tame, M S; Di Franco, C; Wadsworth, W J; Rarity, J G
2014-01-01
We report an experimental demonstration of a one-way implementation of a quantum algorithm solving Simon's Problem - a black box period-finding problem which has an exponential gap between the classical and quantum runtime. Using an all-optical setup and modifying the bases of single-qubit measurements on a five-qubit cluster state, key representative functions of the logical two-qubit version's black box can be queried and solved. To the best of our knowledge, this work represents the first experimental realization of the quantum algorithm solving Simon's Problem. The experimental results are in excellent agreement with the theoretical model, demonstrating the successful performance of the algorithm. With a view to scaling up to larger numbers of qubits, we analyze the resource requirements for an n-qubit version. This work helps highlight how one-way quantum computing provides a practical route to experimentally investigating the quantum-classical gap in the query complexity model.
From Schrödinger’s equation to the quantum search algorithm
Lov K Grover
2001-02-01
The quantum search algorithm is a technique for searching possibilities in only $O(\\sqrt{N})$ steps. Although the algorithm itself is widely known, not so well known is the series of steps that ﬁrst led to it, these are quite different from any of the generally known forms of the algorithm. This paper describes these steps, which start by discretizing Schrödinger’s equation. This paper also provides a self contained introduction to quantum computing algorithms from a new perspective.
Adiabatic optimization versus diffusion Monte Carlo methods
Jarret, Michael; Jordan, Stephen P.; Lackey, Brad
2016-10-01
Most experimental and theoretical studies of adiabatic optimization use stoquastic Hamiltonians, whose ground states are expressible using only real nonnegative amplitudes. This raises a question as to whether classical Monte Carlo methods can simulate stoquastic adiabatic algorithms with polynomial overhead. Here we analyze diffusion Monte Carlo algorithms. We argue that, based on differences between L1 and L2 normalized states, these algorithms suffer from certain obstructions preventing them from efficiently simulating stoquastic adiabatic evolution in generality. In practice however, we obtain good performance by introducing a method that we call Substochastic Monte Carlo. In fact, our simulations are good classical optimization algorithms in their own right, competitive with the best previously known heuristic solvers for MAX-k -SAT at k =2 ,3 ,4 .
Experimental realization of Deutsch's algorithm in a one-way quantum computer.
Tame, M S; Prevedel, R; Paternostro, M; Böhi, P; Kim, M S; Zeilinger, A
2007-04-06
We report the first experimental demonstration of an all-optical one-way implementation of Deutsch's quantum algorithm on a four-qubit cluster state. All the possible configurations of a balanced or constant function acting on a two-qubit register are realized within the measurement-based model for quantum computation. The experimental results are in excellent agreement with the theoretical model, therefore demonstrating the successful performance of the algorithm.
Extracting quantum dynamics from genetic learning algorithms through principal component analysis
White, J L; Bucksbaum, P H
2004-01-01
Genetic learning algorithms are widely used to control ultrafast optical pulse shapes for photo-induced quantum control of atoms and molecules. An outstanding issue is how to use the solutions found by these algorithms to learn about the system's quantum dynamics. We propose a simple method based on principal component analysis of the control space, which can reveal the degrees of freedom responsible for control, and aid in the construction of an effective Hamiltonian for the dynamics.
A better lower bound for quantum algorithms searching an ordered list
Ambainis, A
1999-01-01
We show that any quantum algorithm searching an ordered list of n elements needs to examine at least 1/12 log n-O(1) of them. Classically, log n queries are both necessary and sufficient. This shows that quantum algorithms can achieve only a constant speedup for this problem. Our result improves lower bounds of Buhrman and de Wolf(quant-ph/9811046) and Farhi, Goldstone, Gutmann and Sipser (quant-ph/9812057).
A probabilistic coding based quantum genetic algorithm for multiple sequence alignment.
Huo, Hongwei; Xie, Qiaoluan; Shen, Xubang; Stojkovic, Vojislav
2008-01-01
This paper presents an original Quantum Genetic algorithm for Multiple sequence ALIGNment (QGMALIGN) that combines a genetic algorithm and a quantum algorithm. A quantum probabilistic coding is designed for representing the multiple sequence alignment. A quantum rotation gate as a mutation operator is used to guide the quantum state evolution. Six genetic operators are designed on the coding basis to improve the solution during the evolutionary process. The features of implicit parallelism and state superposition in quantum mechanics and the global search capability of the genetic algorithm are exploited to get efficient computation. A set of well known test cases from BAliBASE2.0 is used as reference to evaluate the efficiency of the QGMALIGN optimization. The QGMALIGN results have been compared with the most popular methods (CLUSTALX, SAGA, DIALIGN, SB_PIMA, and QGMALIGN) results. The QGMALIGN results show that QGMALIGN performs well on the presenting biological data. The addition of genetic operators to the quantum algorithm lowers the cost of overall running time.
A reconstruction algorithm for compressive quantum tomography using various measurement sets.
Zheng, Kai; Li, Kezhi; Cong, Shuang
2016-12-14
Compressed sensing (CS) has been verified that it offers a significant performance improvement for large quantum systems comparing with the conventional quantum tomography approaches, because it reduces the number of measurements from O(d(2)) to O(rd log(d)) in particular for quantum states that are fairly pure. Yet few algorithms have been proposed for quantum state tomography using CS specifically, let alone basis analysis for various measurement sets in quantum CS. To fill this gap, in this paper an efficient and robust state reconstruction algorithm based on compressive sensing is developed. By leveraging the fixed point equation approach to avoid the matrix inverse operation, we propose a fixed-point alternating direction method algorithm for compressive quantum state estimation that can handle both normal errors and large outliers in the optimization process. In addition, properties of five practical measurement bases (including the Pauli basis) are analyzed in terms of their coherences and reconstruction performances, which provides theoretical instructions for the selection of measurement settings in the quantum state estimation. The numerical experiments show that the proposed algorithm has much less calculating time, higher reconstruction accuracy and is more robust to outlier noises than many existing state reconstruction algorithms.
A reconstruction algorithm for compressive quantum tomography using various measurement sets
Zheng, Kai; Li, Kezhi; Cong, Shuang
2016-12-01
Compressed sensing (CS) has been verified that it offers a significant performance improvement for large quantum systems comparing with the conventional quantum tomography approaches, because it reduces the number of measurements from O(d2) to O(rd log(d)) in particular for quantum states that are fairly pure. Yet few algorithms have been proposed for quantum state tomography using CS specifically, let alone basis analysis for various measurement sets in quantum CS. To fill this gap, in this paper an efficient and robust state reconstruction algorithm based on compressive sensing is developed. By leveraging the fixed point equation approach to avoid the matrix inverse operation, we propose a fixed-point alternating direction method algorithm for compressive quantum state estimation that can handle both normal errors and large outliers in the optimization process. In addition, properties of five practical measurement bases (including the Pauli basis) are analyzed in terms of their coherences and reconstruction performances, which provides theoretical instructions for the selection of measurement settings in the quantum state estimation. The numerical experiments show that the proposed algorithm has much less calculating time, higher reconstruction accuracy and is more robust to outlier noises than many existing state reconstruction algorithms.
Vélez, Mario; Ospina, Juan
2012-06-01
Possible quantum algorithms for generalized Khovanov homology and the Rasmussen's invariant are proposed. Such algorithms are resulting from adaptations of the recently proposed Kauffman's algorithm for the standard Khovanov homology. The method that was applied consists in to write the relevant quantum invariant as the trace of a certain unitary operator and then to compute the trace using the Hadamard test. We apply such method to the quantum computation of the Jones polynomial, HOMFLY polynomial, Chromatic polynomial, Tutte polynomial and Bollobàs- Riordan polynomial. These polynomials are quantum topological invariants for knots, links, graphs and ribbon graphs respectively. The Jones polynomial is categorified by the standard Khovanov homology and the others polynomials are categorified by generalized Khovanov homologies, such as the Khovanov-Rozansky homology and the graph homologies. The algorithm for the Rasmussen's invariant is obtained using the gauge theory; and the recently introduced program of homotopyfication is linked with the super-symmetric quantum mechanics. It is claimed that a new program of analytification could be development from the homotopyfication using the celebrated Atiyah-Singer theorem and its super-symmetric interpretations. It is hoped that the super-symmetric quantum mechanics provides the hardware for the implementation of the proposed quantum algorithms.
Eavesdropping in a quantum secret sharing protocol based on Grover algorithm and its solution
无
2010-01-01
A detailed analysis has showed that the quantum secret sharing protocol based on the Grover algorithm (Phys Rev A, 2003, 68: 022306) is insecure. A dishonest receiver may obtain the full information without being detected. A quantum secret-sharing protocol is presents here, which mends the security loophole of the original secret-sharing protocol, and doubles the information capacity.
Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer.
Gulde, Stephan; Riebe, Mark; Lancaster, Gavin P T; Becher, Christoph; Eschner, Jürgen; Häffner, Hartmut; Schmidt-Kaler, Ferdinand; Chuang, Isaac L; Blatt, Rainer
2003-01-02
Determining classically whether a coin is fair (head on one side, tail on the other) or fake (heads or tails on both sides) requires an examination of each side. However, the analogous quantum procedure (the Deutsch-Jozsa algorithm) requires just one examination step. The Deutsch-Jozsa algorithm has been realized experimentally using bulk nuclear magnetic resonance techniques, employing nuclear spins as quantum bits (qubits). In contrast, the ion trap processor utilises motional and electronic quantum states of individual atoms as qubits, and in principle is easier to scale to many qubits. Experimental advances in the latter area include the realization of a two-qubit quantum gate, the entanglement of four ions, quantum state engineering and entanglement-enhanced phase estimation. Here we exploit techniques developed for nuclear magnetic resonance to implement the Deutsch-Jozsa algorithm on an ion-trap quantum processor, using as qubits the electronic and motional states of a single calcium ion. Our ion-based implementation of a full quantum algorithm serves to demonstrate experimental procedures with the quality and precision required for complex computations, confirming the potential of trapped ions for quantum computation.
Quantum Algorithm for K-Nearest Neighbors Classification Based on the Metric of Hamming Distance
Ruan, Yue; Xue, Xiling; Liu, Heng; Tan, Jianing; Li, Xi
2017-08-01
K-nearest neighbors (KNN) algorithm is a common algorithm used for classification, and also a sub-routine in various complicated machine learning tasks. In this paper, we presented a quantum algorithm (QKNN) for implementing this algorithm based on the metric of Hamming distance. We put forward a quantum circuit for computing Hamming distance between testing sample and each feature vector in the training set. Taking advantage of this method, we realized a good analog for classical KNN algorithm by setting a distance threshold value t to select k - n e a r e s t neighbors. As a result, QKNN achieves O(n 3) performance which is only relevant to the dimension of feature vectors and high classification accuracy, outperforms Llyod's algorithm (Lloyd et al. 2013) and Wiebe's algorithm (Wiebe et al. 2014).
Behera, H S; Sahu, Sabyasachi; Bhoi, Sourav Kumar
2011-01-01
CPU being considered a primary computer resource, its scheduling is central to operating-system design. A thorough performance evaluation of various scheduling algorithms manifests that Round Robin Algorithm is considered as optimal in time shared environment because the static time is equally shared among the processes. We have proposed an efficient technique in the process scheduling algorithm by using dynamic time quantum in Round Robin. Our approach is based on the calculation of time quantum twice in single round robin cycle. Taking into consideration the arrival time, we implement the algorithm. Experimental analysis shows better performance of this improved algorithm over the Round Robin algorithm and the Shortest Remaining Burst Round Robin algorithm. It minimizes the overall number of context switches, average waiting time and average turn-around time. Consequently the throughput and CPU utilization is better.
Possible quantum algorithms for the Bollobas-Riordan-Tutte polynomial of a ribbon graph
Vélez, Mario; Ospina, Juan
2008-04-01
Three possible quantum algorithms, for the computation of the Bollobás-Riordan-Tutte polynomial of a given ribbon graph, are presented and discussed. The first possible algorithm is based on the spanning quasi-trees expansion for generalized Tutte polynomials of generalized graphs and on a quantum version of the Binary Decision Diagram (BDD) for quasi-trees . The second possible algorithm is based on the relation between the Kauffman bracket and the Tutte polynomial; and with an application of the recently introduced Aharonov-Arad-Eban-Landau quantum algorithm. The third possible algorithm is based on the relation between the HOMFLY polynomial and the Tutte polynomial; and with an application of the Wocjan-Yard quantum algorithm. It is claimed that these possible algorithms may be more efficient that the best known classical algorithms. These three algorithms may have interesting applications in computer science at general or in computational biology and bio-informatics in particular. A line for future research based on the categorification project is mentioned.
Adiabatic and Non-adiabatic quenches in a Spin-1 Bose Einstein Condensate
Boguslawski, Matthew; Hebbe Madhusudhana, Bharath; Anquez, Martin; Robbins, Bryce; Barrios, Maryrose; Hoang, Thai; Chapman, Michael
2016-05-01
A quantum phase transition (QPT) is observed in a wide range of phenomena. We have studied the dynamics of a spin-1 ferromagnetic Bose-Einstein condensate for both adiabatic and non-adiabatic quenches through a QPT. At the quantum critical point (QCP), finite size effects lead to a non-zero gap, which makes an adiabatic quench possible through the QPT. We experimentally demonstrate such a quench, which is forbidden at the mean field level. For faster quenches through the QCP, the vanishing energy gap causes the reaction timescale of the system to diverge, preventing the system from adiabatically following the ground state. We measure the temporal evolution of the spin populations for different quench speeds and determine the exponents characterizing the scaling of the onset of excitations, which are in good agreement with the predictions of Kibble-Zurek mechanism.
Research on Quantum Genetic Algorithm%量子遗传算法研究
白小宝
2013-01-01
量子遗传算法是在遗传算法中引入量子计算的概念，是20世纪90年代新兴的研究领域。介绍了遗传算法(GA)和量子算法(QC)的特点，以及量子遗传算法(QGA)的基本理论与方法。并在Matlab下编程对量子遗传算法与传统遗传算法的效率进行比较。%Quantum genetic algorithm is a genetic algorithm introduced the concept of quantum computing,it is the emerging field of research in the 90s of the last century. This article describes the characteristics of the genetic algorithm (GA)and quantum algorithm (QC),and the basic theory and method of the quantum genetic algorithm (QGA). To compare the efficiency of quantum genetic algorithm and the traditional genetic algorithm we program in matlab.
Singlet state creation and Universal quantum computation in NMR using Genetic Algorithm
Manu, V S
2012-01-01
Experimental implementation of a quantum algorithm requires unitary operator decomposition. Here we treat the unitary operator decomposition as an optimization problem and use Genetic Algorithm, a global optimization method inspired by nature's evolutionary process for operator decomposition. As an application, we apply this to NMR Quantum Information Processing and find a probabilistic way of doing universal quantum computation using global hard pulses. We also demonstrate efficient creation of singlet state (as a special case of Bell state) directly from thermal equilibrium using an optimum sequence of pulses.
Experimental realization of quantum algorithm for solving linear systems of equations
Pan, Jian; Cao, Yudong; Yao, Xiwei; Li, Zhaokai; Ju, Chenyong; Chen, Hongwei; Peng, Xinhua; Kais, Sabre; Du, Jiangfeng
2014-02-01
Many important problems in science and engineering can be reduced to the problem of solving linear equations. The quantum algorithm discovered recently indicates that one can solve an N-dimensional linear equation in O (logN) time, which provides an exponential speedup over the classical counterpart. Here we report an experimental demonstration of the quantum algorithm when the scale of the linear equation is 2×2 using a nuclear magnetic resonance quantum information processor. For all sets of experiments, the fidelities of the final four-qubit states are all above 96%. This experiment gives the possibility of solving a series of practical problems related to linear systems of equations and can serve as the basis to realize many potential quantum algorithms.
Combinatorial Clustering Algorithm of Quantum-Behaved Particle Swarm Optimization and Cloud Model
Mi-Yuan Shan
2013-01-01
Full Text Available We propose a combinatorial clustering algorithm of cloud model and quantum-behaved particle swarm optimization (COCQPSO to solve the stochastic problem. The algorithm employs a novel probability model as well as a permutation-based local search method. We are setting the parameters of COCQPSO based on the design of experiment. In the comprehensive computational study, we scrutinize the performance of COCQPSO on a set of widely used benchmark instances. By benchmarking combinatorial clustering algorithm with state-of-the-art algorithms, we can show that its performance compares very favorably. The fuzzy combinatorial optimization algorithm of cloud model and quantum-behaved particle swarm optimization (FCOCQPSO in vague sets (IVSs is more expressive than the other fuzzy sets. Finally, numerical examples show the clustering effectiveness of COCQPSO and FCOCQPSO clustering algorithms which are extremely remarkable.
Energy efficiency of adiabatic superconductor logic
Takeuchi, Naoki; Yamanashi, Yuki; Yoshikawa, Nobuyuki
2015-01-01
Adiabatic superconductor logic (ASL), including adiabatic quantum-flux-parametron (AQFP) logic, exhibits high energy efficiency because its bit energy can be decreased below the thermal energy through adiabatic switching operations. In the present paper, we present the general scaling laws of ASL and compare the energy efficiency of ASL with those of other energy-efficient logics. Also, we discuss the minimum energy-delay product (EDP) of ASL at finite temperature. Our study shows that there is a maximum temperature at which the EDP can reach the quantum limit given by ħ/2, which is dependent on the superconductor material and the Josephson junction quality, and that it is reasonable to operate ASL at cryogenic temperatures in order to achieve an EDP that approaches ħ/2.
Experimental investigation of Demon-like Algorithmic Quantum Cooling and its Applications
Li, Chuan-Feng
2015-03-01
Simulation of the low-temperature properties of many-body systems remains one of the major challenges in theoretical and experimental quantum information science. Firstly we demonstrate experimentally a Demon-like algorithmic cooling method that is applicable to any physical system that can be simulated by a quantum computer. This method allows us to distil and eliminate hot components of quantum states like a quantum Maxwell's demon. The experimental implementation is realized with a quantum optical network, and the results are in full agreement with theoretical predictions (with fidelity higher than 0.978). Secondly, we use the demon-like algorithmic cooling method to experimentally investigate Majorana zero modes exhibiting a fundamental property of non-Abelian statistics. This work was supported by the National Basic Research Program of China (2011CB921200), the CAS, The National Natural Science Foundaton of China.
Quantum Partial Searching Algorithm of a Database with Several Target Items
ZHONG Pu-Cha; BAO Wan-Su; WEI Yun
2009-01-01
Choi and Korepin [Quantum Information Processing 6(2007)243] presented a quantum partial search algorithm of a database with several target items which can find a target block quickly when each target block contains the same number of target items. Actually, the number of target items in each target block is arbitrary. Aiming at this case, we give a condition to guarantee performance of the partial search algorithm to be performed and the number of queries to oracle of the algorithm to be minimized. In addition, by further numerical computing we come to the conclusion that the more uniform the distribution of target items, the smaller the number of queries.
A Scheme to Share Information via Employing Discrete Algorithm to Quantum States*
KANG Guo-Dong; FANG Mao-Fa
2011-01-01
We propose a protocol for information sharing between two legitimate parties (Bob and Alice) via public-key cryptography. In particular, we specialize the protocol by employing discrete algorithm under mod that maps integers to quantum states via photon rotations. Based on this algorithm, we find that the protocol is secure under various classes of attacks. Specially, owe to the algorithm, the security of the classical privacy contained in the quantum public-key and the corresponding ciphertext is guaranteed. And the protocol is robust against the impersonation attack and the active wiretapping attack by designing particular checking processing, thus the protocol is valid.
General A Scheme to Share Information via Employing Discrete Algorithm to Quantum States
Kang, Guo-Dong; Fang, Mao-Fa
2011-02-01
We propose a protocol for information sharing between two legitimate parties (Bob and Alice) via public-key cryptography. In particular, we specialize the protocol by employing discrete algorithm under mod that maps integers to quantum states via photon rotations. Based on this algorithm, we find that the protocol is secure under various classes of attacks. Specially, owe to the algorithm, the security of the classical privacy contained in the quantum public-key and the corresponding ciphertext is guaranteed. And the protocol is robust against the impersonation attack and the active wiretapping attack by designing particular checking processing, thus the protocol is valid.
An Improved Quantum-Inspired Genetic Algorithm for Image Multilevel Thresholding Segmentation
Jian Zhang
2014-01-01
Full Text Available A multilevel thresholding algorithm for histogram-based image segmentation is presented in this paper. The proposed algorithm introduces an adaptive adjustment strategy of the rotation angle and a cooperative learning strategy into quantum genetic algorithm (called IQGA. An adaptive adjustment strategy of the quantum rotation which is introduced in this study helps improving the convergence speed, search ability, and stability. Cooperative learning enhances the search ability in the high-dimensional solution space by splitting a high-dimensional vector into several one-dimensional vectors. The experimental results demonstrate good performance of the IQGA in solving multilevel thresholding segmentation problem by compared with QGA, GA and PSO.
Graphene-based room-temperature implementation of a modified Deutsch-Jozsa quantum algorithm.
Dragoman, Daniela; Dragoman, Mircea
2015-12-04
We present an implementation of a one-qubit and two-qubit modified Deutsch-Jozsa quantum algorithm based on graphene ballistic devices working at room temperature. The modified Deutsch-Jozsa algorithm decides whether a function, equivalent to the effect of an energy potential distribution on the wave function of ballistic charge carriers, is constant or not, without measuring the output wave function. The function need not be Boolean. Simulations confirm that the algorithm works properly, opening the way toward quantum computing at room temperature based on the same clean-room technologies as those used for fabrication of very-large-scale integrated circuits.
A novel quantum random number generation algorithm used by smartphone camera
Wu, Nan; Wang, Kun; Hu, Haixing; Song, Fangmin; Li, Xiangdong
2015-05-01
We study an efficient algorithm to extract quantum random numbers (QRN) from the raw data obtained by charge-coupled device (CCD) or complementary metal-oxide semiconductor (CMOS) based sensors, like a camera used in a commercial smartphone. Based on NIST statistical test for random number generators, the proposed algorithm has a high QRN generation rate and high statistical randomness. This algorithm provides a kind of simple, low-priced and reliable devices as a QRN generator for quantum key distribution (QKD) or other cryptographic applications.
Optimized quantum random-walk search algorithm for multi-solution search
张宇超; 鲍皖苏; 汪翔; 付向群
2015-01-01
This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the search on the graph to the multi-solution case, it can be applied to analyze the multi-solution case of quantum random-walk search on the graph directly. Thus, the computational complexity of the optimized quantum random-walk search algorithm for the multi-solution search is obtained. Through numerical simulations and analysis, we obtain a critical value of the proportion of solutions q. For a given q, we derive the relationship between the success rate of the algorithm and the number of iterations when q is no longer than the critical value.
Dorai, Kavita; Arvind; Kumar, Anil
2001-01-01
We describe the experimental implementation of a recently proposed quantum algorithm involving quantum entanglement at the level of two qubits using NMR. The algorithm solves a generalisation of the Deutsch problem and distinguishes between even and odd functions using fewer function calls than is possible classically. The manipulation of entangled states of the two qubits is essential here, unlike the Deutsch-Jozsa algorithm and the Grover's search algorithm for two bits.
Subotnik, Joseph E., E-mail: subotnik@sas.upenn.edu; Ouyang, Wenjun; Landry, Brian R. [Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States)
2013-12-07
In this article, we demonstrate that Tully's fewest-switches surface hopping (FSSH) algorithm approximately obeys the mixed quantum-classical Liouville equation (QCLE), provided that several conditions are satisfied – some major conditions, and some minor. The major conditions are: (1) nuclei must be moving quickly with large momenta; (2) there cannot be explicit recoherences or interference effects between nuclear wave packets; (3) force-based decoherence must be added to the FSSH algorithm, and the trajectories can no longer rigorously be independent (though approximations for independent trajectories are possible). We furthermore expect that FSSH (with decoherence) will be most robust when nonadiabatic transitions in an adiabatic basis are dictated primarily by derivative couplings that are presumably localized to crossing regions, rather than by small but pervasive off-diagonal force matrix elements. In the end, our results emphasize the strengths of and possibilities for the FSSH algorithm when decoherence is included, while also demonstrating the limitations of the FSSH algorithm and its inherent inability to follow the QCLE exactly.
Improved mapping of the travelling salesman problem for quantum annealing
Troyer, Matthias; Heim, Bettina; Brown, Ethan; Wecker, David
2015-03-01
We consider the quantum adiabatic algorithm as applied to the travelling salesman problem (TSP). We introduce a novel mapping of TSP to an Ising spin glass Hamiltonian and compare it to previous known mappings. Through direct perturbative analysis, unitary evolution, and simulated quantum annealing, we show this new mapping to be significantly superior. We discuss how this advantage can translate to actual physical implementations of TSP on quantum annealers.
A fast and efficient algorithm for Slater determinant updates in quantum Monte Carlo simulations.
Nukala, Phani K V V; Kent, P R C
2009-05-28
We present an efficient low-rank updating algorithm for updating the trial wave functions used in quantum Monte Carlo (QMC) simulations. The algorithm is based on low-rank updating of the Slater determinants. In particular, the computational complexity of the algorithm is O(kN) during the kth step compared to traditional algorithms that require O(N(2)) computations, where N is the system size. For single determinant trial wave functions the new algorithm is faster than the traditional O(N(2)) Sherman-Morrison algorithm for up to O(N) updates. For multideterminant configuration-interaction-type trial wave functions of M+1 determinants, the new algorithm is significantly more efficient, saving both O(MN(2)) work and O(MN(2)) storage. The algorithm enables more accurate and significantly more efficient QMC calculations using configuration-interaction-type wave functions.
A Nonhomogeneous Cuckoo Search Algorithm Based on Quantum Mechanism for Real Parameter Optimization.
Cheung, Ngaam J; Ding, Xue-Ming; Shen, Hong-Bin
2017-02-01
Cuckoo search (CS) algorithm is a nature-inspired search algorithm, in which all the individuals have identical search behaviors. However, this simple homogeneous search behavior is not always optimal to find the potential solution to a special problem, and it may trap the individuals into local regions leading to premature convergence. To overcome the drawback, this paper presents a new variant of CS algorithm with nonhomogeneous search strategies based on quantum mechanism to enhance search ability of the classical CS algorithm. Featured contributions in this paper include: 1) quantum-based strategy is developed for nonhomogeneous update laws and 2) we, for the first time, present a set of theoretical analyses on CS algorithm as well as the proposed algorithm, respectively, and conclude a set of parameter boundaries guaranteeing the convergence of the CS algorithm and the proposed algorithm. On 24 benchmark functions, we compare our method with five existing CS-based methods and other ten state-of-the-art algorithms. The numerical results demonstrate that the proposed algorithm is significantly better than the original CS algorithm and the rest of compared methods according to two nonparametric tests.
Constructing quantum circuits for maximally entangled multi-qubit states using the genetic algorithm
Fan, Zheyong; Goertzel, Ben; Ren, Zhongzhou; Zeng, Huabi
2010-01-01
Numerical optimization methods such as hillclimbing and simulated annealing have been applied to search for highly entangled multi-qubit states. Here the genetic algorithm is applied to this optimization problem -- to search not only for highly entangled states, but also for the corresponding quantum circuits creating these states. Simple quantum circuits for maximally (highly) entangled states are discovered for 3, 4, 5, and 6-qubit systems; and extension of the method to systems with more qubits is discussed. Among other results we have found explicit quantum circuits for maximally entangled 5 and 6-qubit circuits, with only 8 and 13 quantum gates respectively. One significant advantage of our method over previous ones is that it allows very simple construction of quantum circuits based on the quantum states found.
Kampermann, H; Veeman, W S
2005-06-01
NMR quantum computing with qubit systems represented by nuclear spins (I=12) in small molecules in liquids has led to the most successful experimental quantum information processors so far. We use the quadrupolar spin-32 sodium nuclei of a NaNO3 single crystal as a virtual two-qubit system. The large quadrupolar coupling in comparison with the environmental interactions and the usage of strongly modulating pulses allow us to manipulate the system fast enough and at the same time keeping the decoherence reasonably slow. The experimental challenge is to characterize the "calculation" behavior of the quantum processor by process tomography which is here adapted to the quadrupolar spin system. The results of a selection of quantum gates and algorithms are presented as well as a detailed analysis of experimental results.
Isothermal and Adiabatic Measurements.
McNairy, William W.
1996-01-01
Describes the working of the Adiabatic Gas Law Apparatus, a useful tool for measuring the pressure, temperature, and volume of a variety of gases undergoing compressions and expansions. Describes the adaptation of this apparatus to perform isothermal measurements and discusses the theory behind the adiabatic and isothermal processes. (JRH)
Appearance of gauge fields and forces beyond the adiabatic approximation
Gosselin, Pierre [Institut Fourier, UMR 5582 CNRS-UJF, UFR de Mathematiques, Universite Grenoble I, BP74, 38402 Saint Martin d' Heres, Cedex (France); Mohrbach, Herve, E-mail: mohrbach@univ-metz.f [Laboratoire de Physique Moleculaire et des Collisions, ICPMB-FR CNRS 2843, Universite Paul Verlaine-Metz, 57078 Metz Cedex 3 (France)
2010-09-03
We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered in studies of the Born-Oppenheimer approximation to arbitrary quantum systems described by matrix-valued quantum Hamiltonians. The results are illustrated by several physical relevant examples.
Amin Qorbani
2011-12-01
Full Text Available Fractal Image Compression is a well-known problem which is in the class of NP-Hard problems.Quantum Evolutionary Algorithm is a novel optimization algorithm which uses a probabilisticrepresentation for solutions and is highly suitable for combinatorial problems like Knapsack problem.Genetic algorithms are widely used for fractal image compression problems, but QEA is not used for thiskind of problems yet. This paper improves QEA whit change population size and used it in fractal imagecompression. Utilizing the self-similarity property of a natural image, the partitioned iterated functionsystem (PIFS will be found to encode an image through Quantum Evolutionary Algorithm (QEA methodExperimental results show that our method has a better performance than GA and conventional fractalimage compression algorithms.
Shortcuts to adiabaticity in cutting a spin chain
Ren, Feng-Hua; Wang, Zhao-Ming; Gu, Yong-Jian
2017-01-01
"Shortcuts to adiabaticity" represents a strategy for accelerating a quantum adiabatic process, is useful for preparing or manipulating a quantum state. In this paper, we investigate the adiabaticity in the dynamics of an XY spin chain. During the process of cutting one long chain into two short chains, a "shortcut" can be obtained by applying a sequence of external pulses. The fidelity which measures the adiabaticity can be dramatically enhanced by increasing the pulse strength or pulse duration time. This reliability can be kept for different types of pulses, such as random pulse time interval or random strength. The free choice of the pulse can be explained by the adiabatic representation of the Hamiltonian, and it shows that the control effects are determined by the integral of the control function in the time domain.
Pang Chao-Yang; Hu Ben-Qiong
2008-01-01
The discrete Fourier transform(DFT)is the base of modern signal processing.1-dimensional fast Fourier transform (1D FFT)and 2D FFT have time complexity O(N log N)and O(N2 log N)respectively.Since 1965,there has been no more essential breakthrough for the design of fast DFT algorithm.DFT has two properties.One property is that DFT is energy conservation transform.The other property is that many DFT coefficients are close to zero.The basic idea of this paper is that the generalized Grover's iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy.One-dimensional quantum DFT(1D QDFT)and two-dimensional quantum DFT(2D QDFT)are presented in this paper.The quantum algorithm for convolution estimation is also presented in this paper.Compared with FFT,1D and 2D QDFT have time complexity O(√N)and O(N)respectively.QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible.