Quantum mechanics and computation; Quanta y Computacion
Energy Technology Data Exchange (ETDEWEB)
Cirac Sasturain, J. I.
2000-07-01
We review how some of the basic principles of Quantum Mechanics can be used in the field of computation. In particular, we explain why a quantum computer can perform certain tasks in a much more efficient way than the computers we have available nowadays. We give the requirements for a quantum system to be able to implement a quantum computer and illustrate these requirements in some particular physical situations. (Author) 16 refs.
Elucidating reaction mechanisms on quantum computers.
Reiher, Markus; Wiebe, Nathan; Svore, Krysta M; Wecker, Dave; Troyer, Matthias
2017-07-18
With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.
Helping Students Learn Quantum Mechanics for Quantum Computing
Singh, Chandralekha
2016-01-01
Quantum information science and technology is a rapidly growing interdisciplinary field drawing researchers from science and engineering fields. Traditional instruction in quantum mechanics is insufficient to prepare students for research in quantum computing because there is a lack of emphasis in the current curriculum on quantum formalism and dynamics. We are investigating the difficulties students have with quantum mechanics and are developing and evaluating quantum interactive learning tutorials (QuILTs) to reduce the difficulties. Our investigation includes interviews with individual students and the development and administration of free-response and multiple-choice tests. We discuss the implications of our research and development project on helping students learn quantum mechanics relevant for quantum computing.
Applications of computational quantum mechanics
Temel, Burcin
This original research dissertation is composed of a new numerical technique based on Chebyshev polynomials that is applied on scattering problems, a phenomenological kinetics study for CO oxidation on RuO2 surface, and an experimental study on methanol coupling with doped metal oxide catalysts. Minimum Error Method (MEM), a least-squares minimization method, provides an efficient and accurate alternative to solve systems of ordinary differential equations. Existing methods usually utilize matrix methods which are computationally costful. MEM, which is based on the Chebyshev polynomials as a basis set, uses the recursion relationships and fast Chebyshev transforms which scale as O(N). For large basis set calculations this provides an enormous computational efficiency in the calculations. Chebyshev polynomials are also able to represent non-periodic problems very accurately. We applied MEM on elastic and inelastic scattering problems: it is more efficient and accurate than traditionally used Kohn variational principle, and it also provides the wave function in the interaction region. Phenomenological kinetics (PK) is widely used in industry to predict the optimum conditions for a chemical reaction. PK neglects the fluctuations, assumes no lateral interactions, and considers an ideal mix of reactants. The rate equations are tested by fitting the rate constants to the results of the experiments. Unfortunately, there are numerous examples where a fitted mechanism was later shown to be erroneous. We have undertaken a thorough comparison between the phenomenological equations and the results of kinetic Monte Carlo (KMC) simulations performed on the same system. The PK equations are qualitatively consistent with the KMC results but are quantitatively erroneous as a result of interplays between the adsorption and desorption events. The experimental study on methanol coupling with doped metal oxide catalysts demonstrates the doped metal oxides as a new class of catalysts
Computations in quantum mechanics made easy
Korsch, H. J.; Rapedius, K.
2016-09-01
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of spectral and dynamical properties for one-dimensional and two-dimensional single-particle systems as well as bosonic many-particle and open quantum systems. Due to their technical simplicity these methods are well suited as a tool for teaching quantum mechanics to undergraduates and graduates. Explicit implementations of the presented numerical methods in Matlab are given.
Quantum ballistic evolution in quantum mechanics application to quantum computers
Benioff, P
1996-01-01
Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators T is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e. motion restricted to a collection of nonintersecting or distinct paths on an arbitrary basis. The main goal of this paper is proof of a theorem which gives necessary and sufficient conditions that T must satisfy so that there exists a Hamiltonian description of quantum ballistic evolution for the process, namely, that T is a partial isometry and is orthogonality preserving and stable on some basis. Simple examples of quantum ballistic evolution for quantum Turing machines with one and with more than one type of elementary step are discussed. It is seen that for nondeterministic machines the basis set can be quite complex with much entanglement present. It is also pr...
Quantum Mechanical Nature in Liquid NMR Quantum Computing
Institute of Scientific and Technical Information of China (English)
LONGGui－Lu; YANHai－Yang; 等
2002-01-01
The quantum nature of bulk ensemble NMR quantum computing-the center of recent heated debate,is addressed.Concepts of the mixed state and entanglement are examined,and the data in a two-qubit liquid NMR quantum computation are analyzed.the main points in this paper are;i) Density matrix describes the "state" of an average particle in an ensemble.It does not describe the state of an individual particle in an ensemble;ii) Entanglement is a property of the wave function of a microscopic particle(such as a molecule in a liquid NMR sample),and separability of the density matrix canot be used to measure the entanglement of mixed ensemble;iii) The state evolution in bulkensemble NMR quantum computation is quantum-mechanical;iv) The coefficient before the effective pure state density matrix,ε,is a measure of the simultaneity of the molecules in an ensemble,It reflets the intensity of the NMR signal and has no significance in quantifying the entanglement in the bulk ensemble NMR system.The decomposition of the density matrix into product states is only an indication that the ensemble can be prepared by an ensemble with the particles unentangeld.We conclude that effective-pure-state NMR quantum computation is genuine,not just classical simulations.
Lecture Script: Introduction to Computational Quantum Mechanics
Schmied, Roman
2014-01-01
This document is the lecture script of a one-semester course taught at the University of Basel in the Fall semesters of 2012 and 2013. It is aimed at advanced students of physics who are familiar with the concepts and notations of quantum mechanics. Quantum mechanics lectures can often be separated into two classes. In the first class you get to know Schroedinger's equation and find the form and dynamics of simple physical systems (square well, harmonic oscillator, hydrogen atom); most calculations are analytic and inspired by calculations originally done in the 1920s and 1930s. In the second class you learn about large systems such as molecular structures, crystalline solids, or lattice models; these calculations are usually so complicated that it is difficult for the student to understand them in all detail. This lecture tries to bridge the gap between simple analytic calculations and complicated large-scale computations. We will revisit most of the problems encountered in introductory quantum mechanics, fo...
Quantum Mechanical Nature in Liquid NMR Quantum Computing
Institute of Scientific and Technical Information of China (English)
LONG Gui-Lu; YAN Hai-Yang; LI Yan-Song; TU Chang-Cun; ZHU Sheng-Jiang; RUAN Dong; SUN Yang; TAO Jia-Xun; CHEN Hao-Ming
2002-01-01
The quantum nature of bulk ensemble NMR quantum computing the center of recent heated debate,is addressed. Concepts of the mixed state and entanglement are examined, and the data in a two-qubit liquid NMRquantum computation are analyzed. The main points in this paper are: i) Density matrix describes the "state" of anaverage particle in an ensemble. It does not describe the state of an individual particle in an ensemble; ii) Entanglementis a property of the wave function of a microscopic particle (such as a molecule in a liquid NMR sample), and separabilityof the density matrix cannot be used to measure the entanglement of mixed ensemble; iii) The state evolution in bulk-ensemble NMRquantum computation is quantum-mechanical; iv) The coefficient before the effective pure state densitymatrix, e, is a measure of the simultaneity of the molecules in an ensemble. It reflects the intensity of the NMR signaland has no significance in quantifying the entanglement in the bulk ensemble NMR system. The decomposition of thedensity matrix into product states is only an indication that the ensemble can be prepared by an ensemble with theparticles unentangled. We conclude that effective-pure-state NMR quantum computation is genuine, not just classicalsimulations.
Non-Mechanism in Quantum Oracle Computing
Castagnoli, G C
1999-01-01
A typical oracle problem is finding which software program is installed on a computer, by running the computer and testing its input-output behaviour. The program is randomly chosen from a set of programs known to the problem solver. As well known, some oracle problems are solved more efficiently by using quantum algorithms; this naturally implies changing the computer to quantum, while the choice of the software program remains sharp. In order to highlight the non-mechanistic origin of this higher efficiency, also the uncertainty about which program is installed must be represented in a quantum way.
Dorit Aharonov; Umesh Vazirani
2012-01-01
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity. We describe how QM can be tested in this regime by extending the usual scientific paradigm to include {\\it interactive experiments}.
Steane, A M
1998-01-01
The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarise not just quantum computing, but the whole subject of quantum information theory. It turns out that information theory and quantum mechanics fit together very well. In order to explain their relationship, the review begins with an introduction to classical information theory and computer science, including Shannon's theorem, error correcting codes, Turing machines and computational complexity. The principles of quantum mechanics are then outlined, and the EPR experiment described. The EPR-Bell correlations, and quantum entanglement in general, form the essential new ingredient which distinguishes quantum from classical information theory, and, arguably, quantum from classical physics. Basic quantum information ideas are described, including key distribution, teleportation, data compression, quantum error correction, the universal quantum computer and qua...
Interactive Quantum Mechanics Quantum Experiments on the Computer
Brandt, S; Dahmen, H.D
2011-01-01
Extra Materials available on extras.springer.com INTERACTIVE QUANTUM MECHANICS allows students to perform their own quantum-physics experiments on their computer, in vivid 3D color graphics. Topics covered include: • harmonic waves and wave packets, • free particles as well as bound states and scattering in various potentials in one and three dimensions (both stationary and time dependent), • two-particle systems, coupled harmonic oscillators, • distinguishable and indistinguishable particles, • coherent and squeezed states in time-dependent motion, • quantized angular momentum, • spin and magnetic resonance, • hybridization. For the present edition the physics scope has been widened appreciably. Moreover, INTERQUANTA can now produce user-defined movies of quantum-mechanical situations. Movies can be viewed directly and also be saved to be shown later in any browser. Sections on spec...
A Rosetta Stone for Quantum Mechanics with an Introduction to Quantum Computation
Lomonaco, S J
2000-01-01
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American Mathematical Society (AMS) Short Course on Quantum Computation held in conjunction with the Annual Meeting of the AMS in Washington, DC, USA in January 2000, and will appear in the AMS PSAPM volume entitled "Quantum Computation." Part 1 of the paper is an introduction the to the concept of the qubit. Part 2 gives an introduction to quantum mechanics covering such topics as Dirac notation, quantum measurement, Heisenberg uncertainty, Schrodinger's equation, density operators, partial trace, multipartite quantum systems, the Heisenberg versus the Schrodinger picture, quantum entanglement, EPR paradox, quantum entropy. Part 3 gives a brief ...
Statistical Mechanics of Classical and Quantum Computational Complexity
Laumann, C. R.; Moessner, R.; Scardicchio, A.; Sondhi, S. L.
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous framework for classifying the hardness of problems according to the computational resources, most notably time, needed to solve them. Its extension to quantum computers allows the relative power of quantum computers to be analyzed. This framework identifies families of problems which are likely hard for classical computers ("NP-complete") and those which are likely hard for quantum computers ("QMA-complete") by indirect methods. That is, they identify problems of comparable worst-case difficulty without directly determining the individual hardness of any given instance. Statistical mechanical methods can be used to complement this classification by directly extracting information about particular families of instances—typically those that involve optimization—by studying random ensembles of them. These pose unusual and interesting (quantum) statistical mechanical questions and the results shed light on the difficulty of problems for large classes of algorithms as well as providing a window on the contrast between typical and worst case complexity. In these lecture notes we present an introduction to this set of ideas with older work on classical satisfiability and recent work on quantum satisfiability as primary examples. We also touch on the connection of computational hardness with the physical notion of glassiness.
Spin Glass a Bridge Between Quantum Computation and Statistical Mechanics
Ohzeki, Masayuki
2013-09-01
In this chapter, we show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Interestingly, the theoretical limitation of the surface code, accuracy threshold, to restore the quantum state has a close connection with the problem on the phase transition in a special model known as spin glasses, which is one of the most active researches in statistical mechanics. The phase transition in spin glasses is an intractable problem, since we must strive many-body system with complicated interactions with change of their signs depending on the distance between spins. Fortunately, recent progress in spin-glass theory enables us to predict the precise location of the critical point, at which the phase transition occurs. It means that statistical mechanics is available for revealing one of the most interesting parts in quantum information processing. We show how to import the special tool in statistical mechanics into the problem on the accuracy threshold in quantum computation. Second, we show another interesting technique to employ quantum nature, quantum annealing. The purpose of quantum annealing is to search for the most favored solution of a multivariable function, namely optimization problem. The most typical instance is the traveling salesman problem to find the minimum tour while visiting all the cities. In quantum annealing, we introduce quantum fluctuation to drive a particular system with the artificial Hamiltonian, in which the ground state represents the optimal solution of the specific problem we desire to solve. Induction of the quantum fluctuation gives rise to the quantum tunneling effect, which allows nontrivial hopping from state to state. We then sketch a strategy to control the quantum fluctuation efficiently reaching the ground state. Such a generic framework is called
2010-03-04
efficient or less costly than their classical counterparts. A large-scale quantum computer is certainly an extremely ambi- tious goal, appearing to us...outperform the largest classical supercomputers in solving some specific problems important for data encryption. In the long term, another application...which the quantum computer depends, causing the quantum mechanically destructive process known as decoherence . Decoherence comes in several forms
Li, Shu-Shen; Long, Gui-lu; Bai, Feng-Shan; Feng, Song-Lin; Zheng, Hou-Zhi
2001-01-01
Quantum computing is a quickly growing research field. This article introduces the basic concepts of quantum computing, recent developments in quantum searching, and decoherence in a possible quantum dot realization.
Entanglement, thermalisation and stationarity The computational foundations of quantum mechanics
Guruprasad, V
2000-01-01
'Tis said, to know others is to be learned, to know oneself, wise - I demonstrate that it could be more fundamental than knowing the rest of nature, by applying classical computational principles and engineering hindsight to derive and explain quantum entanglement, state space formalism and the statistical nature of quantum mechanics. I show that an entangled photon pair is literally no more than a 1-bit hologram, that the quantum state formalism is completely derivable from general considerations of representation of physical information, and that both the probabilistic aspects of quantum theory and the constancy of h are exactly predicted by the thermodynamics of representation, without precluding a fundamental, relative difference in spatial scale between non-colocated observers, leading to logical foundations of relativity and cosmology that show the current thinking in that field to be simplistic and erroneous.
Fano, Guido
2017-01-01
This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell’s inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result...
Computational alanine scanning with linear scaling semiempirical quantum mechanical methods.
Diller, David J; Humblet, Christine; Zhang, Xiaohua; Westerhoff, Lance M
2010-08-01
Alanine scanning is a powerful experimental tool for understanding the key interactions in protein-protein interfaces. Linear scaling semiempirical quantum mechanical calculations are now sufficiently fast and robust to allow meaningful calculations on large systems such as proteins, RNA and DNA. In particular, they have proven useful in understanding protein-ligand interactions. Here we ask the question: can these linear scaling quantum mechanical methods developed for protein-ligand scoring be useful for computational alanine scanning? To answer this question, we assembled 15 protein-protein complexes with available crystal structures and sufficient alanine scanning data. In all, the data set contains Delta Delta Gs for 400 single point alanine mutations of these 15 complexes. We show that with only one adjusted parameter the quantum mechanics-based methods outperform both buried accessible surface area and a potential of mean force and compare favorably to a variety of published empirical methods. Finally, we closely examined the outliers in the data set and discuss some of the challenges that arise from this examination.
Quantum Computer Games: Quantum Minesweeper
Gordon, Michal; Gordon, Goren
2010-01-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…
Quantum Computer Games: Quantum Minesweeper
Gordon, Michal; Gordon, Goren
2010-01-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…
Quantum robots and quantum computers
Energy Technology Data Exchange (ETDEWEB)
Benioff, P.
1998-07-01
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and systems that carry out experiments. The description of quantum computers is under active development. No description of systems to carry out experiments has been given. A small step in this direction is taken here by giving a description of quantum robots as mobile systems with on board quantum computers that interact with different environments. Some properties of these systems are discussed. A specific model based on the literature descriptions of quantum Turing machines is presented.
Parallelism in computations in quantum and statistical mechanics
Clementi, E.; Corongiu, G.; Detrich, J. H.
1985-07-01
Often very fundamental biochemical and biophysical problems defy simulations because of limitations in today's computers. We present and discuss a distributed system composed of two IBM 4341s and/or an IBM 4381 as front-end processors and ten FPS-164 attached array processors. This parallel system - called LCAP - has presently a peak performance of about 110 Mflops; extensions to higher performance are discussed. Presently, the system applications use a modified version of VM/SP as the operating system: description of the modifications is given. Three applications programs have been migrated from sequential to parallel: a molecular quantum mechanical, a Metropolis-Monte Carlo and a molecular dynamics program. Descriptions of the parallel codes are briefly outlined. Use of these parallel codes has already opened up new capabilities for our research. The very positive performance comparisons with today's supercomputers allow us to conclude that parallel computers and programming, of the type we have considered, represent a pragmatic answer to many computationally intensive problems.
Automatic computation of quantum-mechanical bound states and wavefunctions
Ledoux, V.; Van Daele, M.
2013-04-01
We discuss the automatic solution of the multichannel Schrödinger equation. The proposed approach is based on the use of a CP method for which the step size is not restricted by the oscillations in the solution. Moreover, this CP method turns out to form a natural scheme for the integration of the Riccati differential equation which arises when introducing the (inverse) logarithmic derivative. A new Prüfer type mechanism which derives all the required information from the propagation of the inverse of the log-derivative, is introduced. It improves and refines the eigenvalue shooting process and implies that the user may specify the required eigenvalue by its index. Catalogue identifier: AEON_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEON_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/license/license.html No. of lines in distributed program, including test data, etc.: 3822 No. of bytes in distributed program, including test data, etc.: 119814 Distribution format: tar.gz Programming language: Matlab. Computer: Personal computer architectures. Operating system: Windows, Linux, Mac (all systems on which Matlab can be installed). RAM: Depends on the problem size. Classification: 4.3. Nature of problem: Computation of eigenvalues and eigenfunctions of multichannel Schrödinger equations appearing in quantum mechanics. Solution method: A CP-based propagation scheme is used to advance the R-matrix in a shooting process. The shooting algorithm is supplemented by a Prüfer type mechanism which allows the eigenvalues to be computed according to index: the user specifies an integer k≥0, and the code computes an approximation to the kth eigenvalue. Eigenfunctions are also available through an auxiliary routine, called after the eigenvalue has been determined. Restrictions: The program can only deal with non-singular problems. Additional
A Computational Model for Observation in Quantum Mechanics.
1987-03-16
Computer Science Technical Report No. 191, May 1986. [Feynman63j Feynman , R. P., Leighton, R. B., and Sands, M. The Feynman Lectures on Physics...MIT Artificial Intelligence Laboratory Memo 380, Sept. 1976. [Wheeler83] Wheeler , J. A., and Zurek, W. H. Quantum Theory and Measuremrent 72 .4
Mandl, F.
1992-07-01
The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett Quantum Mechanics aims to teach those parts of the subject which every physicist should know. The object is to display the inherent structure of quantum mechanics, concentrating on general principles and on methods of wide applicability without taking them to their full generality. This book will equip students to follow quantum-mechanical arguments in books and scientific papers, and to cope with simple cases. To bring the subject to life, the theory is applied to the all-important field of atomic physics. No prior knowledge of quantum mechanics is assumed. However, it would help most readers to have met some elementary wave mechanics before. Primarily written for students, it should also be of interest to experimental research workers who require a good grasp of quantum mechanics without the full formalism needed by the professional theorist. Quantum Mechanics features: A flow diagram allowing topics to be studied in different orders or omitted altogether. Optional "starred" and highlighted sections containing more advanced and specialized material for the more ambitious reader. Sets of problems at the end of each chapter to help student understanding. Hints and solutions to the problems are given at the end of the book.
Quantum computing and probability.
Ferry, David K
2009-11-25
Over the past two decades, quantum computing has become a popular and promising approach to trying to solve computationally difficult problems. Missing in many descriptions of quantum computing is just how probability enters into the process. Here, we discuss some simple examples of how uncertainty and probability enter, and how this and the ideas of quantum computing challenge our interpretations of quantum mechanics. It is found that this uncertainty can lead to intrinsic decoherence, and this raises challenges for error correction.
Probing the Structure of Quantum Mechanics : Nonlinearity, Nonlocality, Computation and Axiomatics
Durt, Thomas; Czachor, Marek
2002-01-01
During the last decade, scientists working in quantum theory have been engaging in promising new fields such as quantum computation and quantum information processing, and have also been reflecting on the possibilities of nonlinear behavior on the quantum level. These are challenging undertakings because (1) they will result in new solutions to important technical and practical problems that were unsolvable by the classical approaches (for example, quantum computers can calculate problems that are intractable if one uses classical computers); and (2) they open up new 'hard' problems of a fundamental nature that touch the foundation of quantum theory itself (for example, the contradiction between locality and nonlinearity and the interpretation of quantum computing as a universal process). In this book, one can distinguish two main streams of research to approach the just-mentioned problem field: (1) a theoretical structural part, which concentrates on the elaboration of a nonlinear quantum mechanics and the ...
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this article,we make a review on the development of a newly proposed quantum computer,duality computer,or the duality quantum computer and the duality mode of quantum computers.The duality computer is based on the particle-wave duality principle of quantum mechanics.Compared to an ordinary quantum computer,the duality quantum computer is a quantum computer on the move and passing through a multi-slit.It offers more computing operations than is possible with an ordinary quantum computer.The most two distinct operations are:the quantum division operation and the quantum combiner operation.The division operation divides the wave function of a quantum computer into many attenuated,and identical parts.The combiner operation combines the wave functions in different parts into a single part.The duality mode is a way in which a quantum computer with some extra qubit resource simulates a duality computer.The main structure of duality quantum computer and duality mode,the duality mode,their mathematical description and algorithm designs are reviewed.
Ladd, T D; Jelezko, F; Laflamme, R; Nakamura, Y; Monroe, C; O'Brien, J L
2010-03-04
Over the past several decades, quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit unique quantum properties? Today it is understood that the answer is yes, and many research groups around the world are working towards the highly ambitious technological goal of building a quantum computer, which would dramatically improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for quantum computation. However, it remains unclear which technology, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain the major challenges for the future.
Noise in Quantum Devices: A Unified Computational Approach for Different Scattering Mechanisms
Marian, Damiano; Colomés, Enrique
2016-08-01
When talking about noise in quantum devices two issues must be faced: how to model the evolution of an electronic system with scattering and how this noise is practically computed in a quantum device simulator. In the present paper, we address both problems from a practical and computational point of view. In particular, as the electronic quantum subsystem is an open (normally far from equilibrium) system, we use the notion of conditional wave function, the wave function of a subsystem in Bohmian mechanics, an alternative version of quantum mechanics which along with the wave function posited definite positions for the particles. This allows us to define an effective equation in several physical situations, ranging from the simple tunneling barrier to the interaction with a bath of phonons. Finally, we present how this development can be used to compute quantum noise in a quantum device simulator.
Mandl, Franz
1992-01-01
The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scient
Combined quantum mechanics/molecular mechanics (QM/MM) methods in computational enzymology.
van der Kamp, Marc W; Mulholland, Adrian J
2013-04-23
Computational enzymology is a rapidly maturing field that is increasingly integral to understanding mechanisms of enzyme-catalyzed reactions and their practical applications. Combined quantum mechanics/molecular mechanics (QM/MM) methods are important in this field. By treating the reacting species with a quantum mechanical method (i.e., a method that calculates the electronic structure of the active site) and including the enzyme environment with simpler molecular mechanical methods, enzyme reactions can be modeled. Here, we review QM/MM methods and their application to enzyme-catalyzed reactions to investigate fundamental and practical problems in enzymology. A range of QM/MM methods is available, from cheaper and more approximate methods, which can be used for molecular dynamics simulations, to highly accurate electronic structure methods. We discuss how modeling of reactions using such methods can provide detailed insight into enzyme mechanisms and illustrate this by reviewing some recent applications. We outline some practical considerations for such simulations. Further, we highlight applications that show how QM/MM methods can contribute to the practical development and application of enzymology, e.g., in the interpretation and prediction of the effects of mutagenesis and in drug and catalyst design.
Quantum computer for dummies (in Russian)
Grozin, Andrey
2011-01-01
An introduction (in Russian) to quantum computers, quantum cryptography, and quantum teleportation for students who have no previous knowledge of these subjects, but know quantum mechanics. Several simple examples are considered in detail using the quantum computer emulator QCL.
Zak, M.
1998-01-01
Quantum analog computing is based upon similarity between mathematical formalism of quantum mechanics and phenomena to be computed. It exploits a dynamical convergence of several competing phenomena to an attractor which can represent an externum of a function, an image, a solution to a system of ODE, or a stochastic process.
Rae, Alastair I M
2016-01-01
A Thorough Update of One of the Most Highly Regarded Textbooks on Quantum Mechanics Continuing to offer an exceptionally clear, up-to-date treatment of the subject, Quantum Mechanics, Sixth Edition explains the concepts of quantum mechanics for undergraduate students in physics and related disciplines and provides the foundation necessary for other specialized courses. This sixth edition builds on its highly praised predecessors to make the text even more accessible to a wider audience. It is now divided into five parts that separately cover broad topics suitable for any general course on quantum mechanics. New to the Sixth Edition * Three chapters that review prerequisite physics and mathematics, laying out the notation, formalism, and physical basis necessary for the rest of the book * Short descriptions of numerous applications relevant to the physics discussed, giving students a brief look at what quantum mechanics has made possible industrially and scientifically * Additional end-of-chapter problems with...
Computing pKa Values with a Mixing Hamiltonian Quantum Mechanical/Molecular Mechanical Approach.
Liu, Yang; Fan, Xiaoli; Jin, Yingdi; Hu, Xiangqian; Hu, Hao
2013-09-10
Accurate computation of the pKa value of a compound in solution is important but challenging. Here, a new mixing quantum mechanical/molecular mechanical (QM/MM) Hamiltonian method is developed to simulate the free-energy change associated with the protonation/deprotonation processes in solution. The mixing Hamiltonian method is designed for efficient quantum mechanical free-energy simulations by alchemically varying the nuclear potential, i.e., the nuclear charge of the transforming nucleus. In pKa calculation, the charge on the proton is varied in fraction between 0 and 1, corresponding to the fully deprotonated and protonated states, respectively. Inspired by the mixing potential QM/MM free energy simulation method developed previously [H. Hu and W. T. Yang, J. Chem. Phys. 2005, 123, 041102], this method succeeds many advantages of a large class of λ-coupled free-energy simulation methods and the linear combination of atomic potential approach. Theory and technique details of this method, along with the calculation results of the pKa of methanol and methanethiol molecules in aqueous solution, are reported. The results show satisfactory agreement with the experimental data.
Ahn, Doyeol
2011-01-01
A clear introduction to quantum mechanics concepts Quantum mechanics has become an essential tool for modern engineering, particularly due to the recent developments in quantum computing as well as the rapid progress in optoelectronic devices. Engineering Quantum Mechanics explains the fundamentals of this exciting field, providing broad coverage of both traditional areas such as semiconductor and laser physics as well as relatively new yet fast-growing areas such as quantum computation and quantum information technology. The book begins with basic quantum mechanics, reviewing measurements and probability, Dirac formulation, the uncertainty principle, harmonic oscillator, angular momentum eigenstates, and perturbation theory. Then, quantum statistical mechanics is explored, from second quantization and density operators to coherent and squeezed states, coherent interactions between atoms and fields, and the Jaynes-Cummings model. From there, the book moves into elementary and modern applications, discussing s...
Quantum computing: towards reality
Trabesinger, Andreas
2017-03-01
The concept of computers that harness the laws of quantum mechanics has transformed our thinking about how information can be processed. Now the environment exists to make prototype devices a reality.
Powell, John L
2015-01-01
Suitable for advanced undergraduates, this thorough text focuses on the role of symmetry operations and the essentially algebraic structure of quantum-mechanical theory. Based on courses in quantum mechanics taught by the authors, the treatment provides numerous problems that require applications of theory and serve to supplement the textual material.Starting with a historical introduction to the origins of quantum theory, the book advances to discussions of the foundations of wave mechanics, wave packets and the uncertainty principle, and an examination of the Schrödinger equation that includ
Advanced Visual Quantum Mechanics
Thaller, Bernd
2005-01-01
Advanced Visual Quantum Mechanics is a systematic effort to investigate and to teach quantum mechanics with the aid of computer-generated animations. It is a self-contained textbook that combines selected topics from atomic physics (spherical symmetry, the hydrogen atom, and particles with spin) with an introduction to quantum information theory (qubits, EPR paradox, teleportation, quantum computers). It explores relativistic quantum mechanics and the strange behavior of Dirac equation solutions. A series of appendices covers important topics from perturbation and scattering theory. The book places an emphasis on ideas and concepts, with a fair to moderate amount of mathematical rigor. Though this book stands alone, it can also be paired with Thaller Visual Quantum Mechanics to form a comprehensive course in quantum mechanics. The software for the first book earned the European Academic Software Award 2000 for outstanding innovation in its field.
Bolemon, Jay S.; Etzold, David J.
1974-01-01
Discusses the use of a small computer to solve self-consistent field problems of one-dimensional systems of two or more interacting particles in an elementary quantum mechanics course. Indicates that the calculation can serve as a useful introduction to the iterative technique. (CC)
Quantum Computing for Quantum Chemistry
2010-09-01
This three-year project consisted on the development and application of quantum computer algorithms for chemical applications. In particular, we developed algorithms for chemical reaction dynamics, electronic structure and protein folding. The first quantum computing for
Fitzpatrick, Richard
2015-01-01
Quantum mechanics was developed during the first few decades of the twentieth century via a series of inspired guesses made by various physicists, including Planck, Einstein, Bohr, Schroedinger, Heisenberg, Pauli, and Dirac. All these scientists were trying to construct a self-consistent theory of microscopic dynamics that was compatible with experimental observations. The purpose of this book is to present quantum mechanics in a clear, concise, and systematic fashion, starting from the fundamental postulates, and developing the theory in as logical manner as possible. Topics covered in the book include the fundamental postulates of quantum mechanics, angular momentum, time-dependent and time-dependent perturbation theory, scattering theory, identical particles, and relativistic electron theory.
Ghosh, P K
2014-01-01
Quantum mechanics, designed for advanced undergraduate and graduate students of physics, mathematics and chemistry, provides a concise yet self-contained introduction to the formal framework of quantum mechanics, its application to physical problems and the interpretation of the theory. Starting with a review of some of the necessary mathematics, the basic concepts are carefully developed in the text. After building a general formalism, detailed treatment of the standard material - the harmonic oscillator, the hydrogen atom, angular momentum theory, symmetry transformations, approximation methods, identical particle and many-particle systems, and scattering theory - is presented. The concluding chapter discusses the interpretation of quantum mechanics. Some of the important topics discussed in the book are the rigged Hilbert space, deformation quantization, path integrals, coherent states, geometric phases, decoherene, etc. This book is characterized by clarity and coherence of presentation.
Energy Technology Data Exchange (ETDEWEB)
Suhai, Sandor [German Cancer Research Center, Heidelberg
2011-01-01
Retinal proteins are excellent systems for understanding essential physiological processes such as signal transduction and ion pumping. Although the conjugated polyene system of the retinal chromophore is best described with quantum mechanics, simulations of the long-timescale dynamics of a retinal protein in its physiological, flexible, lipid-membrane environment can only be performed at the classical mechanical level. Torsional energy barriers are a critical ingredient of the classical force-field parameters. Here we review briefly current retinal force fields and discuss new quantum mechanical computations to assess how the retinal Schiff base model and the approach used to derive the force-field parameters may influence the torsional potentials.
Duality Computing in Quantum Computers
Institute of Scientific and Technical Information of China (English)
LONG Gui-Lu; LIU Yang
2008-01-01
In this letter, we propose a duality computing mode, which resembles particle-wave duality property when a quantum system such as a quantum computer passes through a double-slit. In this mode, computing operations are not necessarily unitary. The duality mode provides a natural link between classical computing and quantum computing. In addition, the duality mode provides a new tool for quantum algorithm design.
Quantum Computing, Metrology, and Imaging
Lee, H; Dowling, J P; Lee, Hwang; Lougovski, Pavel; Dowling, Jonathan P.
2005-01-01
Information science is entering into a new era in which certain subtleties of quantum mechanics enables large enhancements in computational efficiency and communication security. Naturally, precise control of quantum systems required for the implementation of quantum information processing protocols implies potential breakthoughs in other sciences and technologies. We discuss recent developments in quantum control in optical systems and their applications in metrology and imaging.
Rae, Alastair I M
2007-01-01
PREFACESINTRODUCTION The Photoelectric Effect The Compton Effect Line Spectra and Atomic Structure De Broglie Waves Wave-Particle Duality The Rest of This Book THE ONE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Time-Dependent Schrödinger Equation The Time-Independent Schrödinger Equation Boundary ConditionsThe Infinite Square Well The Finite Square Well Quantum Mechanical Tunneling The Harmonic Oscillator THE THREE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Wave Equations Separation in Cartesian Coordinates Separation in Spherical Polar Coordinates The Hydrogenic Atom THE BASIC POSTULATES OF QUANTUM MEC
Zagoskin, Alexandre
2015-01-01
Written by Dr Alexandre Zagoskin, who is a Reader at Loughborough University, Quantum Mechanics: A Complete Introduction is designed to give you everything you need to succeed, all in one place. It covers the key areas that students are expected to be confident in, outlining the basics in clear jargon-free English, and then providing added-value features like summaries of key ideas, and even lists of questions you might be asked in your exam. The book uses a structure that is designed to make quantum physics as accessible as possible - by starting with its similarities to Newtonian physics, ra
Quantum Computing for Computer Architects
Metodi, Tzvetan
2011-01-01
Quantum computers can (in theory) solve certain problems far faster than a classical computer running any known classical algorithm. While existing technologies for building quantum computers are in their infancy, it is not too early to consider their scalability and reliability in the context of the design of large-scale quantum computers. To architect such systems, one must understand what it takes to design and model a balanced, fault-tolerant quantum computer architecture. The goal of this lecture is to provide architectural abstractions for the design of a quantum computer and to explore
Directory of Open Access Journals (Sweden)
Prashant Anil Patil
2012-04-01
Full Text Available This paper gives the detailed information about Quantum computer, and difference between quantum computer and traditional computers, the basis of Quantum computers which are slightly similar but still different from traditional computer. Many research groups are working towards the highly technological goal of building a quantum computer, which would dramatically improve computational power for particular tasks. Quantum computer is very much use full for computation purpose in field of Science and Research. Large amount of data and information will be computed, processing, storing, retrieving, transmitting and displaying information in less time with that much of accuracy which is not provided by traditional computers.
Nauton, Lionel; Hélaine, Virgil; Théry, Vincent; Hecquet, Laurence
2016-04-12
We propose the first computational model for transketolase (TK), a thiamine diphosphate (ThDP)-dependent enzyme, using a quantum mechanical/molecular mechanical method on the basis of crystallographic TK structures from yeast and Escherichia coli, together with experimental kinetic data reported in the literature with wild-type and mutant TK. This model allowed us to define a new route for ThDP activation in the enzyme environment. We evidenced a strong interaction between ThDP and Glu418B of the TK active site, itself stabilized by Glu162A. The crucial point highlighted here is that deprotonation of ThDP C2 is not performed by ThDP N4' as reported in the literature, but by His481B, involving a HOH688A molecule bridge. Thus, ThDP N4' is converted from an amino form to an iminium form, ensuring the stabilization of the C2 carbanion or carbene. Finally, ThDP activation proceeds via an intermolecular process and not by an intramolecular one as reported in the literature. More generally, this proposed ThDP activation mechanism can be applied to some other ThDP-dependent enzymes and used to define the entire TK mechanism with donor and acceptor substrates more accurately.
Effectively calculable quantum mechanics
Bolotin, Arkady
2015-01-01
According to mathematical constructivism, a mathematical object can exist only if there is a way to compute (or "construct") it; so, what is non-computable is non-constructive. In the example of the quantum model, whose Fock states are associated with Fibonacci numbers, this paper shows that the mathematical formalism of quantum mechanics is non-constructive since it permits an undecidable (or effectively impossible) subset of Hilbert space. On the other hand, as it is argued in the paper, if...
National Research Council Canada - National Science Library
Jeremy L. O'Brien
2007-01-01
In 2001, all-optical quantum computing became feasible with the discovery that scalable quantum computing is possible using only single-photon sources, linear optical elements, and single-photon detectors...
Introduction to Quantum Computation
Ekert, A.
A computation is a physical process. It may be performed by a piece of electronics or on an abacus, or in your brain, but it is a process that takes place in nature and as such it is subject to the laws of physics. Quantum computers are machines that rely on characteristically quantum phenomena, such as quantum interference and quantum entanglement in order to perform computation. In this series of lectures I want to elaborate on the computational power of such machines.
Quantum Computing over Finite Fields
James, Roshan P; Sabry, Amr
2011-01-01
In recent work, Benjamin Schumacher and Michael~D. Westmoreland investigate a version of quantum mechanics which they call "modal quantum theory" but which we prefer to call "discrete quantum theory". This theory is obtained by instantiating the mathematical framework of Hilbert spaces with a finite field instead of the field of complex numbers. This instantiation collapses much the structure of actual quantum mechanics but retains several of its distinguishing characteristics including the notions of superposition, interference, and entanglement. Furthermore, discrete quantum theory excludes local hidden variable models, has a no-cloning theorem, and can express natural counterparts of quantum information protocols such as superdense coding and teleportation. Our first result is to distill a model of discrete quantum computing from this quantum theory. The model is expressed using a monadic metalanguage built on top of a universal reversible language for finite computations, and hence is directly implementab...
Kendon, Vivien M; Nemoto, Kae; Munro, William J
2010-08-13
We briefly review what a quantum computer is, what it promises to do for us and why it is so hard to build one. Among the first applications anticipated to bear fruit is the quantum simulation of quantum systems. While most quantum computation is an extension of classical digital computation, quantum simulation differs fundamentally in how the data are encoded in the quantum computer. To perform a quantum simulation, the Hilbert space of the system to be simulated is mapped directly onto the Hilbert space of the (logical) qubits in the quantum computer. This type of direct correspondence is how data are encoded in a classical analogue computer. There is no binary encoding, and increasing precision becomes exponentially costly: an extra bit of precision doubles the size of the computer. This has important consequences for both the precision and error-correction requirements of quantum simulation, and significant open questions remain about its practicality. It also means that the quantum version of analogue computers, continuous-variable quantum computers, becomes an equally efficient architecture for quantum simulation. Lessons from past use of classical analogue computers can help us to build better quantum simulators in future.
Introduction to quantum computers
Berman, Gennady P; Mainieri, Ronnie; Tsifrinovich, Vladimir I
1998-01-01
Quantum computing promises to solve problems which are intractable on digital computers. Highly parallel quantum algorithms can decrease the computational time for some problems by many orders of magnitude. This important book explains how quantum computers can do these amazing things. Several algorithms are illustrated: the discrete Fourier transform, Shorâ€™s algorithm for prime factorization; algorithms for quantum logic gates; physical implementations of quantum logic gates in ion traps and in spin chains; the simplest schemes for quantum error correction; correction of errors caused by im
Simulation of quantum computers
De Raedt, H; Michielsen, K; Hams, AH; Miyashita, S; Saito, K; Landau, DP; Lewis, SP; Schuttler, HB
2001-01-01
We describe a simulation approach to study the functioning of Quantum Computer hardware. The latter is modeled by a collection of interacting spin-1/2 objects. The time evolution of this spin system maps one-to-one to a quantum program carried out by the Quantum Computer. Our simulation software con
Fujii, Toshiyuki; Matsuo, Shigemasa; Hatakenaka, Noriyuki
2009-01-01
We propose a fluxon-controlled quantum computer incorporated with three-qubit quantum error correction using special gate operations, i.e., joint-phase and SWAP gate operations, inherent in capacitively coupled superconducting flux qubits. The proposed quantum computer acts exactly like a knitting machine at home.
Preskill, J
1997-01-01
The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. Hence, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per quantum gate is less than a certain critical value, the accuracy threshold. A quantum computer storing about 10^6 qubits, with a probability of error per quantum gate of order 10^{-6}, would be a formidable factoring engine. Even a smaller, less accurate quantum computer would be able to perform many useful tasks. (This paper is based on a talk presented at the ITP Conference on Quantum Coherence and Decoherence, 15-18 December 1996.)
Bananaworld quantum mechanics for primates
Bub, Jeffrey
2016-01-01
What on earth do bananas have to do with quantum mechanics? From a modern perspective, quantum mechanics is about strangely counterintuitive correlations between separated systems, which can be exploited in feats like quantum teleportation, unbreakable cryptographic schemes, and computers with enormously enhanced computing power. Schro?dinger coined the term "entanglement" to describe these bizarre correlations. Bananaworld -- an imaginary island with "entangled" bananas -- brings to life the fascinating discoveries of the new field of quantum information without the mathematical machinery of quantum mechanics. The connection with quantum correlations is fully explained in sections written for the non-physicist reader with a serious interest in understanding the mysteries of the quantum world. The result is a subversive but entertaining book that is accessible and interesting to a wide range of readers, with the novel thesis that quantum mechanics is about the structure of information. What we have discovered...
Kearns, F L; Hudson, P S; Boresch, S; Woodcock, H L
2016-01-01
Enzyme activity is inherently linked to free energies of transition states, ligand binding, protonation/deprotonation, etc.; these free energies, and thus enzyme function, can be affected by residue mutations, allosterically induced conformational changes, and much more. Therefore, being able to predict free energies associated with enzymatic processes is critical to understanding and predicting their function. Free energy simulation (FES) has historically been a computational challenge as it requires both the accurate description of inter- and intramolecular interactions and adequate sampling of all relevant conformational degrees of freedom. The hybrid quantum mechanical molecular mechanical (QM/MM) framework is the current tool of choice when accurate computations of macromolecular systems are essential. Unfortunately, robust and efficient approaches that employ the high levels of computational theory needed to accurately describe many reactive processes (ie, ab initio, DFT), while also including explicit solvation effects and accounting for extensive conformational sampling are essentially nonexistent. In this chapter, we will give a brief overview of two recently developed methods that mitigate several major challenges associated with QM/MM FES: the QM non-Boltzmann Bennett's acceptance ratio method and the QM nonequilibrium work method. We will also describe usage of these methods to calculate free energies associated with (1) relative properties and (2) along reaction paths, using simple test cases with relevance to enzymes examples. © 2016 Elsevier Inc. All rights reserved.
Quantum computing classical physics.
Meyer, David A
2002-03-15
In the past decade, quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests that they may also speed up the simulation of some classical systems. I describe one class of discrete quantum algorithms which do so--quantum lattice-gas automata--and show how to implement them efficiently on standard quantum computers.
Quantum Computation Toward Quantum Gravity
Zizzi, P. A.
2001-08-01
The aim of this paper is to enlighten the emerging relevance of Quantum Information Theory in the field of Quantum Gravity. As it was suggested by J. A. Wheeler, information theory must play a relevant role in understanding the foundations of Quantum Mechanics (the "It from bit" proposal). Here we suggest that quantum information must play a relevant role in Quantum Gravity (the "It from qubit" proposal). The conjecture is that Quantum Gravity, the theory which will reconcile Quantum Mechanics with General Relativity, can be formulated in terms of quantum bits of information (qubits) stored in space at the Planck scale. This conjecture is based on the following arguments: a) The holographic principle, b) The loop quantum gravity approach and spin networks, c) Quantum geometry and black hole entropy. From the above arguments, as they stand in the literature, it follows that the edges of spin networks pierce the black hole horizon and excite curvature degrees of freedom on the surface. These excitations are micro-states of Chern-Simons theory and account of the black hole entropy which turns out to be a quarter of the area of the horizon, (in units of Planck area), in accordance with the holographic principle. Moreover, the states which dominate the counting correspond to punctures of spin j = 1/2 and one can in fact visualize each micro-state as a bit of information. The obvious generalization of this result is to consider open spin networks with edges labeled by the spin -1/ 2 representation of SU(2) in a superposed state of spin "on" and spin "down." The micro-state corresponding to such a puncture will be a pixel of area which is "on" and "off" at the same time, and it will encode a qubit of information. This picture, when applied to quantum cosmology, describes an early inflationary universe which is a discrete version of the de Sitter universe.
Quantum Computation and Quantum Spin Dynamics
Raedt, Hans De; Michielsen, Kristel; Hams, Anthony; Miyashita, Seiji; Saito, Keiji
2001-01-01
We analyze the stability of quantum computations on physically realizable quantum computers by simulating quantum spin models representing quantum computer hardware. Examples of logically identical implementations of the controlled-NOT operation are used to demonstrate that the results of a quantum
Quantum Computation and Quantum Spin Dynamics
Raedt, Hans De; Michielsen, Kristel; Hams, Anthony; Miyashita, Seiji; Saito, Keiji
2001-01-01
We analyze the stability of quantum computations on physically realizable quantum computers by simulating quantum spin models representing quantum computer hardware. Examples of logically identical implementations of the controlled-NOT operation are used to demonstrate that the results of a quantum
Probabilistic Cloning and Quantum Computation
Institute of Scientific and Technical Information of China (English)
GAO Ting; YAN Feng-Li; WANG Zhi-Xi
2004-01-01
@@ We discuss the usefulness of quantum cloning and present examples of quantum computation tasks for which the cloning offers an advantage which cannot be matched by any approach that does not resort to quantum cloning.In these quantum computations, we need to distribute quantum information contained in the states about which we have some partial information. To perform quantum computations, we use a state-dependent probabilistic quantum cloning procedure to distribute quantum information in the middle of a quantum computation.
Quantum Mechanics with Applications
Afnan, Iraj R
2011-01-01
The ebook introduces undergraduate students to the basic skills required to use non-relativistic quantum mechanics for bound and scattering problems in atomic, molecular and nuclear physics. Initial emphasis is on problems that admit analytic solutions. These results are then used in conjunction with symmetry to develop approximation methods for both bound and scattering problems. The text concentrates on the application of computational problems to introduce the basic concepts of quantum mechanics. These are then used to study more complex problems that can be reduced to one-body problems.
Explorations in quantum computing
Williams, Colin P
2011-01-01
By the year 2020, the basic memory components of a computer will be the size of individual atoms. At such scales, the current theory of computation will become invalid. ""Quantum computing"" is reinventing the foundations of computer science and information theory in a way that is consistent with quantum physics - the most accurate model of reality currently known. Remarkably, this theory predicts that quantum computers can perform certain tasks breathtakingly faster than classical computers -- and, better yet, can accomplish mind-boggling feats such as teleporting information, breaking suppos
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).
Blind Quantum Signature with Blind Quantum Computation
Li, Wei; Shi, Ronghua; Guo, Ying
2017-04-01
Blind quantum computation allows a client without quantum abilities to interact with a quantum server to perform a unconditional secure computing protocol, while protecting client's privacy. Motivated by confidentiality of blind quantum computation, a blind quantum signature scheme is designed with laconic structure. Different from the traditional signature schemes, the signing and verifying operations are performed through measurement-based quantum computation. Inputs of blind quantum computation are securely controlled with multi-qubit entangled states. The unique signature of the transmitted message is generated by the signer without leaking information in imperfect channels. Whereas, the receiver can verify the validity of the signature using the quantum matching algorithm. The security is guaranteed by entanglement of quantum system for blind quantum computation. It provides a potential practical application for e-commerce in the cloud computing and first-generation quantum computation.
Blind Quantum Signature with Blind Quantum Computation
Li, Wei; Shi, Ronghua; Guo, Ying
2016-12-01
Blind quantum computation allows a client without quantum abilities to interact with a quantum server to perform a unconditional secure computing protocol, while protecting client's privacy. Motivated by confidentiality of blind quantum computation, a blind quantum signature scheme is designed with laconic structure. Different from the traditional signature schemes, the signing and verifying operations are performed through measurement-based quantum computation. Inputs of blind quantum computation are securely controlled with multi-qubit entangled states. The unique signature of the transmitted message is generated by the signer without leaking information in imperfect channels. Whereas, the receiver can verify the validity of the signature using the quantum matching algorithm. The security is guaranteed by entanglement of quantum system for blind quantum computation. It provides a potential practical application for e-commerce in the cloud computing and first-generation quantum computation.
Quantum computing with defects.
Weber, J R; Koehl, W F; Varley, J B; Janotti, A; Buckley, B B; Van de Walle, C G; Awschalom, D D
2010-05-11
Identifying and designing physical systems for use as qubits, the basic units of quantum information, are critical steps in the development of a quantum computer. Among the possibilities in the solid state, a defect in diamond known as the nitrogen-vacancy (NV(-1)) center stands out for its robustness--its quantum state can be initialized, manipulated, and measured with high fidelity at room temperature. Here we describe how to systematically identify other deep center defects with similar quantum-mechanical properties. We present a list of physical criteria that these centers and their hosts should meet and explain how these requirements can be used in conjunction with electronic structure theory to intelligently sort through candidate defect systems. To illustrate these points in detail, we compare electronic structure calculations of the NV(-1) center in diamond with those of several deep centers in 4H silicon carbide (SiC). We then discuss the proposed criteria for similar defects in other tetrahedrally coordinated semiconductors.
Quantum Computational Cryptography
Kawachi, Akinori; Koshiba, Takeshi
As computational approaches to classical cryptography have succeeded in the establishment of the foundation of the network security, computational approaches even to quantum cryptography are promising, since quantum computational cryptography could offer richer applications than the quantum key distribution. Our project focused especially on the quantum one-wayness and quantum public-key cryptosystems. The one-wayness of functions (or permutations) is one of the most important notions in computational cryptography. First, we give an algorithmic characterization of quantum one-way permutations. In other words, we show a necessary and sufficient condition for quantum one-way permutations in terms of reflection operators. Second, we introduce a problem of distinguishing between two quantum states as a new underlying problem that is harder to solve than the graph automorphism problem. The new problem is a natural generalization of the distinguishability problem between two probability distributions, which are commonly used in computational cryptography. We show that the problem has several cryptographic properties and they enable us to construct a quantum publickey cryptosystem, which is likely to withstand any attack of a quantum adversary.
Temperley-Lieb Algebra: From Knot Theory to Logic and Computation via Quantum Mechanics
Abramsky, Samson
2009-01-01
Our aim in this paper is to trace some of the surprising and beautiful connections which are beginning to emerge between a number of apparently disparate topics: Knot Theory, Categorical Quantum Mechanics, and Logic and Computation. We shall focus in particular on the following two topics: - The Temperley-Lieb algebra has always hitherto been presented as a quotient of some sort: either algebraically by generators and relations as in Jones' original presentation, or as a diagram algebra modulo planar isotopy as in Kauffman's presentation. We shall use tools from Geometry of Interaction, a dynamical interpretation of proofs under Cut Elimination developed as an off-shoot of Linear Logic, to give a direct description of the Temperley-Lieb category -- a "fully abstract presentation", in Computer Science terminology. This also brings something new to the Geometry of Interaction, since we are led to develop a planar version of it, and to verify that the interpretation of Cut-Elimination (the "Execution Formula", o...
Diamond NV centers for quantum computing and quantum networks
Childress, L.; Hanson, R.
2013-01-01
The exotic features of quantum mechanics have the potential to revolutionize information technologies. Using superposition and entanglement, a quantum processor could efficiently tackle problems inaccessible to current-day computers. Nonlocal correlations may be exploited for intrinsically secure co
Experimental quantum computing without entanglement.
Lanyon, B P; Barbieri, M; Almeida, M P; White, A G
2008-11-14
Deterministic quantum computation with one pure qubit (DQC1) is an efficient model of computation that uses highly mixed states. Unlike pure-state models, its power is not derived from the generation of a large amount of entanglement. Instead it has been proposed that other nonclassical correlations are responsible for the computational speedup, and that these can be captured by the quantum discord. In this Letter we implement DQC1 in an all-optical architecture, and experimentally observe the generated correlations. We find no entanglement, but large amounts of quantum discord-except in three cases where an efficient classical simulation is always possible. Our results show that even fully separable, highly mixed, states can contain intrinsically quantum mechanical correlations and that these could offer a valuable resource for quantum information technologies.
Quantum Computation: Entangling with the Future
Jiang, Zhang
2017-01-01
Commercial applications of quantum computation have become viable due to the rapid progress of the field in the recent years. Efficient quantum algorithms are discovered to cope with the most challenging real-world problems that are too hard for classical computers. Manufactured quantum hardware has reached unprecedented precision and controllability, enabling fault-tolerant quantum computation. Here, I give a brief introduction on what principles in quantum mechanics promise its unparalleled computational power. I will discuss several important quantum algorithms that achieve exponential or polynomial speedup over any classical algorithm. Building a quantum computer is a daunting task, and I will talk about the criteria and various implementations of quantum computers. I conclude the talk with near-future commercial applications of a quantum computer.
Quantum computing with trapped ions
Energy Technology Data Exchange (ETDEWEB)
Hughes, R.J.
1998-01-01
The significance of quantum computation for cryptography is discussed. Following a brief survey of the requirements for quantum computational hardware, an overview of the ion trap quantum computation project at Los Alamos is presented. The physical limitations to quantum computation with trapped ions are analyzed and an assessment of the computational potential of the technology is made.
2011-12-01
an inspiring speech at the MIT Physics of Computation 1st Conference in 1981, Feynman proposed the development of a computer that would obey the...on ion trap based 36 quantum computing for physics and computer science students would include lecture notes, slides, lesson plans, a syllabus...reading lists, videos, demonstrations, and laboratories. 37 LIST OF REFERENCES [1] R. P. Feynman , “Simulating physics with computers,” Int. J
Greiner, Walter
1989-01-01
"Quantum Dynamics" is a major survey of quantum theory based on Walter Greiner's long-running and highly successful courses at the University of Frankfurt. The key to understanding in quantum theory is to reinforce lecture attendance and textual study by working through plenty of representative and detailed examples. Firm belief in this principle led Greiner to develop his unique course and to transform it into a remarkable and comprehensive text. The text features a large number of examples and exercises involving many of the most advanced topics in quantum theory. These examples give practical and precise demonstrations of how to use the often subtle mathematics behind quantum theory. The text is divided into five volumes: Quantum Mechanics I - An Introduction, Quantum Mechanics II - Symmetries, Relativistic Quantum Mechanics, Quantum Electrodynamics, Gauge Theory of Weak Interactions. These five volumes take the reader from the fundamental postulates of quantum mechanics up to the latest research in partic...
Experimental demonstration of blind quantum computing
Barz, Stefanie; Kashefi, Elham; Broadbent, Anne; Fitzsimons, Joe; Zeilinger, Anton; Walther, Philip
2012-02-01
Quantum computers are among the most promising applications of quantum-enhanced technologies. Quantum effects such as superposition and entanglement enable computational speed-ups that are unattainable using classical computers. The challenges in realising quantum computers suggest that in the near future, only a few facilities worldwide will be capable of operating such devices. In order to exploit these computers, users would seemingly have to give up their privacy. It was recently shown that this is not the case and that, via the universal blind quantum computation protocol, quantum mechanics provides a way to guarantee that the user's data remain private. Here, we demonstrate the first experimental version of this protocol using polarisation-entangled photonic qubits. We demonstrate various blind one- and two-qubit gate operations as well as blind versions of the Deutsch's and Grover's algorithms. When the technology to build quantum computers becomes available, this will become an important privacy-preserving feature of quantum information processing.
Concurrent Quantum Computation
Yamaguchi, F; Yamamoto, Y
2000-01-01
A quantum computer is a multi-particle interferometer that comprises beam splitters at both ends and arms, where the n two-level particles undergo the interactions among them. The arms are designed so that relevant functions required to produce a computational result is stored in the phase shifts of the 2^n arms. They can be detected by interferometry that allows us to utilize quantum parallelism. Quantum algorithms are accountable for what interferometers to be constructed to compute particular problems. A standard formalism for constructing the arms has been developed by the extension of classical reversible gate arrays. By its nature of sequential applications of logic operations, the required number of gates increases exponentially as the problem size grows. This may cause a crucial obstacle to perform a quantum computation within a limited decoherence time. We propose a direct and concurrent construction of the interferometer arms by one-time evolution of a physical system with arbitrary multi-particle i...
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 ...
Faheem, Muhammad; Heyden, Andreas
2014-08-12
We report the development of a quantum mechanics/molecular mechanics free energy perturbation (QM/MM-FEP) method for modeling chemical reactions at metal-water interfaces. This novel solvation scheme combines planewave density function theory (DFT), periodic electrostatic embedded cluster method (PEECM) calculations using Gaussian-type orbitals, and classical molecular dynamics (MD) simulations to obtain a free energy description of a complex metal-water system. We derive a potential of mean force (PMF) of the reaction system within the QM/MM framework. A fixed-size, finite ensemble of MM conformations is used to permit precise evaluation of the PMF of QM coordinates and its gradient defined within this ensemble. Local conformations of adsorbed reaction moieties are optimized using sequential MD-sampling and QM-optimization steps. An approximate reaction coordinate is constructed using a number of interpolated states and the free energy difference between adjacent states is calculated using the QM/MM-FEP method. By avoiding on-the-fly QM calculations and by circumventing the challenges associated with statistical averaging during MD sampling, a computational speedup of multiple orders of magnitude is realized. The method is systematically validated against the results of ab initio QM calculations and demonstrated for C-C cleavage in double-dehydrogenated ethylene glycol on a Pt (111) model surface.
Introduction to quantum mechanics
Villaseñor, Eduardo J. S.
2008-01-01
The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.
Problems and solutions in quantum computing and quantum information
Steeb, Willi-Hans
2012-01-01
Quantum computing and quantum information are two of the fastest growing and most exciting research fields in physics. Entanglement, teleportation and the possibility of using the non-local behavior of quantum mechanics to factor integers in random polynomial time have also added to this new interest. This book supplies a huge collection of problems in quantum computing and quantum information together with their detailed solutions, which will prove to be invaluable to students as well as researchers in these fields. All the important concepts and topics such as quantum gates and quantum circuits, product Hilbert spaces, entanglement and entanglement measures, deportation, Bell states, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gate, von Neumann entropy, quantum cryptography, quantum error corrections, number states and Bose operators, coherent states, squeezed states, Gaussian states, POVM measurement, quantum optics networks, beam splitter, phase shifter and Kerr Hamilton opera...
Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C Language
Blaha, Stephen
2002-01-01
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.
Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C
Blaha, Stephen
2002-01-01
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.
Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C
Blaha, Stephen
2002-01-01
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.
Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C Language
Blaha, Stephen
2002-01-01
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.
Communication: quantum mechanics without wavefunctions.
Schiff, Jeremy; Poirier, Bill
2012-01-21
We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications-theoretical, computational, and interpretational-are discussed.
Testing Nonassociative Quantum Mechanics.
Bojowald, Martin; Brahma, Suddhasattwa; Büyükçam, Umut
2015-11-27
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to nonassociative algebras. Their quantum physics has remained obscure. This Letter presents the first derivation of potentially testable physical results in nonassociative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.
Energy Technology Data Exchange (ETDEWEB)
Raboin, P J
1998-01-01
The Computational Mechanics thrust area is a vital and growing facet of the Mechanical Engineering Department at Lawrence Livermore National Laboratory (LLNL). This work supports the development of computational analysis tools in the areas of structural mechanics and heat transfer. Over 75 analysts depend on thrust area-supported software running on a variety of computing platforms to meet the demands of LLNL programs. Interactions with the Department of Defense (DOD) High Performance Computing and Modernization Program and the Defense Special Weapons Agency are of special importance as they support our ParaDyn project in its development of new parallel capabilities for DYNA3D. Working with DOD customers has been invaluable to driving this technology in directions mutually beneficial to the Department of Energy. Other projects associated with the Computational Mechanics thrust area include work with the Partnership for a New Generation Vehicle (PNGV) for ''Springback Predictability'' and with the Federal Aviation Administration (FAA) for the ''Development of Methodologies for Evaluating Containment and Mitigation of Uncontained Engine Debris.'' In this report for FY-97, there are five articles detailing three code development activities and two projects that synthesized new code capabilities with new analytic research in damage/failure and biomechanics. The article this year are: (1) Energy- and Momentum-Conserving Rigid-Body Contact for NIKE3D and DYNA3D; (2) Computational Modeling of Prosthetics: A New Approach to Implant Design; (3) Characterization of Laser-Induced Mechanical Failure Damage of Optical Components; (4) Parallel Algorithm Research for Solid Mechanics Applications Using Finite Element Analysis; and (5) An Accurate One-Step Elasto-Plasticity Algorithm for Shell Elements in DYNA3D.
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.
Quantum Walks for Computer Scientists
Venegas-Andraca, Salvador
2008-01-01
Quantum computation, one of the latest joint ventures between physics and the theory of computation, is a scientific field whose main goals include the development of hardware and algorithms based on the quantum mechanical properties of those physical systems used to implement such algorithms. Solving difficult tasks (for example, the Satisfiability Problem and other NP-complete problems) requires the development of sophisticated algorithms, many of which employ stochastic processes as their mathematical basis. Discrete random walks are a popular choice among those stochastic processes. Inspir
O'Brien, Jeremy L
2007-12-07
In 2001, all-optical quantum computing became feasible with the discovery that scalable quantum computing is possible using only single-photon sources, linear optical elements, and single-photon detectors. Although it was in principle scalable, the massive resource overhead made the scheme practically daunting. However, several simplifications were followed by proof-of-principle demonstrations, and recent approaches based on cluster states or error encoding have dramatically reduced this worrying resource overhead, making an all-optical architecture a serious contender for the ultimate goal of a large-scale quantum computer. Key challenges will be the realization of high-efficiency sources of indistinguishable single photons, low-loss, scalable optical circuits, high-efficiency single-photon detectors, and low-loss interfacing of these components.
Quantum mechanics a modern development
Ballentine, Leslie E
2015-01-01
Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory. In this edition a new chapter on quantum information is added. As the topic is still in a state of rapid development, a comprehensive treatment is not feasible. The emphasis is on the fundamental principles and some key applications, including quantum cryptography, teleportation of states, and quantum computing. The impact of quantum information theory on the foundations of quantum mechanics is discussed. In addition, there are minor revisions ...
Embracing the quantum limit in silicon computing.
Morton, John J L; McCamey, Dane R; Eriksson, Mark A; Lyon, Stephen A
2011-11-16
Quantum computers hold the promise of massive performance enhancements across a range of applications, from cryptography and databases to revolutionary scientific simulation tools. Such computers would make use of the same quantum mechanical phenomena that pose limitations on the continued shrinking of conventional information processing devices. Many of the key requirements for quantum computing differ markedly from those of conventional computers. However, silicon, which plays a central part in conventional information processing, has many properties that make it a superb platform around which to build a quantum computer.
On the computation of quantum characteristic exponents
Vilela-Mendes, R; Coutinho, Ricardo
1998-01-01
A quantum characteristic exponent may be defined, with the same operational meaning as the classical Lyapunov exponent when the latter is expressed as a functional of densities. Existence conditions and supporting measure properties are discussed as well as the problems encountered in the numerical computation of the quantum exponents. Although an example of true quantum chaos may be exhibited, the taming effect of quantum mechanics on chaos is quite apparent in the computation of the quantum exponents. However, even when the exponents vanish, the functionals used for their definition may still provide a characterization of distinct complexity classes for quantum behavior.
Introduction to topological quantum matter & quantum computation
Stanescu, Tudor D
2017-01-01
What is -topological- about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture, this book is ideal for graduate students and researchers entering this field as it allows for the fruitful transfer of paradigms and ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-know...
Quantum probabilistically cloning and computation
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this article we make a review on the usefulness of probabilistically cloning and present examples of quantum computation tasks for which quantum cloning offers an advantage which cannot be matched by any approach that does not resort to it.In these quantum computations,one needs to distribute quantum information contained in states about which we have some partial information.To perform quantum computations,one uses state-dependent probabilistic quantum cloning procedure to distribute quantum information in the middle of a quantum computation.And we discuss the achievable efficiencies and the efficient quantum logic network for probabilistic cloning the quantum states used in implementing quantum computation tasks for which cloning provides enhancement in performance.
Quantum mechanics in chemistry
Schatz, George C
2002-01-01
Intended for graduate and advanced undergraduate students, this text explores quantum mechanical techniques from the viewpoint of chemistry and materials science. Dynamics, symmetry, and formalism are emphasized. An initial review of basic concepts from introductory quantum mechanics is followed by chapters examining symmetry, rotations, and angular momentum addition. Chapter 4 introduces the basic formalism of time-dependent quantum mechanics, emphasizing time-dependent perturbation theory and Fermi's golden rule. Chapter 5 sees this formalism applied to the interaction of radiation and matt
Abstract quantum computing machines and quantum computational logics
Chiara, Maria Luisa Dalla; Giuntini, Roberto; Sergioli, Giuseppe; Leporini, Roberto
2016-06-01
Classical and quantum parallelism are deeply different, although it is sometimes claimed that quantum Turing machines are nothing but special examples of classical probabilistic machines. We introduce the concepts of deterministic state machine, classical probabilistic state machine and quantum state machine. On this basis, we discuss the question: To what extent can quantum state machines be simulated by classical probabilistic state machines? Each state machine is devoted to a single task determined by its program. Real computers, however, behave differently, being able to solve different kinds of problems. This capacity can be modeled, in the quantum case, by the mathematical notion of abstract quantum computing machine, whose different programs determine different quantum state machines. The computations of abstract quantum computing machines can be linguistically described by the formulas of a particular form of quantum logic, termed quantum computational logic.
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...
2014-01-01
Since the second half of the 20th century machine computations have played a critical role in science and engineering. Computer-based techniques have become especially important in molecular biology, since they often represent the only viable way to gain insights into the behavior of a biological system as a whole. The complexity of biological systems, which usually needs to be analyzed on different time- and size-scales and with different levels of accuracy, requires the application of different approaches, ranging from comparative analysis of sequences and structural databases, to the analysis of networks of interdependence between cell components and processes, through coarse-grained modeling to atomically detailed simulations, and finally to molecular quantum mechanics. This book provides a comprehensive overview of modern computer-based techniques for computing the structure, properties and dynamics of biomolecules and biomolecular processes. The twenty-two chapters, written by scientists from all over t...
Quantum Computer Games: Schrodinger Cat and Hounds
Gordon, Michal; Gordon, Goren
2012-01-01
The quantum computer game "Schrodinger cat and hounds" is the quantum extension of the well-known classical game fox and hounds. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. "Schrodinger cat and hounds" demonstrates the effects of superposition, destructive and constructive interference, measurements and…
Quantum Computer Games: Schrodinger Cat and Hounds
Gordon, Michal; Gordon, Goren
2012-01-01
The quantum computer game "Schrodinger cat and hounds" is the quantum extension of the well-known classical game fox and hounds. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. "Schrodinger cat and hounds" demonstrates the effects of superposition, destructive and constructive interference, measurements and…
Quantum mechanics for pedestrians
Pade, Jochen
2014-01-01
This book provides an introduction into the fundamentals of non-relativistic quantum mechanics. In Part 1, the essential principles are developed. Applications and extensions of the formalism can be found in Part 2. The book includes not only material that is presented in traditional textbooks on quantum mechanics, but also discusses in detail current issues such as interaction-free quantum measurements, neutrino oscillations, various topics in the field of quantum information as well as fundamental problems and epistemological questions, such as the measurement problem, entanglement, Bell's inequality, decoherence, and the realism debate. A chapter on current interpretations of quantum mechanics concludes the book. To develop quickly and clearly the main principles of quantum mechanics and its mathematical formulation, there is a systematic change between wave mechanics and algebraic representation in the first chapters. The required mathematical tools are introduced step by step. Moreover, the appendix coll...
Demonstration of blind quantum computing.
Barz, Stefanie; Kashefi, Elham; Broadbent, Anne; Fitzsimons, Joseph F; Zeilinger, Anton; Walther, Philip
2012-01-20
Quantum computers, besides offering substantial computational speedups, are also expected to preserve the privacy of a computation. We present an experimental demonstration of blind quantum computing in which the input, computation, and output all remain unknown to the computer. We exploit the conceptual framework of measurement-based quantum computation that enables a client to delegate a computation to a quantum server. Various blind delegated computations, including one- and two-qubit gates and the Deutsch and Grover quantum algorithms, are demonstrated. The client only needs to be able to prepare and transmit individual photonic qubits. Our demonstration is crucial for unconditionally secure quantum cloud computing and might become a key ingredient for real-life applications, especially when considering the challenges of making powerful quantum computers widely available.
Decoherence, Control, and Symmetry in Quantum Computers
Bacon, D J
2003-01-01
In this thesis we describe methods for avoiding the detrimental effects of decoherence while at the same time still allowing for computation of the quantum information. The philosophy of the method discussed in the first part of this thesis is to use a symmetry of the decoherence mechanism to find robust encodings of the quantum information. Stability, control, and methods for using decoherence-free information in a quantum computer are presented with a specific emphasis on decoherence due to a collective coupling between the system and its environment. Universal quantum computation on such collective decoherence decoherence-free encodings is demonstrated. Rigorous definitions of control and the use of encoded universality in quantum computers are addressed. Explicit gate constructions for encoded universality on ion trap and exchange based quantum computers are given. In the second part of the thesis we examine physical systems with error correcting properties. We examine systems that can store quantum infor...
Basic concepts in quantum computation
Ekert, A K; Inamori, H; Ekert, Artur; Hayden, Patrick; Inamori, Hitoshi
2000-01-01
Section headings: 1 Qubits, gates and networks 2 Quantum arithmetic and function evaluations 3 Algorithms and their complexity 4 From interferometers to computers 5 The first quantum algorithms 6 Quantum search 7 Optimal phase estimation 8 Periodicity and quantum factoring 9 Cryptography 10 Conditional quantum dynamics 11 Decoherence and recoherence 12 Concluding remarks
Quantum Mobile Crypto-Computation
Institute of Scientific and Technical Information of China (English)
XIONGYan; CHENHuanhuan; GUNaijie; MIAOFuyou
2005-01-01
In this paper, a quantum approach for solving the mobile crypto-computation problem is proposed. In our approach, quantum signature and quantum entanglement have been employed to strengthen the security of mobile computation. Theory analysis shows that our solution is secure against classic and quantum attacks.
Dirac, Paul A M
2001-01-01
The author of this concise, brilliant series of lectures on mathematical methods in quantum mechanics was one of the shining intellects in the field, winning a Nobel prize in 1933 for his pioneering work in the quantum mechanics of the atom. Beyond that, he developed the transformation theory of quantum mechanics (which made it possible to calculate the statistical distribution of certain variables), was one of the major authors of the quantum theory of radiation, codiscovered the Fermi-Dirac statistics, and predicted the existence of the positron.The four lectures in this book were delivered
Facing quantum mechanical reality.
Rohrlich, F
1983-09-23
Two recent precision experiments provide conclusive evidence against any local hidden variables theory and in favor of standard quantum mechanics. Therefore the epistemology and the ontology of quantum mechanics must now be taken more seriously than ever before. The consequences of the standard interpretation of quantum mechanics are summarized in nontechnical language. The implications of the finiteness of Planck's constant (h > 0) for the quantum world are as strange as the implications of the finiteness of the speed of light (c < infinity for space and time in relativity theory. Both lead to realities beyond our common experience that cannot be rejected.
Quantum mechanics of leptogenesis
Energy Technology Data Exchange (ETDEWEB)
Mendizabal Cofre, Sebastian
2010-08-15
Leptogenesis is an attractive mechanism that simultaneously explains the matterantimatter asymmetry of the universe as well as the small masses of the standard model neutrinos. This is performed by naturally extending the standard model with the insertion of right handed neutrinos. Leptogenesis is usually studied via the semi-classical Boltzmann equations. However, these equations suffer from basic conceptual problems and they lack to include many quantum phenomena, such as memory effects and coherence oscillations. In order to fully describe leptogenesis, a full quantum treatment is required. In this work we show how to address leptogenesis systematically in a purely quantum way. We start by studying scalar and fermionic excitations in a plasma by solving the Kadanoff-Baym equations of motion for Green's functions, with significant emphasis on the initial and boundary conditions of the solutions. We compute analytically the asymmetry generated from the departure of equilibrium of a particle in a thermal bath. The comparison with the semi-classical Boltzmann approach is also analysed, leading to a qualitative difference between both methods. The non-locality of the Kadanoff-Baym equations shows how off-shell effects can have a huge impact on the generated asymmetry, effects that cannot be studied with the Boltzmann equations. The insertion of standard model interactions like the decay widths for the particles of the bath is also discussed. We explain how with a trivial insertion of these widths we regain locality on the processes, i.e. we regain the Boltzmann equations. (orig.)
Holography and Quantum Mechanics
Wang, X J
2002-01-01
It is illustrated that quantum mechanics can be interpreted as holographic projection of higher dimension classical gravity. In this explanation every quantum path in D-dimension is dual to a classical path of (D+1)-dimension gravity under definite holographic projection. I consider 2-dimension non-relativitic free particle and harmonic oscillator as two examples, and find their gravity dual. I conjecture that every quantum mechanics system has their dual gravity description.
Elementary Nonrelativistic Quantum Mechanics
Rosu, H C
2000-01-01
This is a graduate course on elementary quantum mechanics written for the benefit of undergraduate and graduate students. It is the English version of physics/0003106, which I did at the suggestion of several students from different countries. The topics included refer to the postulates of quantum mechanics, one-dimensional barriers and wells, angular momentum and spin, WKB method, harmonic oscillator, hydrogen atom, quantum scattering, and partial waves
Gol'dman, I I
2010-01-01
A comprehensive collection of problems of varying degrees of difficulty in nonrelativistic quantum mechanics, with answers and completely worked-out solutions. Among the topics: one-dimensional motion, transmission through a potential barrier, commutation relations, angular momentum and spin, and motion of a particle in a magnetic field. An ideal adjunct to any textbook in quantum mechanics, useful in courses in atomic and nuclear physics, mathematical methods in physics, quantum statistics and applied differential equations. 1961 edition.
Holographic quantum computing.
Tordrup, Karl; Negretti, Antonio; Mølmer, Klaus
2008-07-25
We propose to use a single mesoscopic ensemble of trapped polar molecules for quantum computing. A "holographic quantum register" with hundreds of qubits is encoded in collective excitations with definite spatial phase variations. Each phase pattern is uniquely addressed by optical Raman processes with classical optical fields, while one- and two-qubit gates and qubit readout are accomplished by transferring the qubit states to a stripline microwave cavity field and a Cooper pair box where controllable two-level unitary dynamics and detection is governed by classical microwave fields.
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...
Elements of quantum computing history, theories and engineering applications
Akama, Seiki
2015-01-01
A quantum computer is a computer based on a computational model which uses quantum mechanics, which is a subfield of physics to study phenomena at the micro level. There has been a growing interest on quantum computing in the 1990's, and some quantum computers at the experimental level were recently implemented. Quantum computers enable super-speed computation, and can solve some important problems whose solutions were regarded impossible or intractable with traditional computers. This book provides a quick introduction to quantum computing for readers who have no backgrounds of both theory of computation and quantum mechanics. “Elements of Quantum Computing” presents the history, theories, and engineering applications of quantum computing. The book is suitable to computer scientists, physicist, and software engineers.
Chang, Lay Nam; Minic, Djordje; Takeuchi, Tatsu
2012-01-01
We construct a discrete quantum mechanics using a vector space over the Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discrete quantum mechanics cannot be reproduced with any hidden variable theory.
Goldman, Iosif Ilich; Geilikman, B T
2006-01-01
This challenging book contains a comprehensive collection of problems in nonrelativistic quantum mechanics of varying degrees of difficulty. It features answers and completely worked-out solutions to each problem. Geared toward advanced undergraduates and graduate students, it provides an ideal adjunct to any textbook in quantum mechanics.
Contextuality supplies the 'magic' for quantum computation.
Howard, Mark; Wallman, Joel; Veitch, Victor; Emerson, Joseph
2014-06-19
Quantum computers promise dramatic advantages over their classical counterparts, but the source of the power in quantum computing has remained elusive. Here we prove a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via 'magic state' distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer. This is a conceptually satisfying link, because contextuality, which precludes a simple 'hidden variable' model of quantum mechanics, provides one of the fundamental characterizations of uniquely quantum phenomena. Furthermore, this connection suggests a unifying paradigm for the resources of quantum information: the non-locality of quantum theory is a particular kind of contextuality, and non-locality is already known to be a critical resource for achieving advantages with quantum communication. In addition to clarifying these fundamental issues, this work advances the resource framework for quantum computation, which has a number of practical applications, such as characterizing the efficiency and trade-offs between distinct theoretical and experimental schemes for achieving robust quantum computation, and putting bounds on the overhead cost for the classical simulation of quantum algorithms.
Quantum communication between remote mechanical resonators
Felicetti, S.; Fedortchenko, S.; Rossi, R.; Ducci, S.; Favero, I.; Coudreau, T.; Milman, P.
2017-02-01
Mechanical resonators represent one of the most promising candidates to mediate the interaction between different quantum technologies, bridging the gap between efficient quantum computation and long-distance quantum communication. Here, we introduce an interferometric scheme where the interaction of a mechanical resonator with input-output quantum pulses is controlled by an independent classical drive. We design protocols for state teleportation and direct quantum state transfer, between distant mechanical resonators. The proposed device, feasible with state-of-the-art technology, can serve as a building block for the implementation of long-distance quantum networks of mechanical resonators.
Directory of Open Access Journals (Sweden)
Tadashi Okazaki
2015-01-01
Full Text Available We consider the multiple M2-branes wrapped on a compact Riemann surface and study the arising quantum mechanics by taking the limit where the size of the Riemann surface goes to zero. The IR quantum mechanical models resulting from the BLG-model and the ABJM-model compactified on a torus are N=16 and N=12 superconformal gauged quantum mechanics. After integrating out the auxiliary gauge fields we find OSp(16|2 and SU(1,1|6 quantum mechanics from the reduced systems. The curved Riemann surface is taken as a holomorphic curve in a Calabi–Yau space to preserve supersymmetry and we present a prescription of the topological twisting. We find the N=8 superconformal gauged quantum mechanics that may describe the motion of two wrapped M2-branes in a K3 surface.
Prospects for quantum computation with trapped ions
Energy Technology Data Exchange (ETDEWEB)
Hughes, R.J.; James, D.F.V.
1997-12-31
Over the past decade information theory has been generalized to allow binary data to be represented by two-state quantum mechanical systems. (A single two-level system has come to be known as a qubit in this context.) The additional freedom introduced into information physics with quantum systems has opened up a variety of capabilities that go well beyond those of conventional information. For example, quantum cryptography allows two parties to generate a secret key even in the presence of eavesdropping. But perhaps the most remarkable capabilities have been predicted in the field of quantum computation. Here, a brief survey of the requirements for quantum computational hardware, and an overview of the in trap quantum computation project at Los Alamos are presented. The physical limitations to quantum computation with trapped ions are discussed.
Quantum Computation and Spin Electronics
DiVincenzo, David P.; Burkard, Guido; Loss, Daniel; Sukhorukov, Eugene V.
1999-01-01
In this chapter we explore the connection between mesoscopic physics and quantum computing. After giving a bibliography providing a general introduction to the subject of quantum information processing, we review the various approaches that are being considered for the experimental implementation of quantum computing and quantum communication in atomic physics, quantum optics, nuclear magnetic resonance, superconductivity, and, especially, normal-electron solid state physics. We discuss five ...
Arrighi, P; Arrighi, Pablo; Salvail, Louis
2003-01-01
We investigate the possibility of having someone carry out the work of executing a function for you, but without letting him learn anything about your input. Say Alice wants Bob to compute some well-known function f upon her input x, but wants to prevent Bob from learning anything about x. The situation arises for instance if client Alice has limited computational resources in comparison with mistrusted server Bob, or if x is an inherently mobile piece of data. Could there be a protocol whereby Bob is forced to compute f(x) "blindly", i.e. without observing x? We provide such a blind computation protocol for the class of functions which admit an efficient procedure to generate random input-output pairs, e.g. factorization. The setting is quantum, the security is unconditional, the eavesdropper is as malicious as can be. Keywords: Secure Circuit Evaluation, Secure Two-party Computation, Information Hiding, Information gain vs disturbance.
Quantum Mechanics interpreted in Quantum Real Numbers
Corbett, J V; Corbett, John V; Durt, Thomas
2002-01-01
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms of quantum mechanics are re-interpreted. Our aim is to show that, when formulated in the language of quantum real numbers, the laws of quantum mechanics appear more natural, less counterintuitive than when they are presented in terms of standard numbers.
Short Introduction to Quantum Computation
2007-11-02
Proceedings of the Air Force Office of Scientific Research Computational Mathematics Meeting 1996 Revision 2 Short Introduction to Quantum...useful for nanoscale computing and quantum computing. KEY WORDS: quantum computing, nano-scale computing, Moore’s law 1 Introduction It is likely that...memory) Digital Devices magnetostrictive delay line Intel 1103 integrated circuit IBM 3340 disk drive Smallest DRAM cell reported on at ISSC Current
Relativistic quantum chemistry on quantum computers
DEFF Research Database (Denmark)
Veis, L.; Visnak, J.; Fleig, T.
2012-01-01
The past few years have witnessed a remarkable interest in the application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, proof-of-principle experimental realizations have been reported. However, so far only...... the nonrelativistic regime (i.e., the Schrodinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. We present a quantum algorithm for relativistic computations of molecular energies. We show how to efficiently solve the eigenproblem of the Dirac......-Coulomb Hamiltonian on a quantum computer and demonstrate the functionality of the proposed procedure by numerical simulations of computations of the spin-orbit splitting in the SbH molecule. Finally, we propose quantum circuits with three qubits and nine or ten controlled-NOT (CNOT) gates, which implement a proof...
Quantum computing of semiclassical formulas.
Georgeot, B; Giraud, O
2008-04-01
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from classical trajectories, and which alternatively test the semiclassical approximation by computing classical actions from quantum evolution. The gain over classical computation is in general quadratic, and can be larger in some specific cases.
Bibliographic guide to the foundations of quantum mechanics and quantum information
Cabello, A
2000-01-01
This is a collection of references (papers, books, preprints, book reviews, Ph. D. thesis, patents, etc.), sorted alphabetically and (some of them) classified by subject, on foundations of quantum mechanics and quantum information. Specifically, it covers hidden variables (``no-go'' theorems, experiments), interpretations of quantum mechanics, entanglement, quantum effects (quantum Zeno effect, quantum erasure, ``interaction-free'' measurements, quantum ``non-demolition'' measurements), quantum information (cryptography, cloning, dense coding, teleportation), and quantum computation.
Quantum computing on encrypted data.
Fisher, K A G; Broadbent, A; Shalm, L K; Yan, Z; Lavoie, J; Prevedel, R; Jennewein, T; Resch, K J
2014-01-01
The ability to perform computations on encrypted data is a powerful tool for protecting privacy. Recently, protocols to achieve this on classical computing systems have been found. Here, we present an efficient solution to the quantum analogue of this problem that enables arbitrary quantum computations to be carried out on encrypted quantum data. We prove that an untrusted server can implement a universal set of quantum gates on encrypted quantum bits (qubits) without learning any information about the inputs, while the client, knowing the decryption key, can easily decrypt the results of the computation. We experimentally demonstrate, using single photons and linear optics, the encryption and decryption scheme on a set of gates sufficient for arbitrary quantum computations. As our protocol requires few extra resources compared with other schemes it can be easily incorporated into the design of future quantum servers. These results will play a key role in enabling the development of secure distributed quantum systems.
Quantum computing on encrypted data
Fisher, K. A. G.; Broadbent, A.; Shalm, L. K.; Yan, Z.; Lavoie, J.; Prevedel, R.; Jennewein, T.; Resch, K. J.
2014-01-01
The ability to perform computations on encrypted data is a powerful tool for protecting privacy. Recently, protocols to achieve this on classical computing systems have been found. Here, we present an efficient solution to the quantum analogue of this problem that enables arbitrary quantum computations to be carried out on encrypted quantum data. We prove that an untrusted server can implement a universal set of quantum gates on encrypted quantum bits (qubits) without learning any information about the inputs, while the client, knowing the decryption key, can easily decrypt the results of the computation. We experimentally demonstrate, using single photons and linear optics, the encryption and decryption scheme on a set of gates sufficient for arbitrary quantum computations. As our protocol requires few extra resources compared with other schemes it can be easily incorporated into the design of future quantum servers. These results will play a key role in enabling the development of secure distributed quantum systems.
Energy Technology Data Exchange (ETDEWEB)
Kapustin, Anton [California Institute of Technology, Pasadena, California 91125 (United States)
2013-06-15
We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from the usual a priori assumptions about the laws of nature.
Quantum mechanics for mathematicians
Takhtajan, Leon A
2008-01-01
This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. It addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks ...
Quantum Chaos and Statistical Mechanics
Srednicki, Mark
1994-01-01
We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.
Quantum Computation and Decision Trees
Farhi, E; Farhi, Edward; Gutmann, Sam
1998-01-01
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root. We devise a quantum mechanical algorithm that evolves a state, initially localized at the root, through the tree. We prove that if the classical strategy succeeds in reaching level n in time polynomial in n, then so does the quantum algorithm. Moreover, we find examples of trees for which the classical algorithm requires time exponential in n, but for which the quantum algorithm succeeds in polynomial time. The examples we have so far, however, could also be solved in polynomial time by different classical algorithms.
Programmable architecture for quantum computing
Chen, J.; Wang, L.; Charbon, E.; Wang, B.
2013-01-01
A programmable architecture called “quantum FPGA (field-programmable gate array)” (QFPGA) is presented for quantum computing, which is a hybrid model combining the advantages of the qubus system and the measurement-based quantum computation. There are two kinds of buses in QFPGA, the local bus and t
Fluxon-controlled quantum computer
Fujii, Toshiyuki; Matsuo, Shigemasa; Hatakenaka, Noriyuki
2016-11-01
We propose a fluxon-controlled quantum computer incorporated with three-qubit quantum error correction using special gate operations, i.e. joint-phase and SWAP gate operations, inherent in capacitively coupled superconducting flux qubits. The proposed quantum computer acts exactly like a knitting machine at home.
Programmable architecture for quantum computing
Chen, J.; Wang, L.; Charbon, E.; Wang, B.
2013-01-01
A programmable architecture called “quantum FPGA (field-programmable gate array)” (QFPGA) is presented for quantum computing, which is a hybrid model combining the advantages of the qubus system and the measurement-based quantum computation. There are two kinds of buses in QFPGA, the local bus and t
Quantum mechanical Carnot engine
Bender, C M; Meister, B K
2000-01-01
A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing an ideal gas. Here, we present an example of a cyclic engine based on a single quantum-mechanical particle confined to a potential well. The efficiency of this engine is shown to equal the Carnot efficiency because quantum dynamics is reversible. The quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes that are close analogues of the corresponding classical processes.
The potential of the quantum computer
2006-01-01
The Physics Section of the University of Geneva is continuing its series of lectures, open to the general public, on the most recent developments in the field of physics. The next lecture, given by Professor Michel Devoret of Yale University in the United States, will be on the potential of the quantum computer. The quantum computer is, as yet, a hypothetical machine which would operate on the basic principles of quantum mechanics. Compared to standard computers, it represents a significant gain in computing power for certain complex calculations. Quantum operations can simultaneously explore a very large number of possibilities. The correction of quantum errors, which until recently had been deemed impossible, has now become a well-established technique. Several prototypes for, as yet, very simple quantum processors have been developed. The lecture will begin with a demonstration in the auditorium of the detection of cosmic rays and, in collaboration with Professor E. Ellberger of the Conservatoire de M...
Alzate-Morales, Jans H; Contreras, Renato; Soriano, Alejandro; Tuñon, Iñaki; Silla, Estanislao
2007-01-15
We report a combined quantum mechanics/molecular mechanics (QM/MM) study to determine the protein-ligand interaction energy between CDK2 (cyclin-dependent kinase 2) and five inhibitors with the N(2)-substituted 6-cyclohexyl-methoxy-purine scaffold. The computational results in this work show that the QM/MM interaction energy is strongly correlated to the biological activity and can be used as a predictor, at least within a family of substrates. A detailed analysis of the protein-ligand structures obtained from molecular dynamics simulations shows specific interactions within the active site that, in some cases, have not been reported before to our knowledge. The computed interaction energy gauges the strength of protein-ligand interactions. Finally, energy decomposition and multiple regression analyses were performed to check the contribution of the electrostatic and van der Waals energies to the total interaction energy and to show the capabilities of the computational model to identify new potent inhibitors.
Layered Architecture for Quantum Computing
National Research Council Canada - National Science Library
Jones, N. Cody; Van Meter, Rodney; Fowler, Austin G; McMahon, Peter L; Kim, Jungsang; Ladd, Thaddeus D; Yamamoto, Yoshihisa
2012-01-01
.... We discuss many of the prominent techniques for implementing circuit-model quantum computing and introduce several new methods, with an emphasis on employing surface-code quantum error correction...
Quantum computing: Efficient fault tolerance
Gottesman, Daniel
2016-12-01
Dealing with errors in a quantum computer typically requires complex programming and many additional quantum bits. A technique for controlling errors has been proposed that alleviates both of these problems.
Odake, Satoru; Sasaki, Ryu
2011-01-01
A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creati...
Rosu, H C
2000-01-01
This is the first graduate course on elementary quantum mechanics in Internet written in Romanian for the benefit of Romanian speaking students (Romania and Moldova). It is a translation (with corrections) of the Spanish version of the course (physics/9808031, English translation is under consideration), which I did at the request of students of physics in Bucharest. The topics included refer to the postulates of quantum mechanics, one-dimensional barriers and wells, angular momentum and spin, WKB method, harmonic oscillator, hydrogen atom, quantum scattering, and partial waves
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.
Addition on a Quantum Computer
Draper, Thomas G
2000-01-01
A new method for computing sums on a quantum computer is introduced. This technique uses the quantum Fourier transform and reduces the number of qubits necessary for addition by removing the need for temporary carry bits. This approach also allows the addition of a classical number to a quantum superposition without encoding the classical number in the quantum register. This method also allows for massive parallelization in its execution.
Computational quantum-classical boundary of noisy commuting quantum circuits.
Fujii, Keisuke; Tamate, Shuhei
2016-05-18
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region.
Interfacing external quantum devices to a universal quantum computer.
Lagana, Antonio A; Lohe, Max A; von Smekal, Lorenz
2011-01-01
We present a scheme to use external quantum devices using the universal quantum computer previously constructed. We thereby show how the universal quantum computer can utilize networked quantum information resources to carry out local computations. Such information may come from specialized quantum devices or even from remote universal quantum computers. We show how to accomplish this by devising universal quantum computer programs that implement well known oracle based quantum algorithms, namely the Deutsch, Deutsch-Jozsa, and the Grover algorithms using external black-box quantum oracle devices. In the process, we demonstrate a method to map existing quantum algorithms onto the universal quantum computer.
Interfacing external quantum devices to a universal quantum computer.
Directory of Open Access Journals (Sweden)
Antonio A Lagana
Full Text Available We present a scheme to use external quantum devices using the universal quantum computer previously constructed. We thereby show how the universal quantum computer can utilize networked quantum information resources to carry out local computations. Such information may come from specialized quantum devices or even from remote universal quantum computers. We show how to accomplish this by devising universal quantum computer programs that implement well known oracle based quantum algorithms, namely the Deutsch, Deutsch-Jozsa, and the Grover algorithms using external black-box quantum oracle devices. In the process, we demonstrate a method to map existing quantum algorithms onto the universal quantum computer.
Effectively Emergent Quantum Mechanics
Exirifard, Qasem
2008-01-01
We consider non minimal coupling between matters and gravity in modified theories of gravity. In contrary to the current common sense, we report that quantum mechanics can effectively emerge when the space-time geometry is sufficiently flat. In other words, quantum mechanics might play no role when and where the space-time geometry is highly curved. We study the first two simple models of Effectively Emergent Quantum Mechanics(EEQM): R-dependent EEQM and G-dependent EEQM where R is the Ricci scalar and G is the Gauss-Bonnet Lagrangian density. We discuss that these EEQM theories might be fine tuned to remain consistent with all the implemented experiments and performed observations. In particular, we observe that G-dependent EEQM softens the problem of quantum gravity.
Massively parallel quantum computer simulator
De Raedt, K.; Michielsen, K.; De Raedt, H.; Trieu, B.; Arnold, G.; Richter, M.; Lippert, Th.; Watanabe, H.; Ito, N.
2007-01-01
We describe portable software to simulate universal quantum computers on massive parallel Computers. We illustrate the use of the simulation software by running various quantum algorithms on different computer architectures, such as a IBM BlueGene/L, a IBM Regatta p690+, a Hitachi SR11000/J1, a Cray
Towards quantum chemistry on a quantum computer.
Lanyon, B P; Whitfield, J D; Gillett, G G; Goggin, M E; Almeida, M P; Kassal, I; Biamonte, J D; Mohseni, M; Powell, B J; Barbieri, M; Aspuru-Guzik, A; White, A G
2010-02-01
Exact first-principles calculations of molecular properties are currently intractable because their computational cost grows exponentially with both the number of atoms and basis set size. A solution is to move to a radically different model of computing by building a quantum computer, which is a device that uses quantum systems themselves to store and process data. Here we report the application of the latest photonic quantum computer technology to calculate properties of the smallest molecular system: the hydrogen molecule in a minimal basis. We calculate the complete energy spectrum to 20 bits of precision and discuss how the technique can be expanded to solve large-scale chemical problems that lie beyond the reach of modern supercomputers. These results represent an early practical step toward a powerful tool with a broad range of quantum-chemical applications.
Fault-tolerant quantum computation
Preskill, J
1997-01-01
The discovery of quantum error correction has greatly improved the long-term prospects for quantum computing technology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment, or due to imperfect implementations of quantum logical operations. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. In principle, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per gate is less than a certain critical value, the accuracy threshold. It may be possible to incorporate intrinsic fault tolerance into the design of quantum computing hardware, perhaps by invoking topological Aharonov-Bohm interactions to process quantum information.
Dolev, S; Kolenda, N
2005-01-01
For more than a century, quantum mechanics has served as a very powerful theory that has expanded physics and technology far beyond their classical limits, yet it has also produced some of the most difficult paradoxes known to the human mind. This book represents the combined efforts of sixteen of today's most eminent theoretical physicists to lay out future directions for quantum physics. The authors include Yakir Aharonov, Anton Zeilinger; the Nobel laureates Anthony Leggett and Geradus 't Hooft; Basil Hiley, Lee Smolin and Henry Stapp. Following a foreword by Roger Penrose, the individual chapters address questions such as quantum non-locality, the measurement problem, quantum insights into relativity, cosmology and thermodynamics, and the possible bearing of quantum phenomena on biology and consciousness.
Vianna, R O; Monken, C H; Vianna, Reinaldo O.; Rabelo, Wilson R. M.
2003-01-01
We discuss the performance of the Search and Fourier Transform algorithms on a hybrid computer constituted of classical and quantum processors working together. We show that this semi-quantum computer would be an improvement over a pure classical architecture, no matter how few qubits are available and, therefore, it suggests an easier implementable technology than a pure quantum computer with arbitrary number of qubits.
Is the Brain a Quantum Computer?
Litt, Abninder; Eliasmith, Chris; Kroon, Frederick W.; Weinstein, Steven; Thagard, Paul
2006-01-01
We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substantial physical obstacles to any organic…
Gonzalez, E; Lino, J; Deriabina, A; Herrera, J N F; Poltev, V I
2013-01-01
To elucidate details of the DNA-water interactions we performed the calculations and systemaitic search for minima of interaction energy of the systems consisting of one of DNA bases and one or two water molecules. The results of calculations using two force fields of molecular mechanics (MM) and correlated ab initio method MP2/6-31G(d, p) of quantum mechanics (QM) have been compared with one another and with experimental data. The calculations demonstrated a qualitative agreement between geometry characteristics of the most of local energy minima obtained via different methods. The deepest minima revealed by MM and QM methods correspond to water molecule position between two neighbor hydrophilic centers of the base and to the formation by water molecule of hydrogen bonds with them. Nevertheless, the relative depth of some minima and peculiarities of mutual water-base positions in' these minima depend on the method used. The analysis revealed insignificance of some differences in the results of calculations performed via different methods and the importance of other ones for the description of DNA hydration. The calculations via MM methods enable us to reproduce quantitatively all the experimental data on the enthalpies of complex formation of single water molecule with the set of mono-, di-, and trimethylated bases, as well as on water molecule locations near base hydrophilic atoms in the crystals of DNA duplex fragments, while some of these data cannot be rationalized by QM calculations.
Energy Technology Data Exchange (ETDEWEB)
Koenneker, Carsten (comp.)
2012-11-01
The following topics are dealt with: Reality in the test facility, quantum teleportation, the reality of quanta, interaction-free quantum measurement, rules for quantum computers, quantum computers with ions, spintronics with diamond, the limits of the quantum computers, a view in the future of quantum optics. (HSI)
Mayato, R; Egusquiza, I
2002-01-01
The treatment of time in quantum mechanics is still an important and challenging open question in the foundation of the theory. This book describes the problems, and the attempts and achievements in defining, formalizing and measuring different time quantities in quantum theory, such as the parametric (clock) time, tunneling times, decay times, dwell times, delay times, arrival times or jump times. This multiauthored book, written as an introductory guide for the non-initiated as well as a useful source of information for the expert, covers many of the open questions. A brief historical overview is to be found in the introduction. It is followed by 12 chapters devoted to conceptual and theoretical investigations as well as experimental issues in quantum-mechanical time measurements. This unique monograph should attract physicists as well as philosophers of science working in the foundations of quantum physics.
Probability in quantum mechanics
Directory of Open Access Journals (Sweden)
J. G. Gilson
1982-01-01
Full Text Available By using a fluid theory which is an alternative to quantum theory but from which the latter can be deduced exactly, the long-standing problem of how quantum mechanics is related to stochastic processes is studied. It can be seen how the Schrödinger probability density has a relationship to time spent on small sections of an orbit, just as the probability density has in some classical contexts.
Mechanics classical and quantum
Taylor, T T
2015-01-01
Mechanics: Classical and Quantum explains the principles of quantum mechanics via the medium of analytical mechanics. The book describes Schrodinger's formulation, the Hamilton-Jacobi equation, and the Lagrangian formulation. The author discusses the Harmonic Oscillator, the generalized coordinates, velocities, as well as the application of the Lagrangian formulation to systems that are partially or entirely electromagnetic in character under certain conditions. The book examines waves on a string under tension, the isothermal cavity radiation, and the Rayleigh-Jeans result pertaining to the e
Interactive learning tutorials on quantum mechanics
Singh, Chandralekha
2016-01-01
We discuss the development and evaluation of quantum interactive learning tutorials (QuILTs) which are suitable for undergraduate courses in quantum mechanics. QuILTs are based on the investigation of student difficulties in learning quantum physics. They exploit computer-based visualization tools and help students build links between the formal and conceptual aspects of quantum physics without compromising the technical content. They can be used both as supplements to lectures or as a self-study tool.
The quantum mechanics of cosmology.
Hartle, James B.
The following sections are included: * INTRODUCTION * POST-EVERETT QUANTUM MECHANICS * Probability * Probabilities in general * Probabilities in Quantum Mechanics * Decoherent Histories * Fine and Coarse Grained Histories * Decohering Sets of Coarse Grained Histories * No Moment by Moment Definition of Decoherence * Prediction, Retrodiction, and History * Prediction and Retrodiction * The Reconstruction of History * Branches (Illustrated by a Pure ρ) * Sets of Histories with the Same Probabilities * The Origins of Decoherence in Our Universe * On What Does Decoherence Depend? * Two Slit Model * The Caldeira-Leggett Oscillator Model * The Evolution of Reduced Density Matrices * Towards a Classical Domain * The Branch Dependence of Decoherence * Measurement * The Ideal Measurement Model and the Copenhagen Approximation to Quantum Mechanics * Approximate Probabilities Again * Complex Adaptive Systems * Open Questions * GENERALIZED QUANTUM MECHANICS * General Features * Hamiltonian Quantum Mechanics * Sum-Over-Histories Quantum Mechanics for Theories with a Time * Differences and Equivalences between Hamiltonian and Sum-Over-Histories Quantum Mechanics for Theories with a Time * Classical Physics and the Classical Limit of Quantum Mechanics * Generalizations of Hamiltonian Quantum Mechanics * TIME IN QUANTUM MECHANICS * Observables on Spacetime Regions * The Arrow of Time in Quantum Mechanics * Topology in Time * The Generality of Sum Over Histories Quantum Mechanics * THE QUANTUM MECHANICS OF SPACETIME * The Problem of Time * General Covariance and Time in Hamiltonian Quantum Mechanics * The "Marvelous Moment" * A Quantum Mechanics for Spacetime * What we Need * Sum-Over-Histories Quantum Mechanics for Theories Without a Time * Sum-Over-Spacetime-Histories Quantum Mechanics * Extensions and Contractions * The Construction of Sums Over Spacetime Histories * Some Open Questions * PRACTICAL QUANTUM COSMOLOGY * The Semiclassical Regime * The Semiclassical Approximation
Simulating chemistry using quantum computers
Kassal, Ivan; Perdomo-Ortiz, Alejandro; Yung, Man-Hong; Aspuru-Guzik, Alán
2010-01-01
The difficulty of simulating quantum systems, well-known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks. Although theory is still ahead of experiment, we outline recent advances that have led to the first chemical calculations on small quantum information processors.
Simulating chemistry using quantum computers.
Kassal, Ivan; Whitfield, James D; Perdomo-Ortiz, Alejandro; Yung, Man-Hong; Aspuru-Guzik, Alán
2011-01-01
The difficulty of simulating quantum systems, well known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks. Although theory is still ahead of experiment, we outline recent advances that have led to the first chemical calculations on small quantum information processors.
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.
Fundamentals of quantum mechanics
House, J E
2017-01-01
Fundamentals of Quantum Mechanics, Third Edition is a clear and detailed introduction to quantum mechanics and its applications in chemistry and physics. All required math is clearly explained, including intermediate steps in derivations, and concise review of the math is included in the text at appropriate points. Most of the elementary quantum mechanical models-including particles in boxes, rigid rotor, harmonic oscillator, barrier penetration, hydrogen atom-are clearly and completely presented. Applications of these models to selected “real world” topics are also included. This new edition includes many new topics such as band theory and heat capacity of solids, spectroscopy of molecules and complexes (including applications to ligand field theory), and small molecules of astrophysical interest.
Quantum information processing in nanostructures Quantum optics; Quantum computing
Reina-Estupinan, J H
2002-01-01
Since information has been regarded os a physical entity, the field of quantum information theory has blossomed. This brings novel applications, such as quantum computation. This field has attracted the attention of numerous researchers with backgrounds ranging from computer science, mathematics and engineering, to the physical sciences. Thus, we now have an interdisciplinary field where great efforts are being made in order to build devices that should allow for the processing of information at a quantum level, and also in the understanding of the complex structure of some physical processes at a more basic level. This thesis is devoted to the theoretical study of structures at the nanometer-scale, 'nanostructures', through physical processes that mainly involve the solid-state and quantum optics, in order to propose reliable schemes for the processing of quantum information. Initially, the main results of quantum information theory and quantum computation are briefly reviewed. Next, the state-of-the-art of ...
Models of optical quantum computing
Directory of Open Access Journals (Sweden)
Krovi Hari
2017-03-01
Full Text Available I review some work on models of quantum computing, optical implementations of these models, as well as the associated computational power. In particular, we discuss the circuit model and cluster state implementations using quantum optics with various encodings such as dual rail encoding, Gottesman-Kitaev-Preskill encoding, and coherent state encoding. Then we discuss intermediate models of optical computing such as boson sampling and its variants. Finally, we review some recent work in optical implementations of adiabatic quantum computing and analog optical computing. We also provide a brief description of the relevant aspects from complexity theory needed to understand the results surveyed.
Quantum Computer Using Coupled Quantum Dot Molecules
Wu, N J; Natori, A; Yasunaga, H; Wu*, Nan-Jian
1999-01-01
We propose a method for implementation of a quantum computer using artificial molecules. The artificial molecule consists of two coupled quantum dots stacked along z direction and one single electron. One-qubit and two-qubit gates are constructed by one molecule and two coupled molecules, respectively.The ground state and the first excited state of the molecule are used to encode the |0> and |1> states of a qubit. The qubit is manipulated by a resonant electromagnetic wave that is applied directly to the qubit through a microstrip line. The coupling between two qubits in a quantum controlled NOT gate is switched on (off) by floating (grounding) the metal film electrodes. We study the operations of the gates by using a box-shaped quantum dot model and numerically solving a time-dependent Schridinger equation, and demonstrate that the quantum gates can perform the quantum computation. The operating speed of the gates is about one operation per 4ps. The reading operation of the output of the quantum computer can...
Supersymmetric Quantum Mechanics and Topology
Directory of Open Access Journals (Sweden)
Muhammad Abdul Wasay
2016-01-01
Full Text Available Supersymmetric quantum mechanical models are computed by the path integral approach. In the β→0 limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of supersymmetric localization, and we will show how the geometry of target space enters the physics of sigma models resulting in the relationship between the supersymmetric model and the geometry of the target space in the form of topological invariants. Explicit computation details are given for the Euler characteristics of the target manifold and the index of Dirac operator for the model on a spin manifold.
Quantum Genetic Algorithms for Computer Scientists
Directory of Open Access Journals (Sweden)
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.
Quasicrystals and Quantum Computing
Berezin, Alexander A.
1997-03-01
In Quantum (Q) Computing qubits form Q-superpositions for macroscopic times. One scheme for ultra-fast (Q) computing can be based on quasicrystals. Ultrafast processing in Q-coherent structures (and the very existence of durable Q-superpositions) may be 'consequence' of presence of entire manifold of integer arithmetic (A0, aleph-naught of Georg Cantor) at any 4-point of space-time, furthermore, at any point of any multidimensional phase space of (any) N-particle Q-system. The latter, apart from quasicrystals, can include dispersed and/or diluted systems (Berezin, 1994). In such systems such alleged centrepieces of Q-Computing as ability for fast factorization of long integers can be processed by sheer virtue of the fact that entire infinite pattern of prime numbers is instantaneously available as 'free lunch' at any instant/point. Infinitely rich pattern of A0 (including pattern of primes and almost primes) acts as 'independent' physical effect which directly generates Q-dynamics (and physical world) 'out of nothing'. Thus Q-nonlocality can be ultimately based on instantaneous interconnectedness through ever- the-same structure of A0 ('Platonic field' of integers).
Kogan, VI; Gersch, Harold
2011-01-01
Written by a pair of distinguished Soviet mathematicians, this compilation presents 160 lucidly expressed problems in nonrelativistic quantum mechanics plus completely worked-out solutions. Some were drawn from the authors' courses at the Moscow Institute of Engineering, but most were prepared especially for this book. A high-level supplement rather than a primary text, it constitutes a masterful complement to advanced undergraduate and graduate texts and courses in quantum mechanics.The mathematics employed in the proofs of the problems-asymptotic expansions of functions, Green's functions, u
Saxon, David S
2012-01-01
Based on lectures for an undergraduate UCLA course in quantum mechanics, this volume focuses on the formulas of quantum mechanics rather than applications. Widely used in both upper-level undergraduate and graduate courses, it offers a broad self-contained survey rather than in-depth treatments.Topics include the dual nature of matter and radiation, state functions and their interpretation, linear momentum, the motion of a free particle, Schrödinger's equation, approximation methods, angular momentum, and many other subjects. In the interests of keeping the mathematics as simple as possible, m
Noncommutative quantum mechanics
Gamboa, J.; Loewe, M.; Rojas, J. C.
2001-09-01
A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter θ, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of θ the model can be solved by using perturbation theory.
The Physics of Quantum Computation
Falci, Giuseppe; Paladino, Elisabette
2015-10-01
Quantum Computation has emerged in the past decades as a consequence of down-scaling of electronic devices to the mesoscopic regime and of advances in the ability of controlling and measuring microscopic quantum systems. QC has many interdisciplinary aspects, ranging from physics and chemistry to mathematics and computer science. In these lecture notes we focus on physical hardware, present day challenges and future directions for design of quantum architectures.
Hollowood, Timothy J.
2016-07-01
In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950s development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrödinger cat states are the norm rather than curiosities generated in physicists' laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr's quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics.
Time Asymmetric Quantum Mechanics
Directory of Open Access Journals (Sweden)
Arno R. Bohm
2011-09-01
Full Text Available The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1 for states or the Heisenberg equation (6a for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus and observables (defined by a registration apparatus (detector. If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t_0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.
Avoiding Quantum Chaos in Quantum Computation
Berman, G P; Izrailev, F M; Tsifrinovich, V I
2001-01-01
We study a one-dimensional chain of nuclear $1/2-$spins in an external time-dependent magnetic field. This model is considered as a possible candidate for experimental realization of quantum computation. According to the general theory of interacting particles, one of the most dangerous effects is quantum chaos which can destroy the stability of quantum operations. According to the standard viewpoint, the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits. Contrary to this opinion, we show that the presence of a magnetic field gradient helps to avoid quantum chaos which turns out to disappear with an increase of the number of qubits. We give analytical estimates which explain this effect, together with numerical data supporting
Determinism beneath Quantum Mechanics
Hooft, G
2002-01-01
Contrary to common belief, it is not difficult to construct deterministic models where stochastic behavior is correctly described by quantum mechanical amplitudes, in precise accordance with the Copenhagen-Bohr-Bohm doctrine. What is difficult however is to obtain a Hamiltonian that is bounded from below, and whose ground state is a vacuum that exhibits complicated vacuum fluctuations, as in the real world. Beneath Quantum Mechanics, there may be a deterministic theory with (local) information loss. This may lead to a sufficiently complex vacuum state, and to an apparent non-locality in the relation between the deterministic ("ontological") states and the quantum states, of the kind needed to explain away the Bell inequalities. Theories of this kind would not only be appealing from a philosophical point of view, but may also be essential for understanding causality at Planckian distance scales.
Relativistic quantum mechanics
Wachter, Armin
2010-01-01
Which problems do arise within relativistic enhancements of the Schrödinger theory, especially if one adheres to the usual one-particle interpretation, and to what extent can these problems be overcome? And what is the physical necessity of quantum field theories? In many books, answers to these fundamental questions are given highly insufficiently by treating the relativistic quantum mechanical one-particle concept very superficially and instead introducing field quantization as soon as possible. By contrast, this monograph emphasizes relativistic quantum mechanics in the narrow sense: it extensively discusses relativistic one-particle concepts and reveals their problems and limitations, therefore motivating the necessity of quantized fields in a physically comprehensible way. The first chapters contain a detailed presentation and comparison of the Klein-Gordon and Dirac theory, always in view of the non-relativistic theory. In the third chapter, we consider relativistic scattering processes and develop the...
Institute of Scientific and Technical Information of China (English)
吴宁; 阮图南
1996-01-01
A quantum mechanical model with one bosonic degree of freedom is discussed in detail. Conventionally, when a quantum mechanical model is constructed, one must know the corresponding classical model. And by applying the correspondence between the classical Poisson brackets and the canonical commutator, the canonical quantization condition can be obtained. In the quantum model, study of the corresponding classical model is needed first. In this model, the Lagrangian is an operator gauge invariant. After localization, in order to keep gauge invariance, the operator gauge potential must be introduced. The Eular-Lagrange equation of motion of the dynamical argument gives the usual operator equation of motion. And the operator gauge potential just gjves a constraint. This constraint is just the usual canonical quantization condition.
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.
Quantum entanglement and quantum computational algorithms
Indian Academy of Sciences (India)
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
Computational security of quantum encryption
Alagic, G.; Broadbent, A.; Fefferman, B.; Gagliardoni, T.; Schaffner, C.; St. Jules, M.; Nascimento, A.C.A.; Barreto, P.
2016-01-01
Quantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the security of classical cryptographic schemes against quantum attacks. In this work, we initiate the study of
Quantum Computational Complexity of Spin Glasses
2011-03-19
canonical problem of classical statistical mechanics: computation of the classical partition function. We have approached this problem using the Potts...enumerator polynomial from coding theory and Z and exploited the fact that there exists a quantum algorithm for efficiently estimating Gauss sums in...computational complexity of the canonical problem of classical statistical mechanics: computation of the classical partition function. We have approached this
Model dynamics for quantum computing
Tabakin, Frank
2017-08-01
A model master equation suitable for quantum computing dynamics is presented. In an ideal quantum computer (QC), a system of qubits evolves in time unitarily and, by virtue of their entanglement, interfere quantum mechanically to solve otherwise intractable problems. In the real situation, a QC is subject to decoherence and attenuation effects due to interaction with an environment and with possible short-term random disturbances and gate deficiencies. The stability of a QC under such attacks is a key issue for the development of realistic devices. We assume that the influence of the environment can be incorporated by a master equation that includes unitary evolution with gates, supplemented by a Lindblad term. Lindblad operators of various types are explored; namely, steady, pulsed, gate friction, and measurement operators. In the master equation, we use the Lindblad term to describe short time intrusions by random Lindblad pulses. The phenomenological master equation is then extended to include a nonlinear Beretta term that describes the evolution of a closed system with increasing entropy. An external Bath environment is stipulated by a fixed temperature in two different ways. Here we explore the case of a simple one-qubit system in preparation for generalization to multi-qubit, qutrit and hybrid qubit-qutrit systems. This model master equation can be used to test the stability of memory and the efficacy of quantum gates. The properties of such hybrid master equations are explored, with emphasis on the role of thermal equilibrium and entropy constraints. Several significant properties of time-dependent qubit evolution are revealed by this simple study.
Quantum computing in neural networks
Gralewicz, P
2004-01-01
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits. This raises the possibility of a large-scale quantum computing using PMs, especially with neural networks which have the innate capability for probabilistic information processing. Restricting ourselves to a particular model, we construct and numerically examine the performance of neural circuits implementing universal quantum gates. A discussion on the physiological plausibility of proposed coding scheme is also provided.
Fundamental gravitational limitations to quantum computing
Gambini, R; Pullin, J; Gambini, Rodolfo; Porto, Rafael A.; Pullin, Jorge
2005-01-01
Lloyd has considered the ultimate limitations physics places on quantum computers. He concludes in particular that for an ``ultimate laptop'' (a computer of one liter of volume and one kilogram of mass) the maximum number of operations per second is bounded by $10^{51}$. The limit is derived considering ordinary quantum mechanics. Here we consider additional limits that are placed by quantum gravity ideas, namely the use of a relational notion of time and fundamental gravitational limits that exist on time measurements. We then particularize for the case of an ultimate laptop and show that the maximum number of operations is further constrained to $10^{47}$ per second.
Quantum Computers: A New Paradigm in Information Technology
Directory of Open Access Journals (Sweden)
Mahesh S. Raisinghani
2001-01-01
Full Text Available The word 'quantum' comes from the Latin word quantus meaning 'how much'. Quantum computing is a fundamentally new mode of information processing that can be performed only by harnessing physical phenomena unique to quantum mechanics (especially quantum interference. Paul Benioff of the Argonne National Laboratory first applied quantum theory to computers in 1981 and David Deutsch of Oxford proposed quantum parallel computers in 1985, years before the realization of qubits in 1995. However, it may be well into the 21st century before we see quantum computing used at a commercial level for a variety of reasons discussed in this paper. The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This paper discusses some of the current advances, applications, and chal-lenges of quantum computing as well as its impact on corporate computing and implications for management. It shows how quantum computing can be utilized to process and store information, as well as impact cryptography for perfectly secure communication, algorithmic searching, factorizing large numbers very rapidly, and simulating quantum-mechanical systems efficiently. A broad interdisciplinary effort will be needed if quantum com-puters are to fulfill their destiny as the world's fastest computing devices.
Quantum Computation Beyond the Circuit Model
Jordan, Stephen P.
2008-01-01
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other models of quantum computation exist which provide useful alternative frameworks for both discovering new quantum algorithms and devising new physical implementations of quantum computers. In this thesis, I first present necessary background material for a ge...
Hollowood, Timothy J
2013-01-01
We describe an interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description for macro-systems. The interpretation is a modal one, but does not suffer from the range of problems that plague other modal interpretations. The key feature is that quantum states carry an additional property assignment in the form of one the eigenvectors of the reduced density matrix which evolves evolves according to a stochastic process driven by the unmodified Schrodinger equation, but it is usually hidden from the emergent classical description due to the ergodic nature of its dynamics. However, during a quantum measurement, ergodicity is broken by decoherence and definite outcomes occur with probabilities that agree with the Born rule.
Quantum mechanics with applications
Beard, David B
2014-01-01
This introductory text emphasizes Feynman's development of path integrals and its application to wave theory for particles. Suitable for undergraduate and graduate students of physics, the well-written, clear, and rigorous text was written by two of the nation's leading authorities on quantum physics. A solid foundation in quantum mechanics and atomic physics is assumed. Early chapters provide background in the mathematical treatment and particular properties of ordinary wave motion that also apply to particle motion. The close relation of quantum theory to physical optics is stressed. Subsequent sections emphasize the physical consequences of a wave theory of material properties, and they offer extensive applications in atomic physics, nuclear physics, solid state physics, and diatomic molecules. Four helpful Appendixes supplement the text.
Epigenetics: Biology's Quantum Mechanics.
Jorgensen, Richard A
2011-01-01
The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920s and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene - the molecular biological view and the epigenetic view - are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider.
Epigenetics: Biology's Quantum Mechanics
Directory of Open Access Journals (Sweden)
Richard A Jorgensen
2011-04-01
Full Text Available The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920's and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene - the molecular biological view and the epigenetic view - are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider.
Advanced concepts in quantum mechanics
Esposito, Giampiero; Miele, Gennaro; Sudarshan, George
2015-01-01
Introducing a geometric view of fundamental physics, starting from quantum mechanics and its experimental foundations, this book is ideal for advanced undergraduate and graduate students in quantum mechanics and mathematical physics. Focusing on structural issues and geometric ideas, this book guides readers from the concepts of classical mechanics to those of quantum mechanics. The book features an original presentation of classical mechanics, with the choice of topics motivated by the subsequent development of quantum mechanics, especially wave equations, Poisson brackets and harmonic oscillators. It also presents new treatments of waves and particles and the symmetries in quantum mechanics, as well as extensive coverage of the experimental foundations.
Ion Trap Quantum Computers: Performance Limits and Experimental Progress
Hughes, Richard
1998-03-01
In a quantum computer information would be represented by the quantum mechanical states of suitable atomic-scale systems. (A single bit of information represented by a two-level quantum system is known as a qubit.) This notion leads to the possibility of computing with quantum mechanical superpositions of numbers ("quantum parallelism"), which for certain problems would make Quantum/quantum.html>quantum computation very much more efficient than classical computation. The possibility of rapidly factoring the large integers used in public-key cryptography is an important example. (Public key cryptosystems derive their security from the difficuty of factoring, and similar problems, with conventional computers.) Quantum computational hardware development is in its infancy, but an experimental study of quantum computation with laser-cooled trapped calcium ions that is under way at Los Alamos will be described. One of the pricipal obstacles to practical quantum computation is the inevitable loss of quantum coherence of the complex quantum states involved. The results of a theoretical analysis showing that quantum factoring of small integers should be possible with trapped ions will be presented. The prospects for larger-scale computations will be discussed.
Palazzo, Teresa A.; Truong, Tiana T.; Wong, Shirley M. T.; Mack, Emma T.; Lodewyk, Michael W.; Harrison, Jason G.; Gamage, R. Alan; Siegel, Justin B.; Kurth, Mark J.; Tantillo, Dean J.
2015-01-01
An applied computational chemistry laboratory exercise is described in which students use modern quantum chemical calculations of chemical shifts to assign the structure of a recently isolated natural product. A pre/post assessment was used to measure student learning gains and verify that students demonstrated proficiency of key learning…
Palazzo, Teresa A.; Truong, Tiana T.; Wong, Shirley M. T.; Mack, Emma T.; Lodewyk, Michael W.; Harrison, Jason G.; Gamage, R. Alan; Siegel, Justin B.; Kurth, Mark J.; Tantillo, Dean J.
2015-01-01
An applied computational chemistry laboratory exercise is described in which students use modern quantum chemical calculations of chemical shifts to assign the structure of a recently isolated natural product. A pre/post assessment was used to measure student learning gains and verify that students demonstrated proficiency of key learning…
Cryptography, quantum computation and trapped ions
Energy Technology Data Exchange (ETDEWEB)
Hughes, Richard J.
1998-03-01
The significance of quantum computation for cryptography is discussed. Following a brief survey of the requirements for quantum computational hardware, an overview of the ion trap quantum computation project at Los Alamos is presented. The physical limitations to quantum computation with trapped ions are analyzed and an assessment of the computational potential of the technology is made.
EDITORIAL: Quantum Computing and the Feynman Festival
Brandt, Howard E.; Kim, Young S.; Man'ko, Margarita A.
2003-12-01
The Feynman Festival is a new interdisciplinary conference developed for studying Richard Feynman and his physics. The first meeting of this new conference series was held at the University of Maryland on 23--28 August 2002 (http://www.physics.umd.edu/robot/feynman.html) and the second meeting is scheduled for August 2004 at the same venue. According to Feynman, the different aspects of nature are different aspects of the same thing. Therefore, the ultimate purpose of the conference is to find Feynman's same thing from all different theories. For this reason, the first meeting of the Festival did not begin with a fixed formula, but composed its scientific programme based on responses from the entire physics community. The conference drew the most enthusiastic response from the community of quantum computing, the field initiated by Feynman. Encouraged by the response, we decided to edit a special issue of Journal of Optics B: Quantum and Semiclassical Optics on quantum computing in connection with the first Feynman Festival. The authorship is not restricted to the participants of the Feynman Festival, and all interested parties were encouraged to submit their papers on this subject. Needless to say, all the papers were peer reviewed according to the well-established standards of the journal. The subject of quantum computing is not restricted to building and operating computers. It requires a deeper understanding of how quantum mechanics works in materials as well as in our minds. Indeed, it covers the basic foundations of quantum mechanics, measurement theory, information theory, quantum optics, atomic physics and condensed matter physics. It may be necessary to develop new mathematical tools to accommodate the language that nature speaks. It is gratifying to note that this special issue contains papers covering all these aspects of quantum computing. As Feynman noted, we could be discussing these diversified issues to study one problem. In our case, this `one
Universal blind quantum computation for hybrid system
Huang, He-Liang; Bao, Wan-Su; Li, Tan; Li, Feng-Guang; Fu, Xiang-Qun; Zhang, Shuo; Zhang, Hai-Long; Wang, Xiang
2017-08-01
As progress on the development of building quantum computer continues to advance, first-generation practical quantum computers will be available for ordinary users in the cloud style similar to IBM's Quantum Experience nowadays. Clients can remotely access the quantum servers using some simple devices. In such a situation, it is of prime importance to keep the security of the client's information. Blind quantum computation protocols enable a client with limited quantum technology to delegate her quantum computation to a quantum server without leaking any privacy. To date, blind quantum computation has been considered only for an individual quantum system. However, practical universal quantum computer is likely to be a hybrid system. Here, we take the first step to construct a framework of blind quantum computation for the hybrid system, which provides a more feasible way for scalable blind quantum computation.
Brain-Computer Interfaces and Quantum Robots
Pessa, Eliano
2009-01-01
The actual (classical) Brain-Computer Interface attempts to use brain signals to drive suitable actuators performing the actions corresponding to subject's intention. However this goal is not fully reached, and when BCI works, it does only in particular situations. The reason of this unsatisfactory result is that intention cannot be conceived simply as a set of classical input-output relationships. It is therefore necessary to resort to quantum theory, allowing the occurrence of stable coherence phenomena, in turn underlying high-level mental processes such as intentions and strategies. More precisely, within the context of a dissipative Quantum Field Theory of brain operation it is possible to introduce generalized coherent states associated, within the framework of logic, to the assertions of a quantum metalanguage. The latter controls the quantum-mechanical computing corresponding to standard mental operation. It thus become possible to conceive a Quantum Cyborg in which a human mind controls, through a qu...
Quantum information and computing
Ohya, M; Watanabe, N
2006-01-01
The main purpose of this volume is to emphasize the multidisciplinary aspects of this very active new line of research in which concrete technological and industrial realizations require the combined efforts of experimental and theoretical physicists, mathematicians and engineers. Contents: Coherent Quantum Control of ?-Atoms through the Stochastic Limit (L Accardi et al.); Recent Advances in Quantum White Noise Calculus (L Accardi & A Boukas); Joint Extension of States of Fermion Subsystems (H Araki); Fidelity of Quantum Teleportation Model Using Beam Splittings (K-H Fichtner et al.); Quantum
Avila Ferrer, Francisco José; Improta, Roberto; Santoro, Fabrizio; Barone, Vincenzo
2011-10-14
Starting from Marcus's relationship connecting the inhomogeneous broadening with the solvent reorganization energy and exploiting recent state-specific developments in PCM/TD-DFT calculations, we propose a procedure to estimate the polar broadening of optical transitions. When applied to two representative molecular probes, coumarin C153 and 4-aminophthalimide, in different solvents, our approach provides for the polar broadening values fully consistent with the experimental ones. Thanks to these achievements, for the first time fully ab initio vibrationally resolved absorption spectra in solution are computed, obtaining spectra for coumarin C153 in remarkable agreement with experiments.
Scott, Tony C.
It has been shown that the Fokker-Wheeler-Feynman (FWF) model could be rewritten to yield a physically acceptable relativistic many-particle Lagrangian. Contrary to Wheeler and Feynman's postulates, the model satisfies causality and can be generalised to include arbitrary forces. The 1/c power series of the FWF Lagrangian to order (1/c) ^4 contains accelerations. A procedure of quantizing the theory for such a Lagrangian is presented and it is then found that the accelerations approximately introduce an independent harmonic mode which is in agreement with resonances recently observed in Positronium collisions processes. This result may be of fundamental physical importance and requires further investigation. However, the refinement of this calculation requires the creation of new computational tools. To this end, a new method is presented in which both the eigenfunctions and eigenenergies are determined algebraically as power series in the order parameter, where each coefficient of the series is obtained in closed form. This method avoids the complications of a basis set and makes extensive use of symbolic computation. It is then applied to two model problems, namely the one-body Dirac equation for testing purposes and a special case of the two-body Dirac equation for which one obtains previously unknown closed form solutions.
Symmetry and quantum mechanics
Corry, Scott
2016-01-01
This book offers an introduction to quantum mechanics for professionals, students, and others in the field of mathematics who have a minimal background in physics with an understanding of linear algebra and group theory. It covers such topics as Lie groups, algebras and their representations, and analysis (Hilbert space, distributions, the spectral Theorem, and the Stone-Von Neumann Theorem). The book emphasizes the role of symmetry and is useful to physicists as it provides a mathematical introduction to the topic.
Graduate Quantum Mechanics Reform
Carr, L D
2008-01-01
We address four main areas in which graduate quantum mechanics education in the U.S. can be improved: course content; textbook; teaching methods; and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all four of these areas. In particular, we have modified the content of the course to reflect progress in the field in the last 50 years, use modern textbooks that include such content, incorporate a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We present a new assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further testing of a previously developed assessment tool, the Quantum Mechanics Conceptual Survey (QMCS). We find that graduate students respond well to research-based techniques that have previously been tested mainly in introductory courses, and that they learn a great deal of the new content introduced in each ve...
Quantum Mechanics in the Infrared
Radicevic, Djordje
2016-01-01
This paper presents an algebraic formulation of the renormalization group flow in quantum mechanics on flat target spaces. For any interacting quantum mechanical theory, the fixed point of this flow is a theory of classical probability, not a different effective quantum mechanics. Each energy eigenstate of the UV Hamiltonian flows to a probability distribution whose entropy is a natural diagnostic of quantum ergodicity of the original state. These conclusions are supported by various examples worked out in detail.
Computing on Anonymous Quantum Network
Kobayashi, Hirotada; Tani, Seiichiro
2010-01-01
This paper considers distributed computing on an anonymous quantum network, a network in which no party has a unique identifier and quantum communication and computation are available. It is proved that the leader election problem can exactly (i.e., without error in bounded time) be solved with at most the same complexity up to a constant factor as that of exactly computing symmetric functions (without intermediate measurements for a distributed and superposed input), if the number of parties is given to every party. A corollary of this result is a more efficient quantum leader election algorithm than existing ones: the new quantum algorithm runs in O(n) rounds with bit complexity O(mn^2), on an anonymous quantum network with n parties and m communication links. Another corollary is the first quantum algorithm that exactly computes any computable Boolean function with round complexity O(n) and with smaller bit complexity than that of existing classical algorithms in the worst case over all (computable) Boolea...
Quantum-enhanced Sensing and Efficient Quantum Computation
2015-07-27
Quantum -enhanced sensing and efficient quantum computation Ian Walmsley THE UNIVERSITY OF...COVERED (From - To) 1 February 2013 - 31 January 2015 4. TITLE AND SUBTITLE Quantum -enhanced sensing and efficient quantum computation 5a. CONTRACT...1895616013 Standard Form 298 (Rev. 8/98) Prescribed by ANSI Std. Z39.18 Final report for “ Quantum ‐Enhanced Sensing and Efficient Quantum Computation
Quantum Computing via The Bethe Ansatz
Zhang, Yong,
2011-01-01
We recognize quantum circuit model of computation as factorisable scattering model and propose that a quantum computer is associated with a quantum many-body system solved by the Bethe ansatz. As an typical example to support our perspectives on quantum computation, we study quantum computing in one-dimensional nonrelativistic system with delta-function interaction, where the two-body scattering matrix satisfies the factorisation equation (the quantum Yang--Baxter equation) and acts as a para...
Kesidis, George
2009-01-01
Wong's diffusion network is a stochastic, zero-input Hopfield network with a Gibbs stationary distribution over a bounded, connected continuum. Previously, logarithmic thermal annealing was demonstrated for the diffusion network and digital versions of it were studied and applied to imaging. Recently, "quantum" annealed Markov chains have garnered significant attention because of their improved performance over "pure" thermal annealing. In this note, a joint quantum and thermal version of Wong's diffusion network is described and its convergence properties are studied. Different choices for "auxiliary" functions are discussed, including those of the kinetic type previously associated with quantum annealing.
Basdevant, Jean-Louis
2007-01-01
Beautifully illustrated and engagingly written, Lectures on Quantum Mechanics presents theoretical physics with a breathtaking array of examples and anecdotes. Basdevant's style is clear and stimulating, in the manner of a brisk classroom lecture that students can follow with ease and enjoyment. Here is a sample of the book's style, from the opening of Chapter 1: "If one were to ask a passer-by to quote a great formula of physics, chances are that the answer would be 'E = mc2'. Nevertheless, the formula 'E=hV' which was written in the same year 1905 by the same Albert Einstein, and which started quantum theory, concerns their daily life considerably more. In fact, of the three watershed years for physics toward the beginning of the 20th century - 1905: the Special Relativity of Einstein, Lorentz and Poincaré; 1915: the General Relativity of Einstein, with its extraordinary reflections on gravitation, space and time; and 1925: the full development of Quantum Mechanics - it is surely the last which has the mos...
Hollowood, Timothy J
2015-01-01
In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950's development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrodinger cat states are the norm rather than curiosities generat...
Massive Parallel Quantum Computer Simulator
De Raedt, K; De Raedt, H; Ito, N; Lippert, T; Michielsen, K; Richter, M; Trieu, B; Watanabe, H; Lippert, Th.
2006-01-01
We describe portable software to simulate universal quantum computers on massive parallel computers. We illustrate the use of the simulation software by running various quantum algorithms on different computer architectures, such as a IBM BlueGene/L, a IBM Regatta p690+, a Hitachi SR11000/J1, a Cray X1E, a SGI Altix 3700 and clusters of PCs running Windows XP. We study the performance of the software by simulating quantum computers containing up to 36 qubits, using up to 4096 processors and up to 1 TB of memory. Our results demonstrate that the simulator exhibits nearly ideal scaling as a function of the number of processors and suggest that the simulation software described in this paper may also serve as benchmark for testing high-end parallel computers.
Sakurai, Jun John
2011-01-01
This best-selling classic provides a graduate-level, non-historical, modern introduction of quantum mechanical concepts. The author, J. J. Sakurai, was a renowned theorist in particle theory. This revision by Jim Napolitano retains the original material and adds topics that extend the text’s usefulness into the 21st century. The introduction of new material, and modification of existing material, appears in a way that better prepares the student for the next course in quantum field theory. You will still find such classic developments as neutron interferometer experiments, Feynman path integrals, correlation measurements, and Bell’s inequality. The style and treatment of topics is now more consistent across chapters.
Quantum mechanics theory and experiment
Beck, Mark
2012-01-01
This textbook presents quantum mechanics at the junior/senior undergraduate level. It is unique in that it describes not only quantum theory, but also presents five laboratories that explore truly modern aspects of quantum mechanics. These laboratories include "proving" that light contains photons, single-photon interference, and tests of local realism. The text begins by presenting the classical theory of polarization, moving on to describe the quantum theory of polarization. Analogies between the two theories minimize conceptual difficulties that students typically have when first presented with quantum mechanics. Furthermore, because the laboratories involve studying photons, using photon polarization as a prototypical quantum system allows the laboratory work to be closely integrated with the coursework. Polarization represents a two-dimensional quantum system, so the introduction to quantum mechanics uses two-dimensional state vectors and operators. This allows students to become comfortable with the mat...
Scan Quantum Mechanics: Quantum Inertia Stops Superposition
Gato-Rivera, Beatriz
2015-01-01
A novel interpretation of the quantum mechanical superposition is put forward. Quantum systems scan all possible available states and switch randomly and very rapidly among them. The longer they remain in a given state, the larger the probability of the system to be found in that state during a measurement. A crucial property that we postulate is quantum inertia, that increases whenever a constituent is added, or the system is perturbed with all kinds of interactions. Once the quantum inertia $I_q$ reaches a critical value $I_{cr}$ for an observable, the switching among the different eigenvalues of that observable stops and the corresponding superposition comes to an end. Consequently, increasing the mass, temperature, gravitational force, etc. of a quantum system increases its quantum inertia until the superposition of states disappears for all the observables and the system transmutes into a classical one. The process could be reversible decreasing the size, temperature, gravitational force, etc. leading to...
Matrix Quantum Mechanics from Qubits
Hartnoll, Sean A; Mazenc, Edward A
2016-01-01
We introduce a transverse field Ising model with order N^2 spins interacting via a nonlocal quartic interaction. The model has an O(N,Z), hyperoctahedral, symmetry. We show that the large N partition function admits a saddle point in which the symmetry is enhanced to O(N). We further demonstrate that this `matrix saddle' correctly computes large N observables at weak and strong coupling. The matrix saddle undergoes a continuous quantum phase transition at intermediate couplings. At the transition the matrix eigenvalue distribution becomes disconnected. The critical excitations are described by large N matrix quantum mechanics. At the critical point, the low energy excitations are waves propagating in an emergent 1+1 dimensional spacetime.
Exactly Solvable Quantum Mechanics
Sasaki, Ryu
2014-01-01
A comprehensive review of exactly solvable quantum mechanics is presented with the emphasis of the recently discovered multi-indexed orthogonal polynomials. The main subjects to be discussed are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modifications), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, coherent states, various deformation schemes (multiple Darboux transformations) and the infinite families of multi-indexed orthogonal polynomials, the exceptional orthogonal polynomials, and deformed exactly solvable scattering problems.
Continuous Quantum Computation
2007-03-01
Eigenvalues and Eigenvectors”, by D.S. Abrams and S. Lloyd Physical Review Letters , 1999, Vol. 83, 5162-5156 [6] “Design of Strongly Modulating...by Y.S. Weinstein, S.Lloyd, J.V. Emerson and D.G. Cory, Physical Review Letters , 2002, Vol. 89,157902 [8] “The Edge of Quantum Chaos”, by Y.S...Weinstein, S. Lloyd and C. Tsallis, Physical Review Letters , 2002, Vol. 89, 214101 [9] “Fidelity Decay as an Efficient Indicator of Quantum Chaos
Quantum Mechanics and Quantum Field Theory
Dimock, Jonathan
2011-02-01
Introduction; Part I. Non-relativistic: 1. Mathematical prelude; 2. Classical mechanics; 3. Quantum mechanics; 4. Single particle; 5. Many particles; 6. Statistical mechanics; Part II. Relativistic: 7. Relativity; 8. Scalar particles and fields; 9. Electrons and photons; 10. Field theory on a manifold; Part III. Probabilistic Methods: 11. Path integrals; 12. Fields as random variables; 13. A nonlinear field theory; Appendices; References; Index.
Delegating private quantum computations12
Broadbent, Anne
2015-09-01
We give a protocol for the delegation of quantum computation on encrypted data. More specifically, we show that in a client-server scenario, where the client holds the encryption key for an encrypted quantum register held by the server, it is possible for the server to perform a universal set of quantum gates on the quantum data. All Clifford group gates are non-interactive, while the remaining non-Clifford group gate that we implement (the p/8 gate) requires the client to prepare and send a single random auxiliary qubit (chosen among four possibilities), and exchange classical communication. This construction improves on previous work, which requires either multiple auxiliary qubits or two-way quantum communication. Using a reduction to an entanglement-based protocol, we show privacy against any adversarial server according to a simulation-based security definition.
Energy Technology Data Exchange (ETDEWEB)
Brandt, Siegmund; Dahmen, Hans Dieter [Siegen Univ. (Germany). Dept. Physik
2015-07-01
The text presents the fundamental ideas of quantum mechanics. The introducing chapter 1 puts the cornerstone with a discussion of the particle properties of the light starting from the experimental results on the photoelectric effect and on the Compton effect and the wave properties of particles, as they have been proved by the diffraction of electrons. In chapter 2 it is also described, how wave packets of the light move in the space, and how they are reflected and refracted on glass plates. In chapter 3 material particles are introduced as wave packets of de-Broglie waves. The suitability of de-Broglie waves for the description of the mechanics of particles is explained by means of a discussion of the group velocity, Heisenberg's uncertainty relation, and Born's probability interpretation. The Schroedinger equation is thereby proved as equation of motion. The chapters 4 to 9 are dedicated to quantum-mechanical systems in one dimension. The chapters 8 and 9 treat two-particle systems. The quantum mechanics in three dimension is the object of the chapters 10 to 16. The spin is treated in chapter 17. In the last chapter we discuss experiments from atomic, molecule, solid-state, nuclear, and particle physics.
QCE : A Simulator for Quantum Computer Hardware
Michielsen, Kristel; Raedt, Hans De
2003-01-01
The Quantum Computer Emulator (QCE) described in this paper consists of a simulator of a generic, general purpose quantum computer and a graphical user interface. The latter is used to control the simulator, to define the hardware of the quantum computer and to debug and execute quantum algorithms.
DEFF Research Database (Denmark)
Salvail, Louis; Arrighi, Pablo
2006-01-01
protocol for the class of functions which admit an efficient procedure to generate random input-output pairs, e.g. factorization. The cheat-sensitive security achieved relies only upon quantum theory being true. The security analysis carried out assumes the eavesdropper performs individual attacks....
Cavity QED: applications to quantum computation
Xiong, Han; Zubairy, M. Suhail
2004-10-01
Possible schemes to implement the basic quantum gates for quantum computation have been presented based on cavity quantum electrodynamics (QED) systems. We then discuss schemes to implement several important quantum algorithms such as the discrete quantum fourier transform (QFT) algorithm and Grover's quantum search algorithm based on these quantum gates. Some other applications of cavity QED based systems including the implementations of a quantum disentanglement eraser and an entanglement amplifier are also discussed.
Handbook of computational quantum chemistry
Cook, David B
2005-01-01
Quantum chemistry forms the basis of molecular modeling, a tool widely used to obtain important chemical information and visual images of molecular systems. Recent advances in computing have resulted in considerable developments in molecular modeling, and these developments have led to significant achievements in the design and synthesis of drugs and catalysts. This comprehensive text provides upper-level undergraduates and graduate students with an introduction to the implementation of quantum ideas in molecular modeling, exploring practical applications alongside theoretical explanations.Wri
Quantum mechanics of materials
Energy Technology Data Exchange (ETDEWEB)
Cohen, M.L.; Heine, V.; Phillips, J.C.
1982-06-01
In the past 25 years, new quantum-mechanical methods have been developed for predicting the configuration of the valence electrons in an atom or an aggregate of many atoms, within the range of energy excitations in which the atoms form interatomic bonds. A theory specifying the configuration of the valence electrons has much to say about the bulk properties of matter that depends on the nature of the interatomic bonds. The new method regards the core electrons and the atomic nucleus as if they constituted a single particle without internal structure. The method is called the pseudopotential theory. A general quantum-mechanical prediction of the properties of a substance in terms of the additive properties of separate chemical bonds is not yet feasible for molecules. However, there is one realm where prediction is now practical: crystalline solids. The regularity of the lattice into which the atoms are organized in a crystal makes it possible to calculate the properties of a macroscopic solid. In other words, many properties of an elemental solid such as lead or a simple binary solid such as gallium arsenide can not be deduced from energy considerations alone. (SC)
Submicroscopic Deterministic Quantum Mechanics
Krasnoholovets, V
2002-01-01
So-called hidden variables introduced in quantum mechanics by de Broglie and Bohm have changed their initial enigmatic meanings and acquired quite reasonable outlines of real and measurable characteristics. The start viewpoint was the following: All the phenomena, which we observe in the quantum world, should reflect structural properties of the real space. Thus the scale 10^{-28} cm at which three fundamental interactions (electromagnetic, weak, and strong) intersect has been treated as the size of a building block of the space. The appearance of a massive particle is associated with a local deformation of the cellular space, i.e. deformation of a cell. The mechanics of a moving particle that has been constructed is deterministic by its nature and shows that the particle interacts with cells of the space creating elementary excitations called "inertons". The further study has disclosed that inertons are a substructure of the matter waves which are described by the orthodox wave \\psi-function formalism. The c...
Using a quantum computer to investigate quantum chaos
Schack, Ruediger
1997-01-01
We show that the quantum baker's map, a prototypical map invented for theoretical studies of quantum chaos, has a very simple realization in terms of quantum gates. Chaos in the quantum baker's map could be investigated experimentally on a quantum computer based on only 3 qubits.
Trace anomalies from quantum mechanics
Bastianelli, F; Bastianelli, Fiorenzo; Nieuwenhuizen, Peter van
1993-01-01
The 1-loop anomalies of a d-dimensional quantum field theory can be computed by evaluating the trace of the regulated path integral jacobian matrix, as shown by Fujikawa. In 1983, Alvarez-Gaum\\'e and Witten observed that one can simplify this evaluation by replacing the operators which appear in the regulator and in the jacobian by quantum mechanical operators with the same (anti)commutation relations. By rewriting this quantum mechanical trace as a path integral with periodic boundary conditions for a one-dimensional supersymmetric nonlinear sigma model, they obtained the chiral anomalies for spin 1/2 and 3/2 fields and selfdual antisymmetric tensors in d dimensions. In this article, we treat the case of trace anomalies for spin 0, 1/2 and 1 fields in a gravitational and Yang-Mills background. We do not introduce a supersymmetric sigma model, but keep the original Dirac matrices $\\g^\\m$ and internal symmetry generators $T^a$ in the path integral. As a result, we get a matrix-valued action. Gauge covariance o...
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 mechanics using Fradkin's representation
Shajesh, K V; Milton, Kimball A.
2005-01-01
Fradkin's representation is a general method of attacking problems in quantum field theory, having as its basis the functional approach of Schwinger. As a pedagogical illustration of that method, we explicitly formulate it for quantum mechanics (field theory in one dimension) and apply it to the solution of Schrodinger's equation for the quantum harmonic oscillator.
Can the human brain do quantum computing?
Rocha, A F; Massad, E; Coutinho, F A B
2004-01-01
The electrical membrane properties have been the key issues in the understanding of the cerebral physiology for more than almost two centuries. But, molecular neurobiology has now discovered that biochemical transactions play an important role in neuronal computations. Quantum computing (QC) is becoming a reality both from the theoretical point of view as well as from practical applications. Quantum mechanics is the most accurate description at atomic level and it lies behind all chemistry that provides the basis for biology ... maybe the magic of entanglement is also crucial for life. The purpose of the present paper is to discuss the dendrite spine as a quantum computing device, taking into account what is known about the physiology of the glutamate receptors and the cascade of biochemical transactions triggered by the glutamate binding to these receptors.
Gamification of Quantum Mechanics Teaching
Bjælde, Ole Eggers; Sherson, Jacob
2015-01-01
In this small scale study we demonstrate how a gamified teaching setup can be used effectively to support student learning in a quantum mechanics course. The quantum mechanics games were research games, which were played during lectures and the learning was measured with a pretest/posttest method with promising results. The study works as a pilot study to guide the planning of quantum mechanics courses in the future at Aarhus University in Denmark.
Quantum Mechanics for Electrical Engineers
Sullivan, Dennis M
2011-01-01
The main topic of this book is quantum mechanics, as the title indicates. It specifically targets those topics within quantum mechanics that are needed to understand modern semiconductor theory. It begins with the motivation for quantum mechanics and why classical physics fails when dealing with very small particles and small dimensions. Two key features make this book different from others on quantum mechanics, even those usually intended for engineers: First, after a brief introduction, much of the development is through Fourier theory, a topic that is at
A Quantum Space behind Simple Quantum Mechanics
Directory of Open Access Journals (Sweden)
Chuan Sheng Chew
2017-01-01
Full Text Available In physics, experiments ultimately inform us about what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the configuration space of a free particle (or the center of mass of a closed system of particles. This configuration space (as well as phase space can be constructed as a representation space for the relativity symmetry. From the corresponding quantum symmetry, we illustrate the construction of a quantum configuration space, similar to that of quantum phase space, and recover the classical picture as an approximation through a contraction of the (relativity symmetry and its representations. The quantum Hilbert space reduces into a sum of one-dimensional representations for the observable algebra, with the only admissible states given by coherent states and position eigenstates for the phase and configuration space pictures, respectively. This analysis, founded firmly on known physics, provides a quantum picture of physical space beyond that of a finite-dimensional manifold and provides a crucial first link for any theoretical model of quantum space-time at levels beyond simple quantum mechanics. It also suggests looking at quantum physics from a different perspective.
Quantum mechanics the theoretical minimum
Susskind, Leonard
2014-01-01
From the bestselling author of The Theoretical Minimum, an accessible introduction to the math and science of quantum mechanicsQuantum Mechanics is a (second) book for anyone who wants to learn how to think like a physicist. In this follow-up to the bestselling The Theoretical Minimum, physicist Leonard Susskind and data engineer Art Friedman offer a first course in the theory and associated mathematics of the strange world of quantum mechanics. Quantum Mechanics presents Susskind and Friedman’s crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics. An accessible but rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.
Factorization Method in Quantum Mechanics
Dong, Shi-Hai
2007-01-01
This Work introduces the factorization method in quantum mechanics at an advanced level with an aim to put mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the Reader’s disposal. For this purpose a comprehensive description is provided of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. Related to this classic method are the supersymmetric quantum mechanics, shape invariant potentials and group theoretical approaches. It is no exaggeration to say that this method has become the milestone of these approaches. In fact the Author’s driving force has been his desire to provide a comprehensive review volume that includes some new and significant results about the factorization method in quantum mechanics since the literature is inundated with scattered articles in this field, and to pave the Reader’s way into ...
Reversible computing fundamentals, quantum computing, and applications
De Vos, Alexis
2010-01-01
Written by one of the few top internationally recognized experts in the field, this book concentrates on those topics that will remain fundamental, such as low power computing, reversible programming languages, and applications in thermodynamics. It describes reversible computing from various points of view: Boolean algebra, group theory, logic circuits, low-power electronics, communication, software, quantum computing. It is this multidisciplinary approach that makes it unique.Backed by numerous examples, this is useful for all levels of the scientific and academic community, from undergr
Progress in post-quantum mechanics
Sarfatti, Jack
2017-05-01
Newton's mechanics in the 17th century increased the lethality of artillery. Thermodynamics in the 19th led to the steam-powered industrial revolution. Maxwell's unification of electricity, magnetism and light gave us electrical power, the telegraph, radio and television. The discovery of quantum mechanics in the 20th century by Planck, Bohr, Einstein, Schrodinger, Heisenberg led to the creation of the atomic and hydrogen bombs as well as computer chips, the world-wide-web and Silicon Valley's multibillion dollar corporations. The lesson is that breakthroughs in fundamental physics, both theoretical and experimental, have always led to profound technological wealth-creating industries and will continue to do so. There is now a new revolution brewing in quantum mechanics that can be divided into three periods. The first quantum revolution was from 1900 to about 1975. The second quantum information/computer revolution was from about 1975 to 2015. (The early part of this story is told by Kaiser in his book, How the Hippies Saved Physics, how a small group of Berkeley/San Francisco physicists triggered that second revolution.) The third quantum revolution is how an extension of quantum mechanics may lead to the understanding of consciousness as a natural physical phenomenon that can emerge in many material substrates, not only in our carbon-based biochemistry. In particular, this new post-quantum mechanics may lead to naturally conscious artificial intelligence in nano-electronic machines, as well as perhaps extending human life spans to hundreds of years and more.
D'Ariano, Giacomo Mauro
2010-01-01
I argue that the program on operational foundations of Quantum Mechanics should have top-priority, and that the Lucien Hardy's program on Quantum Gravity should be paralleled by an analogous program on Quantum Field Theory (QFT), which needs to be reformulated, notwithstanding its experimental success. In this paper, after reviewing recently proposed operational "principles of the quantumness", I address the problem on whether Quantum Mechanics and Special Relativity are unrelated theories, or instead, if the one implies the other. I show how Special Relativity can be indeed derived from Quantum Mechanics, within the computational paradigm "the universe is a huge quantum computer", reformulating QFT as a Quantum-Circuit Field Theory (QCFT). In QCFT Special Relativity emerges from the fabric of the computational network, which also naturally embeds gauge invariance, and even the quantization rule and the Plank constant, which resort to being properties of the underlying causal tapestry of space-time. In this w...
Decoherence in quantum mechanics and quantum cosmology
Hartle, James B.
1992-01-01
A sketch of the quantum mechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantum systems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.
Atomic physics: A milestone in quantum computing
Bartlett, Stephen D.
2016-08-01
Quantum computers require many quantum bits to perform complex calculations, but devices with more than a few bits are difficult to program. A device based on five atomic quantum bits shows a way forward. See Letter p.63
Nanophotonic quantum computer based on atomic quantum transistor
Energy Technology Data Exchange (ETDEWEB)
Andrianov, S N [Institute of Advanced Research, Academy of Sciences of the Republic of Tatarstan, Kazan (Russian Federation); Moiseev, S A [Kazan E. K. Zavoisky Physical-Technical Institute, Kazan Scientific Center, Russian Academy of Sciences, Kazan (Russian Federation)
2015-10-31
We propose a scheme of a quantum computer based on nanophotonic elements: two buses in the form of nanowaveguide resonators, two nanosized units of multiatom multiqubit quantum memory and a set of nanoprocessors in the form of photonic quantum transistors, each containing a pair of nanowaveguide ring resonators coupled via a quantum dot. The operation modes of nanoprocessor photonic quantum transistors are theoretically studied and the execution of main logical operations by means of them is demonstrated. We also discuss the prospects of the proposed nanophotonic quantum computer for operating in high-speed optical fibre networks. (quantum computations)
Phase Information in Quantum Oracle Computing
Machta, J.
1998-01-01
Computational devices may be supplied with external sources of information (oracles). Quantum oracles may transmit phase information which is available to a quantum computer but not a classical computer. One consequence of this observation is that there is an oracle which is of no assistance to a classical computer but which allows a quantum computer to solve undecidable problems. Thus useful relativized separations between quantum and classical complexity classes must exclude the transmissio...
Horizon quantum mechanics of rotating black holes
Energy Technology Data Exchange (ETDEWEB)
Casadio, Roberto [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, I.S. FLAG, Bologna (Italy); Giugno, Andrea [Ludwig-Maximilians-Universitaet, Arnold Sommerfeld Center, Munich (Germany); Giusti, Andrea [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, I.S. FLAG, Bologna (Italy); Ludwig-Maximilians-Universitaet, Arnold Sommerfeld Center, Munich (Germany); Micu, Octavian [Institute of Space Science, Bucharest, P.O. Box MG-23, Bucharest-Magurele (Romania)
2017-05-15
The horizon quantum mechanics is an approach that was previously introduced in order to analyze the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. In this work, we first extend the formalism to general space-times with asymptotic (ADM) mass and angular momentum. We then apply the extended horizon quantum mechanics to a harmonic model of rotating corpuscular black holes. We find that simple configurations of this model naturally suppress the appearance of the inner horizon and seem to disfavor extremal (macroscopic) geometries. (orig.)
Quantum Computing in Non Euclidean Geometry
Resconi, Germano
2009-01-01
The recent debate on hyper-computation has raised new questions both on the computational abilities of quantum systems and the Church-Turing Thesis role in Physics. We propose here the idea of geometry of effective physical process as the essentially physical notion of computation. In Quantum mechanics we cannot use the traditional Euclidean geometry but we introduce more sophisticate non Euclidean geometry which include a new kind of information diffuse in the entire universe and that we can represent as Fisher information or active information. We remark that from the Fisher information we can obtain the Bohm and Hiley quantum potential and the classical Schrodinger equation. We can see the quantum phenomena do not affect a limited region of the space but is reflected in a change of the geometry of all the universe. In conclusion any local physical change or physical process is reflected in all the universe by the change of its geometry, This is the deepest meaning of the entanglement in Quantum mechanics a...
Consequences and Limitations of Conventional Computers and their Solutions through Quantum Computers
Directory of Open Access Journals (Sweden)
Nilesh BARDE
2012-08-01
Full Text Available Quantum computer is the current topic of research in the field of computational science, which uses principles of quantum mechanics. Quantum computers will be much more powerful than the classical computer due to its enormous computational speed. Recent developments in quantum computers which are based on the laws of quantum mechanics, shows different ways of performing efficient calculations along with the various results which are not possible on the classical computers in an efficient period of time. One of the most striking results that have obtained on the quantum computers is the prime factorization of the large integer in a polynomial time. The idea of involvement of the quantum mechanics for the computational purpose is outlined briefly in the present work that reflects the importance and advantages of the next generation of the 21st century classical computers, named as quantum computers, in terms of the cost as well as time period required for the computation purpose. Present paper presents a quantum computer simulator for executing the limitations of classical computer with respect to time and the number of digits of a composite integer used for calculating its prime factors.
Quantum mechanics II advanced topics
Rajasekar, S
2015-01-01
Quantum Mechanics II: Advanced Topics uses more than a decade of research and the authors’ own teaching experience to expound on some of the more advanced topics and current research in quantum mechanics. A follow-up to the authors introductory book Quantum Mechanics I: The Fundamentals, this book begins with a chapter on quantum field theory, and goes on to present basic principles, key features, and applications. It outlines recent quantum technologies and phenomena, and introduces growing topics of interest in quantum mechanics. The authors describe promising applications that include ghost imaging, detection of weak amplitude objects, entangled two-photon microscopy, detection of small displacements, lithography, metrology, and teleportation of optical images. They also present worked-out examples and provide numerous problems at the end of each chapter.
Quantum inertia stops superposition: Scan Quantum Mechanics
Gato-Rivera, Beatriz
2017-08-01
Scan Quantum Mechanics is a novel interpretation of some aspects of quantum mechanics in which the superposition of states is only an approximate effective concept. Quantum systems scan all possible states in the superposition and switch randomly and very rapidly among them. A crucial property that we postulate is quantum inertia, that increases whenever a constituent is added, or the system is perturbed with all kinds of interactions. Once the quantum inertia Iq reaches a critical value Icr for an observable, the switching among its different eigenvalues stops and the corresponding superposition comes to an end, leaving behind a system with a well defined value of that observable. Consequently, increasing the mass, temperature, gravitational strength, etc. of a quantum system increases its quantum inertia until the superposition of states disappears for all the observables and the system transmutes into a classical one. Moreover, the process could be reversible. Entanglement can only occur between quantum systems because an exact synchronization between the switchings of the systems involved must be established in the first place and classical systems do not have any switchings to start with. Future experiments might determine the critical inertia Icr corresponding to different observables, which translates into a critical mass Mcr for fixed environmental conditions as well as critical temperatures, critical electric and magnetic fields, etc. In addition, this proposal implies a new radiation mechanism from astrophysical objects with strong gravitational fields, giving rise to non-thermal synchrotron emission, that could contribute to neutron star formation. Superconductivity, superfluidity, Bose-Einstein condensates, and any other physical phenomena at very low temperatures must be reanalyzed in the light of this interpretation, as well as mesoscopic systems in general.
Bender, Carl M; DeKieviet, Maarten; Klevansky, S P
2013-04-28
PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantum mechanics.
Quantum Computing: Theoretical versus Practical Possibility
Paraoanu, G S
2011-01-01
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is possible in principle - there are no known laws of Nature that prevent it - yet scaling up the few qubits demonstrated so far has proven to be exceedingly difficult. While this could be regarded merely as a technological or practical impediment, I argue that this difficulty might be a symptom of new laws of physics waiting to be discovered. I also introduce a distinction between "strong" and "weak" emergentist positions. The former assumes that a critical value of a parameter exists (one that is most likely related to the complexity of the states involved) at which the quantum-mechanical description breaks down, in other words, that quantum mechanics will turn out to be an incomplete description of reality. The latter assumes that quantum mechanics will remain as a universal...
Popper's test of Quantum Mechanics
Bramon, A
2005-01-01
A test of quantum mechanics proposed by K. Popper and dealing with two-particle entangled states emitted from a fixed source has been criticized by several authors. Some of them claim that the test becomes inconclusive once all the quantum aspects of the source are considered. Moreover, another criticism states that the predictions attributed to quantum mechanics in Popper's analysis are untenable. We reconsider these criticisms and show that, to a large extend, the `falsifiability' potential of the test remains unaffected.
The theoretical foundations of quantum mechanics
Baaquie, Belal E
2013-01-01
The Theoretical Foundations of Quantum Mechanics addresses fundamental issues that are not discussed in most books on quantum mechanics. This book focuses on analyzing the underlying principles of quantum mechanics and explaining the conceptual and theoretical underpinning of quantum mechanics. In particular, the concepts of quantum indeterminacy, quantum measurement and quantum superposition are analyzed to clarify the concepts that are implicit in the formulation of quantum mechanics. The Schrodinger equation is never solved in the book. Rather, the discussion on the fundamentals of quantum mechanics is treated in a rigorous manner based on the mathematics of quantum mechanics. The new concept of the interplay of empirical and trans-empirical constructs in quantum mechanics is introduced to clarify the foundations of quantum mechanics and to explain the counter-intuitive construction of nature in quantum mechanics. The Theoretical Foundations of Quantum Mechanics is aimed at the advanced undergraduate and a...
ASCR Workshop on Quantum Computing for Science
Energy Technology Data Exchange (ETDEWEB)
Aspuru-Guzik, Alan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Van Dam, Wim [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Farhi, Edward [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Gaitan, Frank [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Humble, Travis [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Jordan, Stephen [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Landahl, Andrew J [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Love, Peter [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lucas, Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Preskill, John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Muller, Richard P. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Svore, Krysta [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Wiebe, Nathan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Williams, Carl [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-06-01
This report details the findings of the DOE ASCR Workshop on Quantum Computing for Science that was organized to assess the viability of quantum computing technologies to meet the computational requirements of the DOE’s science and energy mission, and to identify the potential impact of quantum technologies. The workshop was held on February 17-18, 2015, in Bethesda, MD, to solicit input from members of the quantum computing community. The workshop considered models of quantum computation and programming environments, physical science applications relevant to DOE's science mission as well as quantum simulation, and applied mathematics topics including potential quantum algorithms for linear algebra, graph theory, and machine learning. This report summarizes these perspectives into an outlook on the opportunities for quantum computing to impact problems relevant to the DOE’s mission as well as the additional research required to bring quantum computing to the point where it can have such impact.
Barium Ions for Quantum Computation
Dietrich, M R; Bowler, R; Kurz, N; Salacka, J S; Shu, G; Blinov, B B
2009-01-01
Individually trapped 137Ba+ in an RF Paul trap is proposed as a qubit ca ndidate, and its various benefits are compared to other ionic qubits. We report the current experimental status of using this ion for quantum computation. Fut ure plans and prospects are discussed.
An Early Quantum Computing Proposal
Energy Technology Data Exchange (ETDEWEB)
Lee, Stephen Russell [Los Alamos National Laboratory; Alexander, Francis Joseph [Los Alamos National Laboratory; Barros, Kipton Marcos [Los Alamos National Laboratory; Daniels, Marcus G. [Los Alamos National Laboratory; Gattiker, James R. [Los Alamos National Laboratory; Hamada, Michael Scott [Los Alamos National Laboratory; Howse, James Walter [Los Alamos National Laboratory; Loncaric, Josip [Los Alamos National Laboratory; Pakin, Scott D. [Los Alamos National Laboratory; Somma, Rolando Diego [Los Alamos National Laboratory; Vernon, Louis James [Los Alamos National Laboratory
2016-04-04
The D-Wave 2X is the third generation of quantum processing created by D-Wave. NASA (with Google and USRA) and Lockheed Martin (with USC), both own D-Wave systems. Los Alamos National Laboratory (LANL) purchased a D-Wave 2X in November 2015. The D-Wave 2X processor contains (nominally) 1152 quantum bits (or qubits) and is designed to specifically perform quantum annealing, which is a well-known method for finding a global minimum of an optimization problem. This methodology is based on direct execution of a quantum evolution in experimental quantum hardware. While this can be a powerful method for solving particular kinds of problems, it also means that the D-Wave 2X processor is not a general computing processor and cannot be programmed to perform a wide variety of tasks. It is a highly specialized processor, well beyond what NNSA currently thinks of as an “advanced architecture.”A D-Wave is best described as a quantum optimizer. That is, it uses quantum superposition to find the lowest energy state of a system by repeated doses of power and settling stages. The D-Wave produces multiple solutions to any suitably formulated problem, one of which is the lowest energy state solution (global minimum). Mapping problems onto the D-Wave requires defining an objective function to be minimized and then encoding that function in the Hamiltonian of the D-Wave system. The quantum annealing method is then used to find the lowest energy configuration of the Hamiltonian using the current D-Wave Two, two-level, quantum processor. This is not always an easy thing to do, and the D-Wave Two has significant limitations that restrict problem sizes that can be run and algorithmic choices that can be made. Furthermore, as more people are exploring this technology, it has become clear that it is very difficult to come up with general approaches to optimization that can both utilize the D-Wave and that can do better than highly developed algorithms on conventional computers for
Noncommutative Quantum Mechanics and Quantum Cosmology
Bastos, Catarina; Dias, Nuno; Prata, Joao Nuno
2009-01-01
We present a phase-space noncommutative version of quantum mechanics and apply this extension to Quantum Cosmology. We motivate this type of noncommutative algebra through the gravitational quantum well (GQW) where the noncommutativity between momenta is shown to be relevant. We also discuss some qualitative features of the GQW such as the Berry phase. In the context of quantum cosmology we consider a Kantowski-Sachs cosmological model and obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM formalism and a suitable Seiberg-Witten (SW) map. The WDW equation is explicitly dependent on the noncommutative parameters, $\\theta$ and $\\eta$. We obtain numerical solutions of the noncommutative WDW equation for different values of the noncommutative parameters. We conclude that the noncommutativity in the momenta sector leads to a damped wave function implying that this type of noncommmutativity can be relevant for a selection of possible initial states for the universe.
Methodological testing: Are fast quantum computers illusions?
Energy Technology Data Exchange (ETDEWEB)
Meyer, Steven [Tachyon Design Automation, San Francisco, CA (United States)
2013-07-01
Popularity of the idea for computers constructed from the principles of QM started with Feynman's 'Lectures On Computation', but he called the idea crazy and dependent on statistical mechanics. In 1987, Feynman published a paper in 'Quantum Implications - Essays in Honor of David Bohm' on negative probabilities which he said gave him cultural shock. The problem with imagined fast quantum computers (QC) is that speed requires both statistical behavior and truth of the mathematical formalism. The Swedish Royal Academy 2012 Nobel Prize in physics press release touted the discovery of methods to control ''individual quantum systems'', to ''measure and control very fragile quantum states'' which enables ''first steps towards building a new type of super fast computer based on quantum physics.'' A number of examples where widely accepted mathematical descriptions have turned out to be problematic are examined: Problems with the use of Oracles in P=NP computational complexity, Paul Finsler's proof of the continuum hypothesis, and Turing's Enigma code breaking versus William tutte's Colossus. I view QC research as faith in computational oracles with wished for properties. Arther Fine's interpretation in 'The Shaky Game' of Einstein's skepticism toward QM is discussed. If Einstein's reality as space-time curvature is correct, then space-time computers will be the next type of super fast computer.
Principles of Quantum Mechanics
Landé, Alfred
2013-10-01
ödinger's equation for non-conservative systems; 46. Pertubation theory; 47. Orthogonality, normalization and Hermitian conjugacy; 48. General matrix elements; Part IV. The Principle of Correspondence: 49. Contact transformations in classical mechanics; 50. Point transformations; 51. Contact transformations in quantum mechanics; 52. Constants of motion and angular co-ordinates; 53. Periodic orbits; 54. De Broglie and Schrödinger function; correspondence to classical mechanics; 55. Packets of probability; 56. Correspondence to hydrodynamics; 57. Motion and scattering of wave packets; 58. Formal correspondence between classical and quantum mechanics; Part V. Mathematical Appendix: Principle of Invariance: 59. The general theorem of transformation; 60. Operator calculus; 61. Exchange relations; three criteria for conjugacy; 62. First method of canonical transformation; 63. Second method of canonical transformation; 64. Proof of the transformation theorem; 65. Invariance of the matrix elements against unitary transformations; 66. Matrix mechanics; Index of literature; Index of names and subjects.
Experimental realization of nonadiabatic holonomic quantum computation.
Feng, Guanru; Xu, Guofu; Long, Guilu
2013-05-10
Because of its geometric nature, holonomic quantum computation is fault tolerant against certain types of control errors. Although proposed more than a decade ago, the experimental realization of holonomic quantum computation is still an open challenge. In this Letter, we report the first experimental demonstration of nonadiabatic holonomic quantum computation in a liquid NMR quantum information processor. Two noncommuting one-qubit holonomic gates, rotations about x and z axes, and the two-qubit holonomic CNOT gate are realized by evolving the work qubits and an ancillary qubit nonadiabatically. The successful realizations of these universal elementary gates in nonadiabatic holonomic quantum computation demonstrates the experimental feasibility of this quantum computing paradigm.
Quantum mechanics & the big world
Wezel, Jasper van
2007-01-01
Quantum Mechanics is one of the most successful physical theories of the last century. It explains physical phenomena from the smallest to the largest lengthscales. Despite this triumph, quantum mechanics is often perceived as a mysterious theory, involving superposition states that are alien to our
Discovering Quantum Mechanics Once Again
Duck, Ian M
2003-01-01
We expand on a recent development by Hardy, in which quantum mechanics is derived from classical probability theory supplemented by a single new axiom, Hardy's Axiom 5. Our scenario involves a `pretend world' with a `pretend' Heisenberg who seeks to construct a dynamical theory of probabilities and is lead -- seemingly inevitably -- to the Principles of Quantum Mechanics.
Quantum mechanics & the big world
Wezel, Jasper van
2007-01-01
Quantum Mechanics is one of the most successful physical theories of the last century. It explains physical phenomena from the smallest to the largest lengthscales. Despite this triumph, quantum mechanics is often perceived as a mysterious theory, involving superposition states that are alien to our
Quantum mechanics of molecular structures
Yamanouchi, Kaoru
2012-01-01
At a level accessible to advanced undergraduates, this textbook explains the fundamental role of quantum mechanics in determining the structure, dynamics, and other properties of molecules. Readers will come to understand the quantum-mechanical basis for harmonic oscillators, angular momenta and scattering processes. Exercises are provided to help readers deepen their grasp of the essential phenomena.
Mossbauer neutrinos in quantum mechanics and quantum field theory
Kopp, Joachim
2009-01-01
We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Mossbauer neutrino oscillations. First, we compute the combined rate $\\Gamma$ of Mossbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for $\\Gamma$ is identical to the one obtained previously (Akhmedov et al., arXiv:0802.2513) for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Mossbauer neutrinos and show that the oscillation, coherence and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detecti...
Quantum mechanics and quantum information a guide through the quantum world
Fayngold, Moses
2013-01-01
Alongside a thorough definition of the basic concepts and their interrelations, backed by numerous examples, this textbook features a rare discussion of the quantum information theory. It also deals with other important topics hardly found in the literature, including the Robertson-Schrodinger-relation, angle and angular momentum uncertainties, interaction-free measurements, and the limitations of the no-cloning theorem With its interpretations of quantum mechanics and its discussions of quantum computing, this book is poised to become the standard textbook for advanced undergraduate and beginning graduate quantum mechanics courses and as an essential reference for physics students and physics professionals.
On Finite $J$-Hermitian Quantum Mechanics
Lee, Sungwook
2014-01-01
In his recent paper arXiv:1312.7738, the author discussed $J$-Hermitian quantum mechanics and showed that $PT$-symmetric quantum mechanics is essentially $J$-Hermitian quantum mechanics. In this paper, the author discusses finite $J$-Hermitian quantum mechanics which is derived naturally from its continuum one and its relationship with finite $PT$-symmetric quantum mechanics.
Modern Approach to Quantum Mechanics
Townsend, John S.
Inspired by Richard Feynman and J.J. Sakurai, A Modern Approach to Quantum Mechanics lets professors expose their undergraduates to the excitement and insight of Feynman's approach to quantum mechanics while simultaneously giving them a textbook that is well-ordered, logical, and pedagogically sound. This book covers all the topics that are typically presented in a standard upper-level course in quantum mechanics, but its teaching approach is new: Rather than organizing his book according to the historical development of the field and jumping into a mathematical discussion of wave mechanics, Townsend begins his book with the quantum mechanics of spin. Thus, the first five chapters of the book succeed in laying out the fundamentals of quantum mechanics with little or no wave mechanics, so the physics is not obscured by mathematics. Starting with spin systems gives students something new and interesting while providing elegant but straightforward examples of the essential structure of quantum mechanics. When wave mechanics is introduced later, students perceive it correctly as only one aspect of quantum mechanics and not the core of the subject. Praised for its pedagogical brilliance, clear writing, and careful explanations, this book is destined to become a landmark text.
Quantum Chromodynamics: Computational Aspects
Schaefer, Thomas
2016-01-01
We present a brief introduction to QCD, the QCD phase diagram, and non-equilibrium phenomena in QCD. We emphasize aspects of the theory that can be addressed using computational methods, in particular euclidean path integral Monte Carlo, fluid dynamics, kinetic theory, classical field theory and holographic duality.
Modeling fluid dynamics on type II quantum computers
Scoville, James; Weeks, David; Yepez, Jeffrey
2006-03-01
A quantum algorithm is presented for modeling the time evolution of density and flow fields governed by classical equations, such as the diffusion equation, the nonlinear Burgers equation, and the damped wave equation. The algorithm is intended to run on a type-II quantum computer, a parallel quantum computer consisting of a lattice of small type I quantum computers undergoing unitary evolution and interacting via information interchanges represented by an orthogonal matrices. Information is effectively transferred between adjacent quantum computers over classical communications channels because of controlled state demolition following local quantum mechanical qubit-qubit interactions within each quantum computer. The type-II quantum algorithm presented in this paper describes a methodology for generating quantum logic operations as a generalization of classical operations associated with finite-point group symmetries. The quantum mechanical evolution of multiple qubits within each node is described. Presented is a proof that the parallel quantum system obeys a finite-difference quantum Boltzman equation at the mesoscopic scale, leading in turn to various classical linear and nonlinear effective field theories at the macroscopic scale depending on the details of the local qubit-qubit interactions.
General Quantum Interference Principle and Duality Computer
Institute of Scientific and Technical Information of China (English)
LONG Gui-Lu
2006-01-01
In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of thesub-waves of the quantum system itself. A quantum system considered here can be any quantum system: a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer,the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer,it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented:the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.
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.
Strange attractor simulated on a quantum computer
2002-01-01
We show that dissipative classical dynamics converging to a strange attractor can be simulated on a quantum computer. Such quantum computations allow to investigate efficiently the small scale structure of strange attractors, yielding new information inaccessible to classical computers. This opens new possibilities for quantum simulations of various dissipative processes in nature.
Experimental Demonstration of Blind Quantum Computing
Barz, Stefanie; Broadbent, Anne; Fitzsimons, Joseph F; Zeilinger, Anton; Walther, Philip
2011-01-01
Quantum computers, besides offering substantial computational speedups, are also expected to provide the possibility of preserving the privacy of a computation. Here we show the first such experimental demonstration of blind quantum computation where the input, computation, and output all remain unknown to the computer. We exploit the conceptual framework of measurement-based quantum computation that enables a client to delegate a computation to a quantum server. We demonstrate various blind delegated computations, including one- and two-qubit gates and the Deutsch and Grover algorithms. Remarkably, the client only needs to be able to prepare and transmit individual photonic qubits. Our demonstration is crucial for future unconditionally secure quantum cloud computing and might become a key ingredient for real-life applications, especially when considering the challenges of making powerful quantum computers widely available.
Quantum computing and the entanglement frontier
Preskill, John
2012-01-01
Quantum information science explores the frontier of highly complex quantum states, the "entanglement frontier." This study is motivated by the observation (widely believed but unproven) that classical systems cannot simulate highly entangled quantum systems efficiently, and we hope to hasten the day when well controlled quantum systems can perform tasks surpassing what can be done in the classical world. One way to achieve such "quantum supremacy" would be to run an algorithm on a quantum computer which solves a problem with a super-polynomial speedup relative to classical computers, but there may be other ways that can be achieved sooner, such as simulating exotic quantum states of strongly correlated matter. To operate a large scale quantum computer reliably we will need to overcome the debilitating effects of decoherence, which might be done using "standard" quantum hardware protected by quantum error-correcting codes, or by exploiting the nonabelian quantum statistics of anyons realized in solid state sy...
Mathematical foundation of quantum mechanics
Parthasarathy, K R
2005-01-01
This is a brief introduction to the mathematical foundations of quantum mechanics based on lectures given by the author to Ph.D.students at the Delhi Centre of the Indian Statistical Institute in order to initiate active research in the emerging field of quantum probability. The material in the first chapter is included in the author's book "An Introduction to Quantum Stochastic Calculus" published by Birkhauser Verlag in 1992 and the permission of the publishers to reprint it here is acknowledged. Apart from quantum probability, an understanding of the role of group representations in the development of quantum mechanics is always a fascinating theme for mathematicians. The first chapter deals with the definitions of states, observables and automorphisms of a quantum system through Gleason's theorem, Hahn-Hellinger theorem and Wigner's theorem. Mackey's imprimitivity theorem and the theorem of inducing representations of groups in stages are proved directly for projective unitary antiunitary representations ...
The computer-based model of quantum measurements
Sevastianov, L. A.; Zorin, A. V.
2017-07-01
Quantum theory of measurements is an extremely important part of quantum mechanics. Currently perturbations by quantum measurements of observable quantities of atomic systems are rarely taken into account in computing algorithms and calculations. In the previous studies of the authors, constructive model of quantum measurements has been developed and implemented in the form of symbolic and numerical calculations for the hydrogen-like atoms. This work describes a generalization of these results to the alkali metal atoms.
Coherent states in quantum mechanics
Rodrigues, R D L; Fernandes, D
2001-01-01
We present a review work on the coherent states is non-relativistic quantum mechanics analysing the quantum oscillators in the coherent states. The coherent states obtained via a displacement operator that act on the wave function of ground state of the oscillator and the connection with Quantum Optics which were implemented by Glauber have also been considered. A possible generalization to the construction of new coherent states it is point out.
The quantum computer game: citizen science
Damgaard, Sidse; Mølmer, Klaus; Sherson, Jacob
2013-05-01
Progress in the field of quantum computation is hampered by daunting technical challenges. Here we present an alternative approach to solving these by enlisting the aid of computer players around the world. We have previously examined a quantum computation architecture involving ultracold atoms in optical lattices and strongly focused tweezers of light. In The Quantum Computer Game (see http://www.scienceathome.org/), we have encapsulated the time-dependent Schrödinger equation for the problem in a graphical user interface allowing for easy user input. Players can then search the parameter space with real-time graphical feedback in a game context with a global high-score that rewards short gate times and robustness to experimental errors. The game which is still in a demo version has so far been tried by several hundred players. Extensions of the approach to other models such as Gross-Pitaevskii and Bose-Hubbard are currently under development. The game has also been incorporated into science education at high-school and university level as an alternative method for teaching quantum mechanics. Initial quantitative evaluation results are very positive. AU Ideas Center for Community Driven Research, CODER.
Geometry of quantum computation with qutrits.
Li, Bin; Yu, Zu-Huan; Fei, Shao-Ming
2013-01-01
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3(n)). As an example, three-qutrit systems are investigated in detail.
Quantum chemistry simulation on quantum computers: theories and experiments.
Lu, Dawei; Xu, Boruo; Xu, Nanyang; Li, Zhaokai; Chen, Hongwei; Peng, Xinhua; Xu, Ruixue; Du, Jiangfeng
2012-07-14
It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations.
Optically simulated universal quantum computation
Francisco, D.; Ledesma, S.
2008-04-01
Recently, classical optics based systems to emulate quantum information processing have been proposed. The analogy is based on the possibility of encoding a quantum state of a system with a 2N-dimensional Hilbert space as an image in the input of an optical system. The probability amplitude of each state of a certain basis is associated with the complex amplitude of the electromagnetic field in a given slice of the laser wavefront. Temporal evolution is represented as the change of the complex amplitude of the field when the wavefront pass through a certain optical arrangement. Different modules that represent universal gates for quantum computation have been implemented. For instance, unitary operations acting on the qbits space (or U(2) gates) are represented by means of two phase plates, two spherical lenses and a phase grating in a typical image processing set up. In this work, we present CNOT gates which are emulated by means of a cube prism that splits a pair of adjacent rays incoming from the input image. As an example of application, we present an optical module that can be used to simulate the quantum teleportation process. We also show experimental results that illustrate the validity of the analogy. Although the experimental results obtained are promising and show the capability of the system for simulate the real quantum process, we must take into account that any classical simulation of quantum phenomena, has as fundamental limitation the impossibility of representing non local entanglement. In this classical context, quantum teleportation has only an illustrative interpretation.
Brain Neurons as Quantum Computers:
Bershadskii, A.; Dremencov, E.; Bershadskii, J.; Yadid, G.
The question: whether quantum coherent states can sustain decoherence, heating and dissipation over time scales comparable to the dynamical timescales of brain neurons, has been actively discussed in the last years. A positive answer on this question is crucial, in particular, for consideration of brain neurons as quantum computers. This discussion was mainly based on theoretical arguments. In the present paper nonlinear statistical properties of the Ventral Tegmental Area (VTA) of genetically depressive limbic brain are studied in vivo on the Flinders Sensitive Line of rats (FSL). VTA plays a key role in the generation of pleasure and in the development of psychological drug addiction. We found that the FSL VTA (dopaminergic) neuron signals exhibit multifractal properties for interspike frequencies on the scales where healthy VTA dopaminergic neurons exhibit bursting activity. For high moments the observed multifractal (generalized dimensions) spectrum coincides with the generalized dimensions spectrum calculated for a spectral measure of a quantum system (so-called kicked Harper model, actively used as a model of quantum chaos). This observation can be considered as a first experimental (in vivo) indication in the favor of the quantum (at least partially) nature of brain neurons activity.
A Blueprint for a Topologically Fault-tolerant Quantum Computer
Bonderson, Parsa; Freedman, Michael; Nayak, Chetan
2010-01-01
The advancement of information processing into the realm of quantum mechanics promises a transcendence in computational power that will enable problems to be solved which are completely beyond the known abilities of any "classical" computer, including any potential non-quantum technologies the future may bring. However, the fragility of quantum states poses a challenging obstacle for realization of a fault-tolerant quantum computer. The topological approach to quantum computation proposes to surmount this obstacle by using special physical systems -- non-Abelian topologically ordered phases of matter -- that would provide intrinsic fault-tolerance at the hardware level. The so-called "Ising-type" non-Abelian topological order is likely to be physically realized in a number of systems, but it can only provide a universal gate set (a requisite for quantum computation) if one has the ability to perform certain dynamical topology-changing operations on the system. Until now, practical methods of implementing thes...
Computational Continuum Mechanics
Shabana, Ahmed A
2011-01-01
This text presents the theory of continuum mechanics using computational methods. Ideal for students and researchers, the second edition features a new chapter on computational geometry and finite element analysis.
Exploiting Locality in Quantum Computation for Quantum Chemistry.
McClean, Jarrod R; Babbush, Ryan; Love, Peter J; Aspuru-Guzik, Alán
2014-12-18
Accurate prediction of chemical and material properties from first-principles quantum chemistry is a challenging task on traditional computers. Recent developments in quantum computation offer a route toward highly accurate solutions with polynomial cost; however, this solution still carries a large overhead. In this Perspective, we aim to bring together known results about the locality of physical interactions from quantum chemistry with ideas from quantum computation. We show that the utilization of spatial locality combined with the Bravyi-Kitaev transformation offers an improvement in the scaling of known quantum algorithms for quantum chemistry and provides numerical examples to help illustrate this point. We combine these developments to improve the outlook for the future of quantum chemistry on quantum computers.
Quantum approach to classical statistical mechanics.
Somma, R D; Batista, C D; Ortiz, G
2007-07-20
We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.
Quantum Computation with Nonlinear Optics
Liu, Yang; Zhang, Wen-Hong; Zhang, Cun-Lin; Long, Gui-Lu
2008-01-01
We propose a scheme of quantum computation with nonlinear quantum optics. Polarization states of photons are used for qubits. Photons with different frequencies represent different qubits. Single qubit rotation operation is implemented through optical elements like the Faraday polarization rotator. Photons are separated into different optical paths, or merged into a single optical path using dichromatic mirrors. The controlled-NOT gate between two qubits is implemented by the proper combination of parametric up and down conversions. This scheme has the following features: (1) No auxiliary qubits are required in the controlled-NOT gate operation; (2) No measurement is required in the course of the computation; (3) It is resource efficient and conceptually simple.
Quantum Computation with Nonlinear Optics
Institute of Scientific and Technical Information of China (English)
LU Ke; LIU Yang; LIN Zhen-Quan; ZHANG Wen-Hong; SUN Yun-Fei; ZHANG Cun-Lin; LONG Gui-Lu
2008-01-01
We propose a scheme of quantum computation with nonlinear quantum optics. Polarization states of photons are used for qubits. Photons with different frequencies represent different qubits. Single qubit rotation operation is implemented through optical elements like the Faraday polarization rotator. Photons are separated into different optical paths, or merged into a single optical path using dichromatic mirrors. The controlled-NOT gate between two qubits is implemented by the proper combination of parametric up and down conversions. This scheme has the following features: (1) No auxiliary qubits are required in the controlled-NOT gate operation; (2) No measurement is required in the courseof the computation; (3) It is resource efficient and conceptually simple.
Quantum Mechanics of Extended Objects
Sastry, R R
2000-01-01
We propose a quantum mechanics of extended objects that accounts for the finite extent of a particle defined via its Compton wavelength. The Hilbert space representation theory of such a quantum mechanics is presented and this representation is used to demonstrate the quantization of spacetime. The quantum mechanics of extended objects is then applied to two paradigm examples, the fuzzy (extended object) harmonic oscillator and the Yukawa potential. In the second example the phenomenological coupling constant of the $\\omega$ meson which mediates the short range and repulsive nucleon force as well as the repulsive core radius are theoretically predicted.
Quantum mechanics in Hilbert space
Prugovecki, Eduard
2006-01-01
A critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels. Its readable and self-contained form is accessible even to students without an extensive mathematical background. Applications of basic theorems to quantum mechanics make it of particular interest to mathematicians working in functional analysis and related areas.This text features the rigorous proofs of all the main functional-analytic statements encountered in books on quantum mechanics. It fills the
Linear operators for quantum mechanics
Jordan, Thomas F
2006-01-01
This compact treatment highlights the logic and simplicity of the mathematical structure of quantum mechanics. Suitable for advanced undergraduates and graduate students, it treats the language of quantum mechanics as expressed in the mathematics of linear operators.Originally oriented toward atomic physics, quantum mechanics became a basic language for solid-state, nuclear, and particle physics. Its grammar consists of the mathematics of linear operators, and with this text, students will find it easier to understand and use the language of physics. Topics include linear spaces and linear fun
EXPLORATIONS IN QUANTUM COMPUTING FOR FINANCIAL APPLICATIONS
Gare, Jesse
2010-01-01
Quantum computers have the potential to increase the solution speed for many computational problems. This paper is a first step into possible applications for quantum computing in the context of computational finance. The fundamental ideas of quantum computing are introduced, followed by an exposition of the algorithms of Deutsch and Grover. Improved mean and median estimation are shown as results of Grover?s generalized framework. The algorithm for mean estimation is refined to an improved M...
Holonomic Quantum Computation in Subsystems
Oreshkov, Ognyan
2009-08-01
We introduce a generalized method of holonomic quantum computation (HQC) based on encoding in subsystems. As an application, we propose a scheme for applying holonomic gates to unencoded qubits by the use of a noisy ancillary qubit. This scheme does not require initialization in a subspace since all dynamical effects factor out as a transformation on the ancilla. We use this approach to show how fault-tolerant HQC can be realized via 2-local Hamiltonians with perturbative gadgets.
Holonomic quantum computation in subsystems
Oreshkov, Ognyan
2009-01-01
We introduce a generalized method of holonomic quantum computation (HQC) based on encoding in subsystems. As an application, we propose a scheme for applying holonomic gates to unencoded qubits by the use of a noisy ancillary qubit. This scheme does not require initialization in a subspace since all dynamical effects factor out as a transformation on the ancilla. We use this approach to show how fault-tolerant HQC can be realized via 2-local Hamiltonians with perturbative gadgets.
Toward a superconducting quantum computer. Harnessing macroscopic quantum coherence.
Tsai, Jaw-Shen
2010-01-01
Intensive research on the construction of superconducting quantum computers has produced numerous important achievements. The quantum bit (qubit), based on the Josephson junction, is at the heart of this research. This macroscopic system has the ability to control quantum coherence. This article reviews the current state of quantum computing as well as its history, and discusses its future. Although progress has been rapid, the field remains beset with unsolved issues, and there are still many new research opportunities open to physicists and engineers.
Geometry of discrete quantum computing
Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung
2013-05-01
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.
Computation in Classical Mechanics
Timberlake, Todd
2007-01-01
There is a growing consensus that physics majors need to learn computational skills, but many departments are still devoid of computation in their physics curriculum. Some departments may lack the resources or commitment to create a dedicated course or program in computational physics. One way around this difficulty is to include computation in a standard upper-level physics course. An intermediate classical mechanics course is particularly well suited for including computation. We discuss the ways we have used computation in our classical mechanics courses, focusing on how computational work can improve students' understanding of physics as well as their computational skills. We present examples of computational problems that serve these two purposes. In addition, we provide information about resources for instructors who would like to include computation in their courses.
Stochastic methods in quantum mechanics
Gudder, Stanley P
2005-01-01
Practical developments in such fields as optical coherence, communication engineering, and laser technology have developed from the applications of stochastic methods. This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory.The text assumes a basic knowledge of fun
Quantum mechanical irreversibility and measurement
Grigolini, P
1993-01-01
This book is intended as a tutorial approach to some of the techniques used to deal with quantum dissipation and irreversibility, with special focus on their applications to the theory of measurements. The main purpose is to provide readers without a deep expertise in quantum statistical mechanics with the basic tools to develop a critical judgement on whether the major achievements in this field have to be considered a satisfactory solution of quantum paradox, or rather this ambitious achievement has to be postponed to when a new physics, more general than quantum and classical physics, will
Time Asymmetric Quantum Mechanics
National Research Council Canada - National Science Library
Arno R Bohm; Manuel Gadella; Piotr Kielanowski
2011-01-01
The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1...
Relativistic quantum mechanics
Horwitz, Lawrence P
2015-01-01
This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. Th...
Experimental one-way quantum computing.
Walther, P; Resch, K J; Rudolph, T; Schenck, E; Weinfurter, H; Vedral, V; Aspelmeyer, M; Zeilinger, A
2005-03-10
Standard quantum computation is based on sequences of unitary quantum logic gates that process qubits. The one-way quantum computer proposed by Raussendorf and Briegel is entirely different. It has changed our understanding of the requirements for quantum computation and more generally how we think about quantum physics. This new model requires qubits to be initialized in a highly entangled cluster state. From this point, the quantum computation proceeds by a sequence of single-qubit measurements with classical feedforward of their outcomes. Because of the essential role of measurement, a one-way quantum computer is irreversible. In the one-way quantum computer, the order and choices of measurements determine the algorithm computed. We have experimentally realized four-qubit cluster states encoded into the polarization state of four photons. We characterize the quantum state fully by implementing experimental four-qubit quantum state tomography. Using this cluster state, we demonstrate the feasibility of one-way quantum computing through a universal set of one- and two-qubit operations. Finally, our implementation of Grover's search algorithm demonstrates that one-way quantum computation is ideally suited for such tasks.
Quantum mechanics of Proca fields
Zamani, Farhad; Mostafazadeh, Ali
2009-05-01
We construct the most general physically admissible positive-definite inner product on the space of Proca fields. Up to a trivial scaling this defines a five-parameter family of Lorentz invariant inner products that we use to construct a genuine Hilbert space for the quantum mechanics of Proca fields. If we identify the generator of time translations with the Hamiltonian, we obtain a unitary quantum system that describes first-quantized Proca fields and does not involve the conventional restriction to the positive-frequency fields. We provide a rather comprehensive analysis of this system. In particular, we examine the conserved current density responsible for the conservation of the probabilities, explore the global gauge symmetry underlying the conservation of the probabilities, obtain a probability current density, construct position, momentum, helicity, spin, and angular momentum operators, and determine the localized Proca fields. We also compute the generalized parity (P), generalized time-reversal (T), and generalized charge or chirality (C) operators for this system and offer a physical interpretation for its PT-, C-, and CPT-symmetries.
Analytical mechanics for relativity and quantum mechanics
Johns, Oliver Davis
2011-01-01
Analytical Mechanics for Relativity and Quantum Mechanics is an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It is intended for use at the introductory graduate level. A distinguishing feature of the book is its integration of special relativity into teaching of classical mechanics. After a thorough review of the traditional theory, Part II of the book introduces extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Langrangians and Hamiltonians, canonical transformations, and Hamilton-Jacobi methods are simplified by the use of this extended theory. And the definition of canonical transformation no longer excludes the Lorenz transformation of special relativity. This is also a book for those who study analytical mechanics to prepare for a critical exploration of quantum...
Propagators in Polymer Quantum Mechanics
Flores-González, Ernesto; Reyes, Juan D
2013-01-01
Polymer Quantum Mechanics is based on some of the techniques used in the loop quantization of gravity that are adapted to describe systems possessing a finite number of degrees of freedom. It has been used in two ways: on one hand it has been used to represent some aspects of the loop quantization in a simpler context, and, on the other, it has been applied to each of the infinite mechanical modes of other systems. Indeed, this polymer approach was recently implemented for the free scalar field propagator. In this work we compute the polymer propagators of the free particle and a particle in a box; amusingly, just as in the non polymeric case, the one of the particle in a box may be computed also from that of the free particle using the method of images. We verify the propagators hereby obtained satisfy standard properties such as: consistency with initial conditions, composition and Green's function character. Furthermore they are also shown to reduce to the usual Schr\\"odinger propagators in the limit of sm...
Quantum machine learning what quantum computing means to data mining
Wittek, Peter
2014-01-01
Quantum Machine Learning bridges the gap between abstract developments in quantum computing and the applied research on machine learning. Paring down the complexity of the disciplines involved, it focuses on providing a synthesis that explains the most important machine learning algorithms in a quantum framework. Theoretical advances in quantum computing are hard to follow for computer scientists, and sometimes even for researchers involved in the field. The lack of a step-by-step guide hampers the broader understanding of this emergent interdisciplinary body of research. Quantum Machine L
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
Quantum Computing with Very Noisy Devices
Knill, E
2004-01-01
There are quantum algorithms that can efficiently simulate quantum physics, factor large numbers and estimate integrals. As a result, quantum computers can solve otherwise intractable computational problems. One of the main problems of experimental quantum computing is to preserve fragile quantum states in the presence of errors. It is known that if the needed elementary operations (gates) can be implemented with error probabilities below a threshold, then it is possible to efficiently quantum compute with arbitrary accuracy. Here we give evidence that for independent errors the theoretical threshold is well above 3%, which is a significant improvement over that of earlier calculations. However, the resources required at such high error probabilities are excessive. Fortunately, they decrease rapidly with decreasing error probabilities. If we had quantum resources comparable to the considerable resources available in today's digital computers, we could implement non-trivial quantum algorithms at error probabil...
Hilbert space and quantum mechanics
Gallone, Franco
2015-01-01
The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Pref...
Quantum mechanics principles and formalism
McWeeny, Roy
2012-01-01
Focusing on main principles of quantum mechanics and their immediate consequences, this graduate student-oriented volume develops the subject as a fundamental discipline, opening with review of origins of Schrödinger's equations and vector spaces.
Quantum mechanical description of waveguides
Institute of Scientific and Technical Information of China (English)
Wang Zhi-Yong; Xiong Cai-Dong; He Bing
2008-01-01
Applying the spinor representation of the electromagnetic field,this paper present a quantum-mechanical description of waveguides.As an example of application,a potential qubit generated by photon tunnelling is discussed.
Quantum Mechanics and Common Sense
Gantsevich, S V
2016-01-01
A physical picture for Quantum Mechanics which permits to conciliate it with the usual common sense is proposed. The picture agrees with the canonical Copenhagen interpretation making more clear its statements.
Quantum mechanics I the fundamentals
Rajasekar, S
2015-01-01
Quantum Mechanics I: The Fundamentals provides a graduate-level account of the behavior of matter and energy at the molecular, atomic, nuclear, and sub-nuclear levels. It covers basic concepts, mathematical formalism, and applications to physically important systems.
Logic and algebraic structures in quantum computing
Eskandarian, Ali; Harizanov, Valentina S
2016-01-01
Arising from a special session held at the 2010 North American Annual Meeting of the Association for Symbolic Logic, this volume is an international cross-disciplinary collaboration with contributions from leading experts exploring connections across their respective fields. Themes range from philosophical examination of the foundations of physics and quantum logic, to exploitations of the methods and structures of operator theory, category theory, and knot theory in an effort to gain insight into the fundamental questions in quantum theory and logic. The book will appeal to researchers and students working in related fields, including logicians, mathematicians, computer scientists, and physicists. A brief introduction provides essential background on quantum mechanics and category theory, which, together with a thematic selection of articles, may also serve as the basic material for a graduate course or seminar.
The Quantum Human Computer (QHC) Hypothesis
Salmani-Nodoushan, Mohammad Ali
2008-01-01
This article attempts to suggest the existence of a human computer called Quantum Human Computer (QHC) on the basis of an analogy between human beings and computers. To date, there are two types of computers: Binary and Quantum. The former operates on the basis of binary logic where an object is said to exist in either of the two states of 1 and…
Universal quantum computation with qudits
Luo, MingXing; Wang, XiaoJun
2014-09-01
Quantum circuit model has been widely explored for various quantum applications such as Shors algorithm and Grovers searching algorithm. Most of previous algorithms are based on the qubit systems. Herein a proposal for a universal circuit is given based on the qudit system, which is larger and can store more information. In order to prove its universality for quantum applications, an explicit set of one-qudit and two-qudit gates is provided for the universal qudit computation. The one-qudit gates are general rotation for each two-dimensional subspace while the two-qudit gates are their controlled extensions. In comparison to previous quantum qudit logical gates, each primitive qudit gate is only dependent on two free parameters and may be easily implemented. In experimental implementation, multilevel ions with the linear ion trap model are used to build the qudit systems and use the coupling of neighbored levels for qudit gates. The controlled qudit gates may be realized with the interactions of internal and external coordinates of the ion.
The physics of quantum mechanics
Binney, James
2014-01-01
The Physics of Quantum Mechanics aims to give students a good understanding of how quantum mechanics describes the material world. It shows that the theory follows naturally from the use of probability amplitudes to derive probabilities. It stresses that stationary states are unphysical mathematical abstractions that enable us to solve the theory's governing equation, the time-dependent Schroedinger equation. Every opportunity is taken to illustrate the emergence of the familiarclassical, dynamical world through the quantum interference of stationary states. The text stresses the continuity be
High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation
Yang, W L; Hu, Y; Feng, M; Du, J F
2011-01-01
We study a hybrid quantum computing system using nitrogen-vacancy center ensemble (NVE) as quantum memory, current-biased Josephson junction (CBJJ) superconducting qubit fabricated in a transmission line resonator (TLR) as quantum computing processor and the microwave photons in TLR as quantum data bus. The storage process is seriously treated by considering all kinds of decoherence mechanisms. Such a hybrid quantum device can also be used to create multi-qubit W states of NVEs through a common CBJJ. The experimental feasibility and challenge are justified using currently available technology.
Energy-efficient quantum computing
Ikonen, Joni; Salmilehto, Juha; Möttönen, Mikko
2017-04-01
In the near future, one of the major challenges in the realization of large-scale quantum computers operating at low temperatures is the management of harmful heat loads owing to thermal conduction of cabling and dissipation at cryogenic components. This naturally raises the question that what are the fundamental limitations of energy consumption in scalable quantum computing. In this work, we derive the greatest lower bound for the gate error induced by a single application of a bosonic drive mode of given energy. Previously, such an error type has been considered to be inversely proportional to the total driving power, but we show that this limitation can be circumvented by introducing a qubit driving scheme which reuses and corrects drive pulses. Specifically, our method serves to reduce the average energy consumption per gate operation without increasing the average gate error. Thus our work shows that precise, scalable control of quantum systems can, in principle, be implemented without the introduction of excessive heat or decoherence.
Efficient quantum computing using coherent photon conversion.
Langford, N K; Ramelow, S; Prevedel, R; Munro, W J; Milburn, G J; Zeilinger, A
2011-10-12
Single photons are excellent quantum information carriers: they were used in the earliest demonstrations of entanglement and in the production of the highest-quality entanglement reported so far. However, current schemes for preparing, processing and measuring them are inefficient. For example, down-conversion provides heralded, but randomly timed, single photons, and linear optics gates are inherently probabilistic. Here we introduce a deterministic process--coherent photon conversion (CPC)--that provides a new way to generate and process complex, multiquanta states for photonic quantum information applications. The technique uses classically pumped nonlinearities to induce coherent oscillations between orthogonal states of multiple quantum excitations. One example of CPC, based on a pumped four-wave-mixing interaction, is shown to yield a single, versatile process that provides a full set of photonic quantum processing tools. This set satisfies the DiVincenzo criteria for a scalable quantum computing architecture, including deterministic multiqubit entanglement gates (based on a novel form of photon-photon interaction), high-quality heralded single- and multiphoton states free from higher-order imperfections, and robust, high-efficiency detection. It can also be used to produce heralded multiphoton entanglement, create optically switchable quantum circuits and implement an improved form of down-conversion with reduced higher-order effects. Such tools are valuable building blocks for many quantum-enabled technologies. Finally, using photonic crystal fibres we experimentally demonstrate quantum correlations arising from a four-colour nonlinear process suitable for CPC and use these measurements to study the feasibility of reaching the deterministic regime with current technology. Our scheme, which is based on interacting bosonic fields, is not restricted to optical systems but could also be implemented in optomechanical, electromechanical and superconducting
Quantum mechanics in a nutshell
Mahan, Gerald D
2009-01-01
Covering the fundamentals as well as many special topics of current interest, this is the most concise, up-to-date, and accessible graduate-level textbook on quantum mechanics available. Written by Gerald Mahan, a distinguished research physicist and author of an acclaimed textbook on many-particle physics, Quantum Mechanics in a Nutshell is the distillation of many years' teaching experience. Emphasizing the use of quantum mechanics to describe actual quantum systems such as atoms and solids, and rich with interesting applications, the book proceeds from solving for the properties of a single particle in potential; to solving for two particles (the helium atom); to addressing many-particle systems. Applications include electron gas, magnetism, and Bose-Einstein Condensation; examples are carefully chosen and worked; and each chapter has numerous homework problems, many of them original
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.
Parallel computing and quantum chromodynamics
Bowler, K C
1999-01-01
The study of Quantum Chromodynamics (QCD) remains one of the most challenging topics in elementary particle physics. The lattice formulation of QCD, in which space-time is treated as a four- dimensional hypercubic grid of points, provides the means for a numerical solution from first principles but makes extreme demands upon computational performance. High Performance Computing (HPC) offers us the tantalising prospect of a verification of QCD through the precise reproduction of the known masses of the strongly interacting particles. It is also leading to the development of a phenomenological tool capable of disentangling strong interaction effects from weak interaction effects in the decays of one kind of quark into another, crucial for determining parameters of the standard model of particle physics. The 1980s saw the first attempts to apply parallel architecture computers to lattice QCD. The SIMD and MIMD machines used in these pioneering efforts were the ICL DAP and the Cosmic Cube, respectively. These wer...
Non-unitary probabilistic quantum computing
Gingrich, Robert M.; Williams, Colin P.
2004-01-01
We present a method for designing quantum circuits that perform non-unitary quantum computations on n-qubit states probabilistically, and give analytic expressions for the success probability and fidelity.
Schwenke, David W.; Truhlar, Donald G.
1990-01-01
The Generalized Newton Variational Principle for 3D quantum mechanical reactive scattering is briefly reviewed. Then three techniques are described which improve the efficiency of the computations. First, the fact that the Hamiltonian is Hermitian is used to reduce the number of integrals computed, and then the properties of localized basis functions are exploited in order to eliminate redundant work in the integral evaluation. A new type of localized basis function with desirable properties is suggested. It is shown how partitioned matrices can be used with localized basis functions to reduce the amount of work required to handle the complex boundary conditions. The new techniques do not introduce any approximations into the calculations, so they may be used to obtain converged solutions of the Schroedinger equation.
Mathematical foundations of quantum mechanics
Mackey, George W
2004-01-01
Designed for students familiar with abstract mathematical concepts but possessing little knowledge of physics, this text focuses on generality and careful formulation rather than problem-solving. Its author, a member of the distinguished National Academy of Science, based this graduate-level text on the course he taught at Harvard University.Opening chapters on classical mechanics examine the laws of particle mechanics; generalized coordinates and differentiable manifolds; oscillations, waves, and Hilbert space; and statistical mechanics. A survey of quantum mechanics covers the old quantum
Scheme for Quantum Computing Immune to Decoherence
Williams, Colin; Vatan, Farrokh
2008-01-01
A constructive scheme has been devised to enable mapping of any quantum computation into a spintronic circuit in which the computation is encoded in a basis that is, in principle, immune to quantum decoherence. The scheme is implemented by an algorithm that utilizes multiple physical spins to encode each logical bit in such a way that collective errors affecting all the physical spins do not disturb the logical bit. The scheme is expected to be of use to experimenters working on spintronic implementations of quantum logic. Spintronic computing devices use quantum-mechanical spins (typically, electron spins) to encode logical bits. Bits thus encoded (denoted qubits) are potentially susceptible to errors caused by noise and decoherence. The traditional model of quantum computation is based partly on the assumption that each qubit is implemented by use of a single two-state quantum system, such as an electron or other spin-1.2 particle. It can be surprisingly difficult to achieve certain gate operations . most notably, those of arbitrary 1-qubit gates . in spintronic hardware according to this model. However, ironically, certain 2-qubit interactions (in particular, spin-spin exchange interactions) can be achieved relatively easily in spintronic hardware. Therefore, it would be fortunate if it were possible to implement any 1-qubit gate by use of a spin-spin exchange interaction. While such a direct representation is not possible, it is possible to achieve an arbitrary 1-qubit gate indirectly by means of a sequence of four spin-spin exchange interactions, which could be implemented by use of four exchange gates. Accordingly, the present scheme provides for mapping any 1-qubit gate in the logical basis into an equivalent sequence of at most four spin-spin exchange interactions in the physical (encoded) basis. The complexity of the mathematical derivation of the scheme from basic quantum principles precludes a description within this article; it must suffice to report
Quantum Mechanics and determinism
Hooft, G. 't
2001-01-01
It is shown how to map the quantum states of a system of free scalar particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group. The mapping is now also applied to free Maxwell fields. Lorentz invariance is demonstrated.
The quantum field theory interpretation of quantum mechanics
de la Torre, Alberto C.
2015-01-01
It is shown that adopting the \\emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.
Quantum fields on the computer
1992-01-01
This book provides an overview of recent progress in computer simulations of nonperturbative phenomena in quantum field theory, particularly in the context of the lattice approach. It is a collection of extensive self-contained reviews of various subtopics, including algorithms, spectroscopy, finite temperature physics, Yukawa and chiral theories, bounds on the Higgs meson mass, the renormalization group, and weak decays of hadrons.Physicists with some knowledge of lattice gauge ideas will find this book a useful and interesting source of information on the recent developments in the field.
Quantum Mechanics and Narratability
Myrvold, Wayne C.
2016-07-01
As has been noted by several authors, in a relativistic context, there is an interesting difference between classical and quantum state evolution. For a classical system, a state history of a quantum system given along one foliation uniquely determines, without any consideration of the system's dynamics, a state history along any other foliation. This is not true for quantum state evolution; there are cases in which a state history along one foliation is compatible with multiple distinct state histories along some other, a phenomenon that David Albert has dubbed "non-narratability." In this article, we address the question of whether non-narratability is restricted to the sorts of special states that so far have been used to illustrate it. The results of the investigation suggest that there has been a misplaced emphasis on underdetermination of state histories; though this is generic for the special cases that have up until now been considered, involving bipartite systems in pure entangled states, it fails generically in cases in which more component systems are taken into account, and for bipartite systems that have some entanglement with their environment. For such cases, if we impose relativistic causality constraints on the evolution, then, except for very special states, a state history along one foliation uniquely determines a state history along any other. But this in itself is a marked difference between classical and quantum state evolution, because, in a classical setting, no considerations of dynamics at all are needed to go from a state history along one foliation to a state history along another.
Distributed Quantum Computation over Noisy Channels
Ekert, A K; Macchiavello, C; Cirac, J I
1999-01-01
We analyse the use of entangled states to perform quantum computations non locally among distant nodes in a quantum network. We show that for a sufficiently large number of nodes maximally entangled states are always advantageous over independent computations in each node, even in the presence of noise during the computation process.
Quantum computation with two-dimensional graphene quantum dots
Institute of Scientific and Technical Information of China (English)
Li Jie-Sen; Li Zhi-Bing; Yao Dao-Xin
2012-01-01
We study an array of graphene nano sheets that form a two-dimensional S =1/2 Kagome spin lattice used for quantum computation.The edge states of the graphene nano sheets axe used to form quantum dots to confine electrons and perform the computation.We propose two schemes of bang-bang control to combat decoherence and realize gate operations on this array of quantum dots.It is shown that both schemes contain a great amount of information for quantum computation.The corresponding gate operations are also proposed.
Quantum Computing in Solid State Systems
Ruggiero, B; Granata, C
2006-01-01
The aim of Quantum Computation in Solid State Systems is to report on recent theoretical and experimental results on the macroscopic quantum coherence of mesoscopic systems, as well as on solid state realization of qubits and quantum gates. Particular attention has been given to coherence effects in Josephson devices. Other solid state systems, including quantum dots, optical, ion, and spin devices which exhibit macroscopic quantum coherence are also discussed. Quantum Computation in Solid State Systems discusses experimental implementation of quantum computing and information processing devices, and in particular observations of quantum behavior in several solid state systems. On the theoretical side, the complementary expertise of the contributors provides models of the various structures in connection with the problem of minimizing decoherence.
An introduction to reliable quantum computation
Aliferis, Panos
2011-01-01
This is an introduction to software methods of quantum fault tolerance. Broadly speaking, these methods describe strategies for using the noisy hardware components of a quantum computer to perform computations while continually monitoring and actively correcting the hardware faults. We discuss parallels and differences with similar methods for ordinary digital computation, we discuss some of the noise models used in designing and analyzing noisy quantum circuits, and we sketch the logic of some of the central results in this area of research.
Quantum computing. Defining and detecting quantum speedup.
Rønnow, Troels F; Wang, Zhihui; Job, Joshua; Boixo, Sergio; Isakov, Sergei V; Wecker, David; Martinis, John M; Lidar, Daniel A; Troyer, Matthias
2014-07-25
The development of small-scale quantum devices raises the question of how to fairly assess and detect quantum speedup. Here, we show how to define and measure quantum speedup and how to avoid pitfalls that might mask or fake such a speedup. We illustrate our discussion with data from tests run on a D-Wave Two device with up to 503 qubits. By using random spin glass instances as a benchmark, we found no evidence of quantum speedup when the entire data set is considered and obtained inconclusive results when comparing subsets of instances on an instance-by-instance basis. Our results do not rule out the possibility of speedup for other classes of problems and illustrate the subtle nature of the quantum speedup question.
Quantum computing with incoherent resources and quantum jumps.
Santos, M F; Cunha, M Terra; Chaves, R; Carvalho, A R R
2012-04-27
Spontaneous emission and the inelastic scattering of photons are two natural processes usually associated with decoherence and the reduction in the capacity to process quantum information. Here we show that, when suitably detected, these photons are sufficient to build all the fundamental blocks needed to perform quantum computation in the emitting qubits while protecting them from deleterious dissipative effects. We exemplify this by showing how to efficiently prepare graph states for the implementation of measurement-based quantum computation.
A theoretical model of multi-agent quantum computing
Mihelic, F. Matthew
2011-05-01
The best design for practical quantum computing is one that emulates the multi-agent quantum logic function of natural biological systems. Such systems are theorized to be based upon a quantum gate formed by a nucleic acid Szilard engine (NASE) that converts Shannon entropy of encountered molecules into useful work of nucleic acid geometric reconfiguration. This theoretical mechanism is logically and thermodynamically reversible in this special case because it is literally constructed out of the (nucleic acid) information necessary for its function, thereby allowing the nucleic acid Szilard engine to function reversibly because, since the information by which it functions exists on both sides of the theoretical mechanism simultaneously, there would be no build-up of information within the theoretical mechanism, and therefore no irreversible thermodynamic energy cost would be necessary to erase information inside the mechanism. This symmetry breaking Szilard engine function is associated with emission and/or absorption of entangled photons that can provide quantum synchronization of other nucleic acid segments within and between cells. In this manner nucleic acids can be considered as a natural model of topological quantum computing in which the nonabelian interaction of genes can be represented within quantum knot/braid theory as anyon crosses determined by entropic loss or gain that leads to changes in nucleic acid covalent bond angles. This naturally occurring biological form of topological quantum computing can serve as a model for workable man-made multi-agent quantum computing systems.
Disciplines, models, and computers: the path to computational quantum chemistry.
Lenhard, Johannes
2014-12-01
Many disciplines and scientific fields have undergone a computational turn in the past several decades. This paper analyzes this sort of turn by investigating the case of computational quantum chemistry. The main claim is that the transformation from quantum to computational quantum chemistry involved changes in three dimensions. First, on the side of instrumentation, small computers and a networked infrastructure took over the lead from centralized mainframe architecture. Second, a new conception of computational modeling became feasible and assumed a crucial role. And third, the field of computa- tional quantum chemistry became organized in a market-like fashion and this market is much bigger than the number of quantum theory experts. These claims will be substantiated by an investigation of the so-called density functional theory (DFT), the arguably pivotal theory in the turn to computational quantum chemistry around 1990.
Quantum Mechanical Earth: Where Orbitals Become Orbits
Keeports, David
2012-01-01
Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…
Quantum Mechanical Earth: Where Orbitals Become Orbits
Keeports, David
2012-01-01
Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…
Non-relativistic quantum mechanics
Puri, Ravinder R.
2017-01-01
This book develops and simplifies the concept of quantum mechanics based on the postulates of quantum mechanics. The text discusses the technique of disentangling the exponential of a sum of operators, closed under the operation of commutation, as the product of exponentials to simplify calculations of harmonic oscillator and angular momentum. Based on its singularity structure, the Schrödinger equation for various continuous potentials is solved in terms of the hypergeometric or the confluent hypergeometric functions. The forms of the potentials for which the one-dimensional Schrödinger equation is exactly solvable are derived in detail. The problem of identifying the states of two-level systems which have no classical analogy is addressed by going beyond Bell-like inequalities and separability. The measures of quantumness of mutual information in two two-level systems is also covered in detail. Offers a new approach to learning quantum mechanics based on the history of quantum mechanics and its postu...
QUANTUM MECHANICS. Quantum squeezing of motion in a mechanical resonator.
Wollman, E E; Lei, C U; Weinstein, A J; Suh, J; Kronwald, A; Marquardt, F; Clerk, A A; Schwab, K C
2015-08-28
According to quantum mechanics, a harmonic oscillator can never be completely at rest. Even in the ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. Using microwave frequency radiation pressure, we have manipulated the thermal fluctuations of a micrometer-scale mechanical resonator to produce a stationary quadrature-squeezed state with a minimum variance of 0.80 times that of the ground state. We also performed phase-sensitive, back-action evading measurements of a thermal state squeezed to 1.09 times the zero-point level. Our results are relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultrasensitive sensing of force and motion.
Framing difficulties in quantum mechanics
Modir, Bahar; Sayre, Eleanor C
2016-01-01
Students' difficulties in quantum mechanics may be the result of unproductive framing and not fundamental inability to solve the problems or misconceptions about physics content. We observed groups of students solving quantum mechanics problems in an upper-division physics course. Using the lens of the epistemological framing, we investigated four frames in our observational data: algorithmic math, conceptual math, algorithmic physics, and conceptual physics. We then used our framework to seek an underlying structure to the long lists of published difficulties that span many topics in quantum mechanics. We mapped descriptions of published difficulties into errors in epistemological framing and resource use. We analyzed descriptions of students' problem solving to find their frames, and compared students' framing to framing (and frame shifting) required by problem statements. We found three categories of error: mismatches between students' framing and problem statement framing; inappropriate or absent transiti...
Algebraic Quantum Mechanics and Pregeometry
Hiley, D J B P G D B J
2006-01-01
We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive idempotents as "generalized points" we suggest an approach that may make it possible to dispense with an a priori given space manifold. In this approach the algebra itself would carry the symmetries of translation, rotation, etc. Our suggestion is illustrated in a preliminary way by using a particular generalized Clifford Algebra proposed originally by Weyl, which approaches the ordinary Heisenberg algebra in a suitable limit. We thus obtain a certain insight into how quantum mechanics may be regarded as a purely algebraic theory, provided that we further introduce a new set of "neighbourhood operators", which remove an important kind of arbitrariness that has thus far been present in the attempt to treat quantum mechanics solely in terms of a Heisenberg algebra.
Quantum computing with realistically noisy devices.
Knill, E
2005-03-03
In theory, quantum computers offer a means of solving problems that would be intractable on conventional computers. Assuming that a quantum computer could be constructed, it would in practice be required to function with noisy devices called 'gates'. These gates cause decoherence of the fragile quantum states that are central to the computer's operation. The goal of so-called 'fault-tolerant quantum computing' is therefore to compute accurately even when the error probability per gate (EPG) is high. Here we report a simple architecture for fault-tolerant quantum computing, providing evidence that accurate quantum computing is possible for EPGs as high as three per cent. Such EPGs have been experimentally demonstrated, but to avoid excessive resource overheads required by the necessary architecture, lower EPGs are needed. Assuming the availability of quantum resources comparable to the digital resources available in today's computers, we show that non-trivial quantum computations at EPGs of as high as one per cent could be implemented.
Multilayer microwave integrated quantum circuits for scalable quantum computing
Brecht, Teresa; Pfaff, Wolfgang; Wang, Chen; Chu, Yiwen; Frunzio, Luigi; Devoret, Michel H.; Schoelkopf, Robert J.
2016-02-01
As experimental quantum information processing (QIP) rapidly advances, an emerging challenge is to design a scalable architecture that combines various quantum elements into a complex device without compromising their performance. In particular, superconducting quantum circuits have successfully demonstrated many of the requirements for quantum computing, including coherence levels that approach the thresholds for scaling. However, it remains challenging to couple a large number of circuit components through controllable channels while suppressing any other interactions. We propose a hardware platform intended to address these challenges, which combines the advantages of integrated circuit fabrication and the long coherence times achievable in three-dimensional circuit quantum electrodynamics. This multilayer microwave integrated quantum circuit platform provides a path towards the realisation of increasingly complex superconducting devices in pursuit of a scalable quantum computer.
Remarks on osmosis, quantum mechanics, and gravity
Carroll, Robert
2011-01-01
Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.
Black holes and quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hooft, G. ' t, E-mail: g.thooft@uu.n [Institute for Theoretical Physics, Utrecht University and Spinoza Institute, P.O. Box 80.195, 3508 TD Utrecht (Netherlands)
2010-07-15
After a brief review of quantum black hole physics, it is shown how the dynamical properties of a quantum black hole may be deduced to a large extent from Standard Model Physics, extended to scales near the Planck length, and combined with results from perturbative quantum gravity. Together, these interactions generate a Hilbert space of states on the black hole horizon, which can be investigated, displaying interesting systematics by themselves. To make such approaches more powerful, a study is made of the black hole complementarity principle, from which one may deduce the existence of a hidden form of local conformal invariance. Finally, the question is raised whether the principles underlying Quantum Mechanics are to be sharpened in this domain of physics as well. There are intriguing possibilities.
PREFACE: Quantum Information, Communication, Computation and Cryptography
Benatti, F.; Fannes, M.; Floreanini, R.; Petritis, D.
2007-07-01
The application of quantum mechanics to information related fields such as communication, computation and cryptography is a fast growing line of research that has been witnessing an outburst of theoretical and experimental results, with possible practical applications. On the one hand, quantum cryptography with its impact on secrecy of transmission is having its first important actual implementations; on the other hand, the recent advances in quantum optics, ion trapping, BEC manipulation, spin and quantum dot technologies allow us to put to direct test a great deal of theoretical ideas and results. These achievements have stimulated a reborn interest in various aspects of quantum mechanics, creating a unique interplay between physics, both theoretical and experimental, mathematics, information theory and computer science. In view of all these developments, it appeared timely to organize a meeting where graduate students and young researchers could be exposed to the fundamentals of the theory, while senior experts could exchange their latest results. The activity was structured as a school followed by a workshop, and took place at The Abdus Salam International Center for Theoretical Physics (ICTP) and The International School for Advanced Studies (SISSA) in Trieste, Italy, from 12-23 June 2006. The meeting was part of the activity of the Joint European Master Curriculum Development Programme in Quantum Information, Communication, Cryptography and Computation, involving the Universities of Cergy-Pontoise (France), Chania (Greece), Leuven (Belgium), Rennes1 (France) and Trieste (Italy). This special issue of Journal of Physics A: Mathematical and Theoretical collects 22 contributions from well known experts who took part in the workshop. They summarize the present day status of the research in the manifold aspects of quantum information. The issue is opened by two review articles, the first by G Adesso and F Illuminati discussing entanglement in continuous variable
Quantum mechanics foundations and applications
Swanson, Donald Gary
2006-01-01
Progressing from the fundamentals of quantum mechanics (QM) to more complicated topics, Quantum Mechanics: Foundations and Applications provides advanced undergraduate and graduate students with a comprehensive examination of many applications that pertain to modern physics and engineering.Based on courses taught by the author, this textbook begins with an introductory chapter that reviews historical landmarks, discusses classical theory, and establishes a set of postulates. The next chapter demonstrates how to find the appropriate wave functions for a variety of physical systems in one dimens
Nonlinear optics quantum computing with circuit QED.
Adhikari, Prabin; Hafezi, Mohammad; Taylor, J M
2013-02-08
One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has improved tolerance to noise in the qubit while maintaining fast operation.
The one-way quantum computer - a non-network model of quantum computation
Raussendorf, R; Briegel, H J; Raussendorf, Robert; Browne, Daniel E.; Briegel, Hans J.
2001-01-01
A one-way quantum computer works by only performing a sequence of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. No non-local operations are required in the process of computation. Any quantum logic network can be simulated on the one-way quantum computer. On the other hand, the network model of quantum computation cannot explain all ways of processing quantum information possible with the one-way quantum computer. In this paper, two examples of the non-network character of the one-way quantum computer are given. First, circuits in the Clifford group can be performed in a single time step. Second, the realisation of a particular circuit --the bit-reversal gate-- on the one-way quantum computer has no network interpretation. (Submitted to J. Mod. Opt, Gdansk ESF QIT conference issue.)
An overview of quantum computation models: quantum automata
Institute of Scientific and Technical Information of China (English)
2008-01-01
Quantum automata,as theoretical models of quantum computers,include quantum finite automata (QFA),quantum sequential machines (QSM),quantum pushdown automata (QPDA),quantum Turing machines (QTM),quantum cellular automata (QCA),and the others,for example,automata theory based on quantum logic (orthomodular lattice-valued automata).In this paper,we try to outline a basic progress in the research on these models,focusing on QFA,QSM,QPDA,QTM,and orthomodular lattice-valued automata.Also,other models closely relative to them are mentioned.In particular,based on the existing results in the literature,we finally address a number of problems to be studied in future.
Quantum state diffusion, localization and computation
Schack, R; Percival, I C
1995-01-01
Numerical simulation of individual open quantum systems has proven advantages over density operator computations. Quantum state diffusion with a moving basis (MQSD) provides a practical numerical simulation method which takes full advantage of the localization of quantum states into wave packets occupying small regions of classical phase space. Following and extending the original proposal of Percival, Alber and Steimle, we show that MQSD can provide a further gain over ordinary QSD and other quantum trajectory methods of many orders of magnitude in computational space and time. Because of these gains, it is even possible to calculate an open quantum system trajectory when the corresponding isolated system is intractable. MQSD is particularly advantageous where classical or semiclassical dynamics provides an adequate qualitative picture but is numerically inaccurate because of significant quantum effects. The principles are illustrated by computations for the quantum Duffing oscillator and for second harmonic...
Lecture Notes in Quantum Mechanics
Cohen, D
2006-01-01
These lecture notes cover undergraduate textbook topics (e.g. as in Sakurai), and also additional advanced topics at the same level of presentation. In particular: EPR and Bell; Basic postulates; The probability matrix; Measurement theory; Entanglement; Quantum computation; Wigner-Weyl formalism; The adiabatic picture; Berry phase; Linear response theory; Kubo formula; Modern approach to scattering theory with mesoscopic orientation; Theory of the resolvent and the Green function; Gauge and Galilei Symmetries; Motion in magnetic field; Quantum Hall effect; Quantization of the electromagnetic field; Fock space formalism.
Distributed measurement-based quantum computation
Danos, V; Kashefi, E; Panangaden, P; Danos, Vincent; Hondt, Ellie D'; Kashefi, Elham; Panangaden, Prakash
2005-01-01
We develop a formal model for distributed measurement-based quantum computations, adopting an agent-based view, such that computations are described locally where possible. Because the network quantum state is in general entangled, we need to model it as a global structure, reminiscent of global memory in classical agent systems. Local quantum computations are described as measurement patterns. Since measurement-based quantum computation is inherently distributed, this allows us to extend naturally several concepts of the measurement calculus, a formal model for such computations. Our goal is to define an assembly language, i.e. we assume that computations are well-defined and we do not concern ourselves with verification techniques. The operational semantics for systems of agents is given by a probabilistic transition system, and we define operational equivalence in a way that it corresponds to the notion of bisimilarity. With this in place, we prove that teleportation is bisimilar to a direct quantum channe...
Effective equations for the quantum pendulum from momentous quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hernandez, Hector H.; Chacon-Acosta, Guillermo [Universidad Autonoma de Chihuahua, Facultad de Ingenieria, Nuevo Campus Universitario, Chihuahua 31125 (Mexico); Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120 (Mexico)
2012-08-24
In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.
Quantum computer of wire circuit architecture
Moiseev, S A; Andrianov, S N
2010-01-01
First solid state quantum computer was built using transmons (cooper pair boxes). The operation of the computer is limited because of using a number of the rigit cooper boxes working with fixed frequency at temperatures of superconducting material. Here, we propose a novel architecture of quantum computer based on a flexible wire circuit of many coupled quantum nodes containing controlled atomic (molecular) ensembles. We demonstrate wide opportunities of the proposed computer. Firstly, we reveal a perfect storage of external photon qubits to multi-mode quantum memory node and demonstrate a reversible exchange of the qubits between any arbitrary nodes. We found optimal parameters of atoms in the circuit and self quantum modes for quantum processing. The predicted perfect storage has been observed experimentally for microwave radiation on the lithium phthalocyaninate molecule ensemble. Then also, for the first time we show a realization of the efficient basic two-qubit gate with direct coupling of two arbitrary...
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
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.
Quantum Computing: Linear Optics Implementations
Sundsøy, Pål
2016-01-01
One of the main problems that optical quantum computing has to overcome is the efficient construction of two-photon gates. Theoretically these gates can be realized using Kerr-nonlinearities, but the techniques involved are experimentally very difficult. We therefore employ linear optics with projective measurements to generate these non-linearities. The downside is that the measurement-induced nonlinearities achieved with linear optics are less versatile and the success rate can be quite low. This project is mainly the result of a literature study but also a theoretical work on the physics behind quantum optical multiports which is essential for realizing two-photon gates. By applying different postcorrection techniques we increase the probability of success in a modifed non-linear sign shift gate which is foundational for the two photon controlled-NOT gate. We prove that it's not possible to correct the states by only using a single beam splitter. We show that it might be possible to increase the probabilit...
On the completeness of quantum computation models
Arrighi, Pablo
2010-01-01
The notion of computability is stable (i.e. independent of the choice of an indexing) over infinite-dimensional vector spaces provided they have a finite "tensorial dimension". Such vector spaces with a finite tensorial dimension permit to define an absolute notion of completeness for quantum computation models and give a precise meaning to the Church-Turing thesis in the framework of quantum theory. (Extra keywords: quantum programming languages, denotational semantics, universality.)
Quantum computation architecture using optical tweezers
DEFF Research Database (Denmark)
Weitenberg, Christof; Kuhr, Stefan; Mølmer, Klaus;
2011-01-01
We present a complete architecture for scalable quantum computation with ultracold atoms in optical lattices using optical tweezers focused to the size of a lattice spacing. We discuss three different two-qubit gates based on local collisional interactions. The gates between arbitrary qubits...... quantum computing....
Quantum computer: an appliance for playing market games
Piotrowski, Edward W.; Jan Sladkowski
2003-01-01
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The authors have recently proposed a quantum description of financial market in terms of quantum game theory. The paper contain an analysis of such markets that shows that there would be advantage in using quantum computers and quantum strategies.
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.
Quantum Mechanics, is it magic
Ferrero, M; Sánchez-Gómez, J L
2008-01-01
We show that quantum mechanics is the first theory in human history that violates the basic a priori principles that have shaped human thought since immemorial times. Therefore although it is more contrary to magic than any body of knowledge could be, what could be called its magic precisely resides in this violation.
Mind, matter and quantum mechanics
Stapp, Henry P
2009-01-01
"Scientists other than quantum physicists often fail to comprehend the enormity of the conceptual change wrought by quantum theory in our basic conception of the nature of matter," writes Henry Stapp. Stapp is a leading quantum physicist who has given particularly careful thought to the implications of the theory that lies at the heart of modern physics. In this book, which contains several of his key papers as well as new material, he focuses on the problem of consciousness and explains how quantum mechanics allows causally effective conscious thought to be combined in a natural way with the physical brain made of neurons and atoms. The book is divided into four sections. The first consists of an extended introduction. Key foundational and somewhat more technical papers are included in the second part, together with a clear exposition of the "orthodox" interpretation of quantum mechanics. The third part addresses, in a non-technical fashion, the implications of the theory for some of the most profound questi...
Thermo-mechanical challenges for quantum devices
Gielen, A.W.J.; McKenzie, F.V.
2014-01-01
In the last few years Technical University of Delft, under leadership of Prof.dr.ir. Leo Kouwenhoven, has developed several successful concepts for quantum devices that are suitable for quantum computing and quantum communication. From a quantum research point of view we are still in a very fundamen
Exploring the Quantum Speed Limit with Computer Games
DEFF Research Database (Denmark)
Sørensen, Jens Jakob Winther Hedemann; Pedersen, Mads Kock; Munch, Michael Kulmback
2016-01-01
scientists and allowing them to provide novel solutions to the research problems. Citizen science games have been used successfully in Foldit, EteRNA and EyeWire to study protein and RNA folding and neuron mapping. However, gamification has never been applied in quantum physics. Everyday experiences of non......-experts are based on classical physics and it is \\textit{a priori} not clear that they should have an intuition for quantum dynamics. Does this premise hinder the use of citizen scientists in the realm of quantum mechanics? Here we report on Quantum Moves, an online platform gamifying optimization problems...... in quantum physics. Quantum Moves aims to use human players to find solutions to a class of problems associated with quantum computing. Players discover novel solution strategies which numerical optimizations fail to find. Guided by player strategies, a new low-dimensional heuristic optimization method...
Philosophic foundations of quantum mechanics
Reichenbach, Hans
1998-01-01
Physics concerns direct analysis of the physical world, while philosophy analyzes knowledge about the physical world. This volume combines both disciplines for a philosophical interpretation of quantum physics - an interpretation free from the imprecision of metaphysics, offering a view of the atomic world and its quantum mechanical results as concrete as the visible everyday world.Written by an internationally renowned philosopher who specialized in symbolic logic and the theory of relativity, this approach consists of three parts. The first section, which requires no background in math or p
Memetics of Quantum Mechanical Interpretations
Chakrabarty, I
2006-01-01
Memes, self reproducing mental information and cognitive structures analogous to genes in biology, can be seen as the basis for an explanatory model of cultural and psychological behavior. Their properties and effects are evolutionary conditioned and ultimately seeks to promote their replication. To survive in a context the memes must meet certain conditions. We here propose a Memetics of Quantum Mechanical Interpretations, which have eluded mankind for a century now. We also see how the ideas of memes best fit the way scientific theories in general and Quantum Theory in particular propagates in the scientific brains and finds its expressions in the scientific community and effects the way we perceive Nature.
Operator methods in quantum mechanics
Schechter, Martin
2003-01-01
This advanced undergraduate and graduate-level text introduces the power of operator theory as a tool in the study of quantum mechanics, assuming only a working knowledge of advanced calculus and no background in physics. The author presents a few simple postulates describing quantum theory, gradually introducing the mathematical techniques that help answer questions important to the physical theory; in this way, readers see clearly the purpose of the method and understand the accomplishment. The entire book is devoted to the study of a single particle moving along a straight line. By posing q
Wigner distributions in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Ercolessi, E; Marmo, G; Morandi, G; Mukunda, N [Physics Department, University of Bologna, INFN and CNISM. 46 v.Irnerio. I-40126, Bologna (Italy); Dip. di Scienze Fisiche. University di Napoli ' Federico II' and INFN. v.Cinzia. I-80100 Naples (Italy); Physics Department, University of Bologna, INFN and CNISM. 6/2 v.le Berti Pichat. I-40127, Bologna (Italy); Centre for High-Energy Physics. Indian Institute of Science. Bamgalore 560012 (India)
2007-11-15
The Weyl-Wigner description of quantum mechanical operators and states in classical phase-space language is well known for Cartesian systems. We describe a new approach based on ideas of Dirac which leads to the same results but with interesting additional insights. A way to set up Wigner distributions in an interesting non-Cartesian case, when the configuration space is a compact connected Lie group, is outlined. Both these methods are adapted to quantum systems with finite-dimensional Hilbert spaces, and the results are contrasted.
Paradoxical reflection in quantum mechanics
Pedro L. Garrido; Goldstein, Sheldon; Lukkarinen, Jani; Tumulka, Roderich
2011-01-01
This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast, classical particles get reflected only at upward steps. The conditions for this effect are that the wave length is much greater than the width of the potential step and the kinetic energy of the particle is much smaller than the depth of the potential step. This p...
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.
Computational statistical mechanics
Hoover, WG
1991-01-01
Computational Statistical Mechanics describes the use of fast computers to simulate the equilibrium and nonequilibrium properties of gases, liquids, and solids at, and away from equilibrium. The underlying theory is developed from basic principles and illustrated by applying it to the simplest possible examples. Thermodynamics, based on the ideal gas thermometer, is related to Gibb's statistical mechanics through the use of Nosé-Hoover heat reservoirs. These reservoirs use integral feedback to control temperature. The same approach is carried through to the simulation and anal
Performing quantum computing experiments in the cloud
Devitt, Simon J.
2016-09-01
Quantum computing technology has reached a second renaissance in the past five years. Increased interest from both the private and public sector combined with extraordinary theoretical and experimental progress has solidified this technology as a major advancement in the 21st century. As anticipated my many, some of the first realizations of quantum computing technology has occured over the cloud, with users logging onto dedicated hardware over the classical internet. Recently, IBM has released the Quantum Experience, which allows users to access a five-qubit quantum processor. In this paper we take advantage of this online availability of actual quantum hardware and present four quantum information experiments. We utilize the IBM chip to realize protocols in quantum error correction, quantum arithmetic, quantum graph theory, and fault-tolerant quantum computation by accessing the device remotely through the cloud. While the results are subject to significant noise, the correct results are returned from the chip. This demonstrates the power of experimental groups opening up their technology to a wider audience and will hopefully allow for the next stage of development in quantum information technology.
Computing a Turing-Incomputable Problem from Quantum Computing
Sicard, A; Ospina, J; Sicard, Andr\\'es; V\\'elez, Mario; Ospina, Juan
2003-01-01
A hypercomputation model named Infinite Square Well Hypercomputation Model (ISWHM) is built from quantum computation. This model is inspired by the model proposed by Tien D. Kieu quant-ph/0203034 and solves an Turing-incomputable problem. For the proposed model and problem, a simulation of its behavior is made. Furthermore, it is demonstrated that ISWHM is a universal quantum computation model.
Universal quantum computation with little entanglement.
Van den Nest, Maarten
2013-02-01
We show that universal quantum computation can be achieved in the standard pure-state circuit model while the entanglement entropy of every bipartition is small in each step of the computation. The entanglement entropy required for large-scale quantum computation even tends to zero. Moreover we show that the same conclusion applies to many entanglement measures commonly used in the literature. This includes e.g., the geometric measure, localizable entanglement, multipartite concurrence, squashed entanglement, witness-based measures, and more generally any entanglement measure which is continuous in a certain natural sense. These results demonstrate that many entanglement measures are unsuitable tools to assess the power of quantum computers.
Symbolic Quantum Computation Simulation in SymPy
Cugini, Addison; Curry, Matt; Granger, Brian
2010-10-01
Quantum computing is an emerging field which aims to use quantum mechanics to solve difficult computational problems with greater efficiency than on a classical computer. There is a need to create software that i) helps newcomers to learn the field, ii) enables practitioners to design and simulate quantum circuits and iii) provides an open foundation for further research in the field. Towards these ends we have created a package, in the open-source symbolic computation library SymPy, that simulates the quantum circuit model of quantum computation using Dirac notation. This framework builds on the extant powerful symbolic capabilities of SymPy to preform its simulations in a fully symbolic manner. We use object oriented design to abstract circuits as ordered collections of quantum gate and qbit objects. The gate objects can either be applied directly to the qbit objects or be represented as matrices in different bases. The package is also capable of performing the quantum Fourier transform and Shor's algorithm. A notion of measurement is made possible through the use of a non-commutative gate object. In this talk, we describe the software and show examples of quantum circuits on single and multi qbit states that involve common algorithms, gates and measurements.
The Picture Book of Quantum Mechanics
Brandt, Siegmund
2012-01-01
The aim of this book is to explain the basic concepts and phenomena of quantum mechanics by means of visualization. Computer-generated illustrations in color are used extensively throughout the text, helping to establish the relation between quantum mechanics—wave functions, interference, atomic structure, and so forth—and classical physics—point mechanics, statistical mechanics, and wave optics. Even more important, by studying the pictures in parallel with the text, readers develop an intuition for such notoriously abstract phenomena as • the tunnel effect • excitation and decay of metastable states • wave-packet motion within a well • systems of distinguishable and indistinguishable particles • free wave packets and scattering in 3 dimensions • angular-momentum decomposition • stationary bound states in various 3-dimensional potentials • hybrid states • Kepler motion of wave packets in the Coulomb field • spin and magnetic resonance Illustrations from experiments in a variety of f...
Teleportation of Two Quantum States via the Quantum Computation
Institute of Scientific and Technical Information of China (English)
FENG Mang; ZHU Xi-Wen; FANG Xi-Ming; YAN Min; SHI Lei
2000-01-01
A scheme of teleportation of two unknown quantum states via quantum computation is proposed. The comparison with the former proposals shows that our scheme is more in tune with the original teleportation proposal and the effciency is higher. The teleportation of an unknown entangled state is also discussed.
Numerical characteristics of quantum computer simulation
Chernyavskiy, A.; Khamitov, K.; Teplov, A.; Voevodin, V.; Voevodin, Vl.
2016-12-01
The simulation of quantum circuits is significantly important for the implementation of quantum information technologies. The main difficulty of such modeling is the exponential growth of dimensionality, thus the usage of modern high-performance parallel computations is relevant. As it is well known, arbitrary quantum computation in circuit model can be done by only single- and two-qubit gates, and we analyze the computational structure and properties of the simulation of such gates. We investigate the fact that the unique properties of quantum nature lead to the computational properties of the considered algorithms: the quantum parallelism make the simulation of quantum gates highly parallel, and on the other hand, quantum entanglement leads to the problem of computational locality during simulation. We use the methodology of the AlgoWiki project (algowiki-project.org) to analyze the algorithm. This methodology consists of theoretical (sequential and parallel complexity, macro structure, and visual informational graph) and experimental (locality and memory access, scalability and more specific dynamic characteristics) parts. Experimental part was made by using the petascale Lomonosov supercomputer (Moscow State University, Russia). We show that the simulation of quantum gates is a good base for the research and testing of the development methods for data intense parallel software, and considered methodology of the analysis can be successfully used for the improvement of the algorithms in quantum information science.
Ha, Nguyen Ngoc; Cam, Le Minh; Ha, Nguyen Thi Thu; Goh, Bee-Min; Saunders, Martin; Jiang, Zhong-Tao; Altarawneh, Mohammednoor; Dlugogorski, Bogdan Z; El-Harbawi, Mohanad; Yin, Chun-Yang
2017-06-07
The prevalence of global arsenic groundwater contamination has driven widespread research on developing effective treatment systems including adsorption using various sorbents. The uptake of arsenic-based contaminants onto established sorbents such as activated carbon (AC) can be effectively enhanced via immobilization/impregnation of iron-based elements on the porous AC surface. Recent suggestions that AC pores structurally consist of an eclectic mix of curved fullerene-like sheets may affect the arsenic adsorption dynamics within the AC pores and is further complicated by the presence of nano-sized iron-based elements. We have therefore, attempted to shed light on the adsorptive interactions of arsenate-iron nanoparticles with curved fullerene-like sheets by using hybridized quantum mechanics/molecular mechanics (QMMM) calculations and microscopy characterization. It is found that, subsequent to optimization, chemisorption between HAsO4(2-) and the AC carbon sheet (endothermic process) is virtually non-existent - this observation is supported by experimental results. Conversely, the incorporation of iron nanoparticles (FeNPs) into the AC carbon sheet greatly facilitates chemisorption of HAsO4(2-). Our calculation implies that iron carbide is formed at the junction between the iron and the AC interface and this tightly chemosorbed layer prevents detachment of the FeNPs on the AC surface. Other aspects including electronic structure/properties, carbon arrangement defects and rate of adsorptive interaction, which are determined using the Climbing-Image NEB method, are also discussed.
Making sense of quantum mechanics
Bricmont, Jean
2016-01-01
This book explains, in simple terms, with a minimum of mathematics, why things can appear to be in two places at the same time, why correlations between simultaneous events occurring far apart cannot be explained by local mechanisms, and why, nevertheless, the quantum theory can be understood in terms of matter in motion. No need to worry, as some people do, whether a cat can be both dead and alive, whether the moon is there when nobody looks at it, or whether quantum systems need an observer to acquire definite properties. The author’s inimitable and even humorous style makes the book a pleasure to read while bringing a new clarity to many of the longstanding puzzles of quantum physics.
The Lagrangian in Quantum Mechanics
Dirac, P. A. M.
Quantum mechanics was built up on a foundation of analogy with the Hamiltonian theory of classical mechanics. This is because the classical notion of canonical coordinates and momenta was found to be one with a very simple quantum analogue, as a result of which the whole of the classical Hamiltonian theory, which is just a structure built up on this notion, could be taken over in all its details into quantum mechanics. Now there is an alternative formulation for classical dynamics, provided by the Lagrangian. This requires one to work in terms of coordinates and velocities instead of coordinates and momenta. The two formulations are, of course, closely related, but there are reasons for believing that the Lagrangian one is the more fundamental. In the first place the Lagrangian method allows one to collect together all the equations of motion and express them as the stationary property of a certain action function. (This action function is just the time-integral of the Lagrangian.) There is no corresponding action principle in terms of the coordinates and momenta of the Hamiltonian theory. Secondly the Lagrangian method can easily be expressed relativistically, on account of the action function being a relativistic invariant; while the Hamiltonian method is essentially non-relativistic in form, since it marks out a particular time variable as the canonical conjugate of the Hamiltonian function. For these reasons it would seem desirable to take up the question of what corresponds in the quantum theory to the Lagrangian method of the classical theory. A little consideration shows, however, that one cannot expect to be able to take over the classical Lagrangian equations in any very direct way. These equations involve partial derivatives of the Lagrangian with respect to the coordinates and velocities and no meaning can be given to such derivatives in quantum mechanics. The only differentiation process that can be carried out with respect to the dynamical variables of
Non-relativistic Quantum Mechanics versus Quantum Field Theories
Pineda, Antonio
2007-01-01
We briefly review the derivation of a non-relativistic quantum mechanics description of a weakly bound non-relativistic system from the underlying quantum field theory. We highlight the main techniques used.
Star Products for Relativistic Quantum Mechanics
Henselder, P.
2007-01-01
The star product formalism has proved to be an alternative formulation for nonrelativistic quantum mechanics. We want introduce here a covariant star product in order to extend the star product formalism to relativistic quantum mechanics in the proper time formulation.
Quantum Computation Using Optically Coupled Quantum Dot Arrays
Pradhan, Prabhakar; Anantram, M. P.; Wang, K. L.; Roychowhury, V. P.; Saini, Subhash (Technical Monitor)
1998-01-01
A solid state model for quantum computation has potential advantages in terms of the ease of fabrication, characterization, and integration. The fundamental requirements for a quantum computer involve the realization of basic processing units (qubits), and a scheme for controlled switching and coupling among the qubits, which enables one to perform controlled operations on qubits. We propose a model for quantum computation based on optically coupled quantum dot arrays, which is computationally similar to the atomic model proposed by Cirac and Zoller. In this model, individual qubits are comprised of two coupled quantum dots, and an array of these basic units is placed in an optical cavity. Switching among the states of the individual units is done by controlled laser pulses via near field interaction using the NSOM technology. Controlled rotations involving two or more qubits are performed via common cavity mode photon. We have calculated critical times, including the spontaneous emission and switching times, and show that they are comparable to the best times projected for other proposed models of quantum computation. We have also shown the feasibility of accessing individual quantum dots using the NSOM technology by calculating the photon density at the tip, and estimating the power necessary to perform the basic controlled operations. We are currently in the process of estimating the decoherence times for this system; however, we have formulated initial arguments which seem to indicate that the decoherence times will be comparable, if not longer, than many other proposed models.
The clock of a quantum computer
Apolloni, B
2002-01-01
If the physical agent (the 'pointer', or 'cursor', or 'clocking mechanism') that sequentially scans the T lines of a long computer program is a microscopic system, two quantum phenomena become relevant: spreading of the probability distribution of the pointer along the program lines, and scattering of the probability amplitude at the two endpoints of the physical space allowed for its motion. We show that the first effect determines an upper bound O(T sup - sup 2 sup / sup 3) on the probability of finding the pointer exactly at the END line. By adding an adequate number delta of further empty lines ('telomers'), one can store the result of the computation up to the moment in which the pointer is scattered back into the active region. This leads to a less severe upper bound O(sq root delta/T) on the probability of finding the pointer either at the END line or within the additional empty lines. Our analysis is performed in the context of Feynman's model of quantum computation, the only model, to our knowledge, ...
Numerical computation for teaching quantum statistics
Price, Tyson; Swendsen, Robert H.
2013-11-01
The study of ideal quantum gases reveals surprising quantum effects that can be observed in macroscopic systems. The properties of bosons are particularly unusual because a macroscopic number of particles can occupy a single quantum state. We describe a computational approach that supplements the usual analytic derivations applicable in the thermodynamic limit. The approach involves directly summing over the quantum states for finite systems and avoids the need for doing difficult integrals. The results display the unusual behavior of quantum gases even for relatively small systems.
Bohmian Mechanics and the Quantum Revolution
Goldstein, Sheldon
1995-01-01
This is a review-essay on ``Speakable and Unspeakable in Quantum Mechanics'' by John Bell and ``The Undivided Universe: An Ontological Interpretation of Quantum Mechanics'' by David Bohm and Basil Hiley. The views of these authors concerning the character of quantum theory and quantum reality---and, in particular, their approaches to the issues of nonlocality, the possibility of hidden variables, and the nature of and desiderata for a satisfactory scientific explanation of quantum phenomena--...
Babaei, Hassan; Mostafazadeh, Ali
2017-08-01
A first-quantized free photon is a complex massless vector field A =(Aμ ) whose field strength satisfies Maxwell's equations in vacuum. We construct the Hilbert space H of the photon by endowing the vector space of the fields A in the temporal-Coulomb gauge with a positive-definite and relativistically invariant inner product. We give an explicit expression for this inner product, identify the Hamiltonian for the photon with the generator of time translations in H , determine the operators representing the momentum and the helicity of the photon, and introduce a chirality operator whose eigenfunctions correspond to fields having a definite sign of energy. We also construct a position operator for the photon whose components commute with each other and with the chirality and helicity operators. This allows for the construction of the localized states of the photon with a definite sign of energy and helicity. We derive an explicit formula for the latter and compute the corresponding electric and magnetic fields. These turn out to diverge not just at the point where the photon is localized but on a plane containing this point. We identify the axis normal to this plane with an associated symmetry axis and show that each choice of this axis specifies a particular position operator, a corresponding position basis, and a position representation of the quantum mechanics of a photon. In particular, we examine the position wave functions determined by such a position basis, elucidate their relationship with the Riemann-Silberstein and Landau-Peierls wave functions, and give an explicit formula for the probability density of the spatial localization of the photon.
Quantum mechanics and the psyche
Galli Carminati, G.; Martin, F.
2008-07-01
In this paper we apply the last developments of the theory of measurement in quantum mechanics to the phenomenon of consciousness and especially to the awareness of unconscious components. Various models of measurement in quantum mechanics can be distinguished by the fact that there is, or there is not, a collapse of the wave function. The passive aspect of consciousness seems to agree better with models in which there is no collapse of the wave function, whereas in the active aspect of consciousness—i.e., that which goes together with an act or a choice—there seems to be a collapse of the wave function. As an example of the second possibility we study in detail the photon delayed-choice experiment and its consequences for subjective or psychological time. We apply this as an attempt to explain synchronicity phenomena. As a model of application of the awareness of unconscious components we study the mourning process. We apply also the quantum paradigm to the phenomenon of correlation at a distance between minds, as well as to group correlations that appear during group therapies or group training. Quantum entanglement leads to the formation of group unconscious or collective unconscious. Finally we propose to test the existence of such correlations during sessions of group training.
Quantum mechanics of black holes.
Witten, Edward
2012-08-03
The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.
Spinning Particles in Quantum Mechanics and Quantum Field Theory
Corradini, Olindo
2015-01-01
The first part of the lectures, given by O. Corradini, covers introductory material on quantum-mechanical Feynman path integrals, which are here derived and applied to several particle models. We start considering the nonrelativistic bosonic particle, for which we compute the exact path integrals for the case of the free particle and for the harmonic oscillator, and then describe perturbation theory for an arbitrary potential. We then move to relativistic particles, both bosonic and fermionic (spinning) particles. We first investigate them from the classical view-point, studying the symmetries of their actions, then consider their canonical quantization and path integrals, and underline the role these models have in the study of space-time quantum field theories (QFT), by introducing the "worldline" path integral representation of propagators and effective actions. We also describe a special class of spinning particles that constitute a first-quantized approach to higher-spin fields. Since the fifties the qua...
Crum's Theorem for `Discrete' Quantum Mechanics
Odake, Satoru; Sasaki, Ryu
2009-01-01
In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its counterpart in `discrete' quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schr\\"odinger equation is a difference equation.
Hyper-parallel photonic quantum computation with coupled quantum dots
Ren, Bao-Cang; Deng, Fu-Guo
2014-01-01
It is well known that a parallel quantum computer is more powerful than a classical one. So far, there are some important works about the construction of universal quantum logic gates, the key elements in quantum computation. However, they are focused on operating on one degree of freedom (DOF) of quantum systems. Here, we investigate the possibility of achieving scalable hyper-parallel quantum computation based on two DOFs of photon systems. We construct a deterministic hyper-controlled-not (hyper-CNOT) gate operating on both the spatial-mode and the polarization DOFs of a two-photon system simultaneously, by exploiting the giant optical circular birefringence induced by quantum-dot spins in double-sided optical microcavities as a result of cavity quantum electrodynamics (QED). This hyper-CNOT gate is implemented by manipulating the four qubits in the two DOFs of a two-photon system without auxiliary spatial modes or polarization modes. It reduces the operation time and the resources consumed in quantum information processing, and it is more robust against the photonic dissipation noise, compared with the integration of several cascaded CNOT gates in one DOF. PMID:24721781
Conceptual aspects of geometric quantum computation
Sjöqvist, Erik; Azimi Mousolou, Vahid; Canali, Carlo M.
2016-10-01
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic evolution, controlled by slowly changing parameters, this form of quantum computation can as well be realized at high speed by using nonadiabatic schemes. Recent advances in quantum gate technology have allowed for experimental demonstrations of different types of geometric gates in adiabatic and nonadiabatic evolution. Here, we address some conceptual issues that arise in the realizations of geometric gates. We examine the appearance of dynamical phases in quantum evolution and point out that not all dynamical phases need to be compensated for in geometric quantum computation. We delineate the relation between Abelian and non-Abelian geometric gates and find an explicit physical example where the two types of gates coincide. We identify differences and similarities between adiabatic and nonadiabatic realizations of quantum computation based on non-Abelian geometric phases.
Geometrical Phases in Quantum Mechanics
Christian, Joy Julius
In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a
Effective pure states for bulk quantum computation
Energy Technology Data Exchange (ETDEWEB)
Knill, E.; Chuang, I.; Laflamme, R.
1997-11-01
In bulk quantum computation one can manipulate a large number of indistinguishable quantum computers by parallel unitary operations and measure expectation values of certain observables with limited sensitivity. The initial state of each computer in the ensemble is known but not pure. Methods for obtaining effective pure input states by a series of manipulations have been described by Gershenfeld and Chuang (logical labeling) and Corey et al. (spatial averaging) for the case of quantum computation with nuclear magnetic resonance. We give a different technique called temporal averaging. This method is based on classical randomization, requires no ancilla qubits and can be implemented in nuclear magnetic resonance without using gradient fields. We introduce several temporal averaging algorithms suitable for both high temperature and low temperature bulk quantum computing and analyze the signal to noise behavior of each.
Quantum Computing with Electron Spins in Quantum Dots
Vandersypen, L M K; Van Beveren, L H W; Elzerman, J M; Greidanus, J S; De Franceschi, S; Kouwenhoven, Leo P
2002-01-01
We present a set of concrete and realistic ideas for the implementation of a small-scale quantum computer using electron spins in lateral GaAs/AlGaAs quantum dots. Initialization is based on leads in the quantum Hall regime with tunable spin-polarization. Read-out hinges on spin-to-charge conversion via spin-selective tunneling to or from the leads, followed by measurement of the number of electron charges on the dot via a charge detector. Single-qubit manipulation relies on a microfabricated wire located close to the quantum dot, and two-qubit interactions are controlled via the tunnel barrier connecting the respective quantum dots. Based on these ideas, we have begun a series of experiments in order to demonstrate unitary control and to measure the coherence time of individual electron spins in quantum dots.
Fault tolerant quantum computation with nondeterministic gates.
Li, Ying; Barrett, Sean D; Stace, Thomas M; Benjamin, Simon C
2010-12-17
In certain approaches to quantum computing the operations between qubits are nondeterministic and likely to fail. For example, a distributed quantum processor would achieve scalability by networking together many small components; operations between components should be assumed to be failure prone. In the ultimate limit of this architecture each component contains only one qubit. Here we derive thresholds for fault-tolerant quantum computation under this extreme paradigm. We find that computation is supported for remarkably high failure rates (exceeding 90%) providing that failures are heralded; meanwhile the rate of unknown errors should not exceed 2 in 10(4) operations.
Measurement Based Quantum Computation on Fractal Lattices
Directory of Open Access Journals (Sweden)
Michal Hajdušek
2010-06-01
Full Text Available In this article we extend on work which establishes an analology between one-way quantum computation and thermodynamics to see how the former can be performed on fractal lattices. We find fractals lattices of arbitrary dimension greater than one which do all act as good resources for one-way quantum computation, and sets of fractal lattices with dimension greater than one all of which do not. The difference is put down to other topological factors such as ramification and connectivity. This work adds confidence to the analogy and highlights new features to what we require for universal resources for one-way quantum computation.
Quantum Computation explained to my Mother
Arrighi, P
2003-01-01
There are many falsely intuitive introductions to quantum theory and quantum computation in a handwave. There are also numerous documents which teach those subjects in a mathematically sound manner. To my knowledge this paper is the shortest of the latter category. The aim is to deliver a short yet rigorous and self-contained introduction to Quantum Computation, whilst assuming the reader has no prior knowledge of anything but the fundamental operations on real numbers. Successively I introduce complex matrices; the postulates of quantum theory and the simplest quantum algorithm. The document originates from a fifty minutes talk addressed to a non-specialist audience, in which I sought to take the shortest mathematical path that proves a quantum algorithm right.
Supersymmetric quantum mechanics with reflections
Energy Technology Data Exchange (ETDEWEB)
Post, Sarah; Vinet, Luc [Centre de Recherches Mathematiques, Universite de Montreal, Montreal CP6128 (QC) H3C 3J7 (Canada); Zhedanov, Alexei, E-mail: post@crm.umontreal.ca, E-mail: luc.vinet@umontreal.ca, E-mail: zhedanov@fti.dn.ua [Donetsk Institute for Physics and Technology, Donetsk 83114 (Ukraine)
2011-10-28
We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q {yields} -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wavefunctions of extended Scarf I potentials with different parameters are presented. (paper)
Fun with supersymmetric quantum mechanics
Freedman, B.; Cooper, F.
1984-04-01
The Hamiltonian and path integral approaches to supersymmetric quantum mechanics were reviewed. The related path integrals for the Witten Index and for stochastic processes were discussed and shown to be indications for supersymmetry breakdown. A system where in the superpotential W(x) has assymetrical values at + or - infinity was considered. Nonperturbative strategies for studying supersymmetry breakdown were described. These strategies are based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed.
On the Relation Between Quantum Computational Speedup and Retrocausality
Directory of Open Access Journals (Sweden)
Giuseppe Castagnoli
2016-01-01
Full Text Available We investigate the reason for the quantum speedup (quantum algorithms require fewer computation steps than their classical counterparts. We extend the representation of the quantum algorithm to the process of setting the problem, namely choosing the function computed by the black box. The initial measurement selects a setting at random, Bob (the problem setter unitarily changes it into the desired one. With reference to the observer dependent quantum states of relational quantum mechanics, this representation is with respect to Bob and any external observer, it cannot be with respect to Alice (the problem solver. It would tell her the function computed by the black box, which to her should be hidden. To Alice, the projection of the quantum state due to the initial measurement is retarded at the end of her problem solving action, so that the algorithm input state remains one of complete ignorance of the setting. By black box computations, she unitarily sends it into the output state that, for each possible setting, encodes the corresponding solution, acquired by the final measurement. Mathematically, we can ascribe to the final measurement the selection of any fraction R of the random outcome of the initial measurement. This projects the input state to Alice on one of lower entropy where she knows the corresponding fraction of the problem setting. Given the appropriate value of R, the quantum algorithm is a sum over classical histories in each of which Alice, knowing in advance one of the R-th parts of the setting, performs the black box computations still required to identify the solution. Given a quantum algorithm, this retrocausality model provides the value of R that explains its speed up; in the major quantum algorithms, R is 1/2 or slightly above it. Conversely, given the problem, R=1/2 always yields the order of magnitude of the number of black box computations required to solve it in an optimal quantum way.Quanta 2016; 5: 34–52.
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.
Materials Frontiers to Empower Quantum Computing
Energy Technology Data Exchange (ETDEWEB)
Taylor, Antoinette Jane [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Sarrao, John Louis [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Richardson, Christopher [Laboratory for Physical Sciences, College Park, MD (United States)
2015-06-11
This is an exciting time at the nexus of quantum computing and materials research. The materials frontiers described in this report represent a significant advance in electronic materials and our understanding of the interactions between the local material and a manufactured quantum state. Simultaneously, directed efforts to solve materials issues related to quantum computing provide an opportunity to control and probe the fundamental arrangement of matter that will impact all electronic materials. An opportunity exists to extend our understanding of materials functionality from electronic-grade to quantum-grade by achieving a predictive understanding of noise and decoherence in qubits and their origins in materials defects and environmental coupling. Realizing this vision systematically and predictively will be transformative for quantum computing and will represent a qualitative step forward in materials prediction and control.
The formalisms of quantum mechanics an introduction
David, Francois
2015-01-01
These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The “standard” formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilistic interpretation given by the Born rule) on one hand, and the path integral and functional integral representations of probabilities amplitudes on the other, are the standard tools used in most applications of quantum theory in physics and chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension and justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics and the “quantum logic” approach. Last but not least, some emphasis will also be put on understanding the relation between quantum physics and ...
Towards scalable quantum communication and computation: Novel approaches and realizations
Jiang, Liang
Quantum information science involves exploration of fundamental laws of quantum mechanics for information processing tasks. This thesis presents several new approaches towards scalable quantum information processing. First, we consider a hybrid approach to scalable quantum computation, based on an optically connected network of few-qubit quantum registers. Specifically, we develop a novel scheme for scalable quantum computation that is robust against various imperfections. To justify that nitrogen-vacancy (NV) color centers in diamond can be a promising realization of the few-qubit quantum register, we show how to isolate a few proximal nuclear spins from the rest of the environment and use them for the quantum register. We also demonstrate experimentally that the nuclear spin coherence is only weakly perturbed under optical illumination, which allows us to implement quantum logical operations that use the nuclear spins to assist the repetitive-readout of the electronic spin. Using this technique, we demonstrate more than two-fold improvement in signal-to-noise ratio. Apart from direct application to enhance the sensitivity of the NV-based nano-magnetometer, this experiment represents an important step towards the realization of robust quantum information processors using electronic and nuclear spin qubits. We then study realizations of quantum repeaters for long distance quantum communication. Specifically, we develop an efficient scheme for quantum repeaters based on atomic ensembles. We use dynamic programming to optimize various quantum repeater protocols. In addition, we propose a new protocol of quantum repeater with encoding, which efficiently uses local resources (about 100 qubits) to identify and correct errors, to achieve fast one-way quantum communication over long distances. Finally, we explore quantum systems with topological order. Such systems can exhibit remarkable phenomena such as quasiparticles with anyonic statistics and have been proposed as
Reducing computational complexity of quantum correlations
Chanda, Titas; Das, Tamoghna; Sadhukhan, Debasis; Pal, Amit Kumar; SenDe, Aditi; Sen, Ujjwal
2015-12-01
We address the issue of reducing the resource required to compute information-theoretic quantum correlation measures such as quantum discord and quantum work deficit in two qubits and higher-dimensional systems. We show that determination of the quantum correlation measure is possible even if we utilize a restricted set of local measurements. We find that the determination allows us to obtain a closed form of quantum discord and quantum work deficit for several classes of states, with a low error. We show that the computational error caused by the constraint over the complete set of local measurements reduces fast with an increase in the size of the restricted set, implying usefulness of constrained optimization, especially with the increase of dimensions. We perform quantitative analysis to investigate how the error scales with the system size, taking into account a set of plausible constructions of the constrained set. Carrying out a comparative study, we show that the resource required to optimize quantum work deficit is usually higher than that required for quantum discord. We also demonstrate that minimization of quantum discord and quantum work deficit is easier in the case of two-qubit mixed states of fixed ranks and with positive partial transpose in comparison to the corresponding states having nonpositive partial transpose. Applying the methodology to quantum spin models, we show that the constrained optimization can be used with advantage in analyzing such systems in quantum information-theoretic language. For bound entangled states, we show that the error is significantly low when the measurements correspond to the spin observables along the three Cartesian coordinates, and thereby we obtain expressions of quantum discord and quantum work deficit for these bound entangled states.
Halpern, Arthur M.
2010-01-01
Using readily available computational applications and resources, students can construct a high-level ab initio potential energy surface (PES) for the argon dimer. From this information, they can obtain detailed molecular constants of the dimer, including its dissociation energy, which compare well with experimental determinations. Using both…
Experimental comparison of two quantum computing architectures
Linke, Norbert M.; Maslov, Dmitri; Roetteler, Martin; Debnath, Shantanu; Figgatt, Caroline; Landsman, Kevin A.; Wright, Kenneth; Monroe, Christopher
2017-01-01
We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device (www.research.ibm.com/ibm-q) with limited connectivity, and the other is a fully connected trapped-ion system. Even though the two systems have different native quantum interactions, both can be programed in a way that is blind to the underlying hardware, thus allowing a comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that use more connectivity clearly benefit from a better-connected system of qubits. Although the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that codesigning particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future. PMID:28325879
Experimental comparison of two quantum computing architectures.
Linke, Norbert M; Maslov, Dmitri; Roetteler, Martin; Debnath, Shantanu; Figgatt, Caroline; Landsman, Kevin A; Wright, Kenneth; Monroe, Christopher
2017-03-28
We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device (www. ibm.com/ibm-q) with limited connectivity, and the other is a fully connected trapped-ion system. Even though the two systems have different native quantum interactions, both can be programed in a way that is blind to the underlying hardware, thus allowing a comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that use more connectivity clearly benefit from a better-connected system of qubits. Although the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that codesigning particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future.
Directional coupling for quantum computing and communication.
Nikolopoulos, Georgios M
2008-11-14
We introduce the concept of directional coupling, i.e., the selective transfer of a state between adjacent quantum wires, in the context of quantum computing and communication. Our analysis rests upon a mathematical analogy between a dual-channel directional coupler and a composite spin system.
Scaling ion traps for quantum computing
CSIR Research Space (South Africa)
Uys, H
2010-09-01
Full Text Available The design, fabrication and preliminary testing of a chipscale, multi-zone, surface electrode ion trap is reported. The modular design and fabrication techniques used are anticipated to advance scalability of ion trap quantum computing architectures...
Optimised resource construction for verifiable quantum computation
Kashefi, Elham; Wallden, Petros
2017-04-01
Recent developments have brought the possibility of achieving scalable quantum networks and quantum devices closer. From the computational point of view these emerging technologies become relevant when they are no longer classically simulatable. Hence a pressing challenge is the construction of practical methods to verify the correctness of the outcome produced by universal or non-universal quantum devices. A promising approach that has been extensively explored is the scheme of verification via encryption through blind quantum computation. We present here a new construction that simplifies the required resources for any such verifiable protocol. We obtain an overhead that is linear in the size of the input (computation), while the security parameter remains independent of the size of the computation and can be made exponentially small (with a small extra cost). Furthermore our construction is generic and could be applied to any universal or non-universal scheme with a given underlying graph.
Universality of Black Hole Quantum Computing
Dvali, Gia; Lust, Dieter; Omar, Yasser; Richter, Benedikt
2016-01-01
By analyzing the key properties of black holes from the point of view of quantum information, we derive a model-independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with quantum critical condensates, allowing the use of a common language to describe quantum computing in both systems. We analyze such quantum computing by allowing coupling to external modes, under the condition that the external influence must be soft-enough in order not to offset the basic properties of the system. We derive model-independent bounds on some crucial time-scales, such as the times of gate operation, decoherence, maximal entanglement and total scrambling. We show that for black hole type quantum computers all these time-scales are of the order of the black hole half-life time. Furthermore, we construct explicitly a set of Hamiltonians that generates a universal set of quantum gates for the black hole type computer. We find that the gates work at maximal energy e...
Delayed Commutation in Quantum Computer Networks
García-Escartín, Juan Carlos; Chamorro-Posada, Pedro
2006-09-01
In the same way that classical computer networks connect and enhance the capabilities of classical computers, quantum networks can combine the advantages of quantum information and communication. We propose a nonclassical network element, a delayed commutation switch, that can solve the problem of switching time in packet switching networks. With the help of some local ancillary qubits and superdense codes, we can route a qubit packet after part of it has left the network node.
Delayed commutation in quantum computer networks
Garcia-Escartin, J C; Chamorro-Posada, Pedro; Garcia-Escartin, Juan Carlos
2005-01-01
In the same way that classical computer networks connect and enhance the capabilities of classical computers, quantum networks can combine the advantages of quantum information and communications. We propose a non-classical network element, a delayed commutation switch, that can solve the problem of switching time in packet switching networks. With the help of some local ancillary qubits and superdense codes we can route the information after part of it has left the network node.
Braid group representation on quantum computation
Energy Technology Data Exchange (ETDEWEB)
Aziz, Ryan Kasyfil, E-mail: kasyfilryan@gmail.com [Department of Computational Sciences, Bandung Institute of Technology (Indonesia); Muchtadi-Alamsyah, Intan, E-mail: ntan@math.itb.ac.id [Algebra Research Group, Bandung Institute of Technology (Indonesia)
2015-09-30
There are many studies about topological representation of quantum computation recently. One of diagram representation of quantum computation is by using ZX-Calculus. In this paper we will make a diagrammatical scheme of Dense Coding. We also proved that ZX-Calculus diagram of maximally entangle state satisfies Yang-Baxter Equation and therefore, we can construct a Braid Group representation of set of maximally entangle state.
The Linguistic Interpretation of Quantum Mechanics
Ishikawa, Shiro
2012-01-01
About twenty years ago, we proposed the mathematical formulation of Heisenberg's uncertainty principle, and further, we concluded that Heisenberg's uncertainty principle and EPR-paradox are not contradictory. This is true, however we now think that we should have argued about it under a certain firm interpretation of quantum mechanics. Recently we proposed the linguistic quantum interpretation (called quantum and classical measurement theory), which was characterized as a kind of metaphysical and linguistic turn of the Copenhagen interpretation. This turn from physics to language does not only extend quantum theory to classical systems but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics, in other words, quantum philosophy). In fact, we can consider that traditional philosophies have progressed toward quantum philosophy. In this paper, we first review the linguistic quantum interpretation, and further, clarify the relation between EPR-paradox and Heisenberg's uncertainty...
Dynamic Multiscale Quantum Mechanics/Electromagnetics Simulation Method.
Meng, Lingyi; Yam, ChiYung; Koo, SiuKong; Chen, Quan; Wong, Ngai; Chen, GuanHua
2012-04-10
A newly developed hybrid quantum mechanics and electromagnetics (QM/EM) method [Yam et al. Phys. Chem. Chem. Phys.2011, 13, 14365] is generalized to simulate the real time dynamics. Instead of the electric and magnetic fields, the scalar and vector potentials are used to integrate Maxwell's equations in the time domain. The TDDFT-NEGF-EOM method [Zheng et al. Phys. Rev. B2007, 75, 195127] is employed to simulate the electronic dynamics in the quantum mechanical region. By allowing the penetration of a classical electromagnetic wave into the quantum mechanical region, the electromagnetic wave for the entire simulating region can be determined consistently by solving Maxwell's equations. The transient potential distributions and current density at the interface between quantum mechanical and classical regions are employed as the boundary conditions for the quantum mechanical and electromagnetic simulations, respectively. Charge distribution, current density, and potentials at different temporal steps and spatial scales are integrated seamlessly within a unified computational framework.
Negative entropy and information in quantum mechanics
Cerf, N. J.; Adami, C.
1995-01-01
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon) information theory, quantum (von Neumann) conditional entropies can be negative when considering quantum entangled systems, a fact related to quantum non-separability. The possibility that negative (virtual) information can be carried by entangled particles sug...
Teaching Quantum Mechanics on an Introductory Level.
Muller, Rainer; Wiesner, Hartmut
2002-01-01
Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)
Teaching Quantum Mechanics on an Introductory Level.
Muller, Rainer; Wiesner, Hartmut
2002-01-01
Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)
The quantum mechanics of materials
Cohen, M. L.; Heine, V.; Phillips, J. C.
1982-06-01
The prediction of the properties of materials from fundamental principles, i.e., quantum mechanics, by the use of pseudopotential theory is discussed. Following a review of previous difficulties encountered in the application of quantum theory to complex aggregates of matter, and the failures of early theories to resolve differences corresponding to important phase transitions in solids, the idea first proposed by Herring concerning the energy cancellation of valence electrons and the possibility of neglecting core electron effects is examined as the basis of pseudopotential theory. The application of the electron pseudopotential, representing the scattering strength of one atomic core with respect to a single Fourier component of one valence-electron wave, to the calculation of the scattering of an electron wave in crystalline solids is examined, and the derivation of structural properties from the pseudopotentials is discussed. Recent advances in pseudopotential theory explaining the properties of surface and interface structures, and the total energy of semiconducting materials are indicated.
Hidden scale in quantum mechanics
Giri, Pulak Ranjan
2007-01-01
We show that the intriguing localization of a free particle wave-packet is possible due to a hidden scale present in the system. Self-adjoint extensions (SAE) is responsible for introducing this scale in quantum mechanical models through the nontrivial boundary conditions. We discuss a couple of classically scale invariant free particle systems to illustrate the issue. In this context it has been shown that a free quantum particle moving on a full line may have localized wave-packet around the origin. As a generalization, it has also been shown that particles moving on a portion of a plane or on a portion of a three dimensional space can have unusual localized wave-packet.
Quantum mechanics: Myths and facts
Nikolic, H
2006-01-01
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.
Quantum Mechanics: Myths and Facts
Nikolić, Hrvoje
2007-11-01
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of “myths”, that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.
Deformation of noncommutative quantum mechanics
Jiang, Jian-Jian; Chowdhury, S. Hasibul Hassan
2016-09-01
In this paper, the Lie group GNC α , β , γ , of which the kinematical symmetry group GNC of noncommutative quantum mechanics (NCQM) is a special case due to fixed nonzero α, β, and γ, is three-parameter deformation quantized using the method suggested by Ballesteros and Musso [J. Phys. A: Math. Theor. 46, 195203 (2013)]. A certain family of QUE algebras, corresponding to GNC α , β , γ with two of the deformation parameters approaching zero, is found to be in agreement with the existing results of the literature on quantum Heisenberg group. Finally, we dualize the underlying QUE algebra to obtain an expression for the underlying star-product between smooth functions on GNC α , β , γ .
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.
Geometric algebra and information geometry for quantum computational software
Cafaro, Carlo
2017-03-01
The art of quantum algorithm design is highly nontrivial. Grover's search algorithm constitutes a masterpiece of quantum computational software. In this article, we use methods of geometric algebra (GA) and information geometry (IG) to enhance the algebraic efficiency and the geometrical significance of the digital and analog representations of Grover's algorithm, respectively. Specifically, GA is used to describe the Grover iterate and the discretized iterative procedure that exploits quantum interference to amplify the probability amplitude of the target-state before measuring the query register. The transition from digital to analog descriptions occurs via Stone's theorem which relates the (unitary) Grover iterate to a suitable (Hermitian) Hamiltonian that controls Schrodinger's quantum mechanical evolution of a quantum state towards the target state. Once the discrete-to-continuos transition is completed, IG is used to interpret Grover's iterative procedure as a geodesic path on the manifold of the parametric density operators of pure quantum states constructed from the continuous approximation of the parametric quantum output state in Grover's algorithm. Finally, we discuss the dissipationless nature of quantum computing, recover the quadratic speedup relation, and identify the superfluity of the Walsh-Hadamard operation from an IG perspective with emphasis on statistical mechanical considerations.
Private quantum computation: an introduction to blind quantum computing and related protocols
Fitzsimons, Joseph F.
2017-06-01
Quantum technologies hold the promise of not only faster algorithmic processing of data, via quantum computation, but also of more secure communications, in the form of quantum cryptography. In recent years, a number of protocols have emerged which seek to marry these concepts for the purpose of securing computation rather than communication. These protocols address the task of securely delegating quantum computation to an untrusted device while maintaining the privacy, and in some instances the integrity, of the computation. We present a review of the progress to date in this emerging area.
Superadiabatic holonomic quantum computation in cavity QED
Liu, Bao-Jie; Huang, Zhen-Hua; Xue, Zheng-Yuan; Zhang, Xin-Ding
2017-06-01
Adiabatic quantum control is a powerful tool for quantum engineering and a key component in some quantum computation models, where accurate control over the timing of the involved pulses is not needed. However, the adiabatic condition requires that the process be very slow and thus limits its application in quantum computation, where quantum gates are preferred to be fast due to the limited coherent times of the quantum systems. Here, we propose a feasible scheme to implement universal holonomic quantum computation based on non-Abelian geometric phases with superadiabatic quantum control, where the adiabatic manipulation is sped up while retaining its robustness against errors in the timing control. Consolidating the advantages of both strategies, our proposal is thus both robust and fast. The cavity QED system is adopted as a typical example to illustrate the merits where the proposed scheme can be realized in a tripod configuration by appropriately controlling the pulse shapes and their relative strength. To demonstrate the distinct performance of our proposal, we also compare our scheme with the conventional adiabatic strategy.
Natural and artificial atoms for quantum computation
Energy Technology Data Exchange (ETDEWEB)
Buluta, Iulia; Ashhab, Sahel; Nori, Franco, E-mail: fnori@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama, 351-0198 (Japan)
2011-10-15
Remarkable progress towards realizing quantum computation has been achieved using natural and artificial atoms as qubits. This paper presents a brief overview of the current status of different types of qubits. On the one hand, natural atoms (such as neutral atoms and ions) have long coherence times, and could be stored in large arrays, providing ideal 'quantum memories'. On the other hand, artificial atoms (such as superconducting circuits or semiconductor quantum dots) have the advantage of custom-designed features and could be used as 'quantum processing units'. Natural and artificial atoms can be coupled with each other and can also be interfaced with photons for long-distance communications. Hybrid devices made of natural/artificial atoms and photons may provide the next-generation design for quantum computers.
Quantum Fourier transform in computational basis
Zhou, S. S.; Loke, T.; Izaac, J. A.; Wang, J. B.
2017-03-01
The quantum Fourier transform, with exponential speed-up compared to the classical fast Fourier transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, Shor's factoring algorithm). However, situations arise where it is not sufficient to encode the Fourier coefficients within the quantum amplitudes, for example in the implementation of control operations that depend on Fourier coefficients. In this paper, we detail a new quantum scheme to encode Fourier coefficients in the computational basis, with fidelity 1 - δ and digit accuracy ɛ for each Fourier coefficient. Its time complexity depends polynomially on log (N), where N is the problem size, and linearly on 1/δ and 1/ɛ . We also discuss an application of potential practical importance, namely the simulation of circulant Hamiltonians.
Cat-qubits for quantum computation
Mirrahimi, Mazyar
2016-08-01
The development of quantum Josephson circuits has created a strong expectation for reliable processing of quantum information. While this progress has already led to various proof-of-principle experiments on small-scale quantum systems, a major scaling step is required towards many-qubit protocols. Fault-tolerant computation with protected logical qubits usually comes at the expense of a significant overhead in the hardware. Each of the involved physical qubits still needs to satisfy the best achieved properties (coherence times, coupling strengths and tunability). Here, and in the aim of addressing alternative approaches to deal with these obstacles, I overview a series of recent theoretical proposals, and the experimental developments following these proposals, to enable a hardware-efficient paradigm for quantum memory protection and universal quantum computation. xml:lang="fr"
A quantum mechanical model of "dark matter"
Belokurov, V V
2014-01-01
The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.
Quantum Jacobi fields in Hamiltonian mechanics
Giachetta, G; Sardanashvily, G
2000-01-01
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.
Energy Technology Data Exchange (ETDEWEB)
Dong Cunku [Department of Chemistry, Harbin Institute of Technology, Harbin 150090 (China); Li Xin, E-mail: lixin@hit.edu.cn [Department of Chemistry, Harbin Institute of Technology, Harbin 150090 (China); Guo Zechong [School of Municipal Environmental Engineering, Harbin Institute of Technology, Harbin 150090 (China); Qi Jingyao, E-mail: jyq@hit.edu.cn [School of Municipal Environmental Engineering, Harbin Institute of Technology, Harbin 150090 (China)
2009-08-04
A new rational approach for the preparation of molecularly imprinted polymer (MIP) based on the combination of molecular dynamics (MD) simulations and quantum mechanics (QM) calculations is described in this work. Before performing molecular modeling, a virtual library of functional monomers was created containing forty frequently used monomers. The MD simulations were first conducted to screen the top three monomers from virtual library in each porogen-acetonitrile, chloroform and carbon tetrachloride. QM simulations were then performed with an aim to select the optimum monomer and progen solvent in which the QM simulations were carried out; the monomers giving the highest binding energies were chosen as the candidate to prepare MIP in its corresponding solvent. The acetochlor, a widely used herbicide, was chosen as the target analyte. According to the theoretical calculation results, the MIP with acetochlor as template was prepared by emulsion polymerization method using N,N-methylene bisacrylamide (MBAAM) as functional monomer and divinylbenzene (DVB) as cross-linker in chloroform. The synthesized MIP was then tested by equilibrium-adsorption method, and the MIP demonstrated high removal efficiency to the acetochlor. Mulliken charge distribution and {sup 1}H NMR spectroscopy of the synthesized MIP provided insight on the nature of recognition during the imprinting process probing the governing interactions for selective binding site formation at a molecular level. We think the computer simulation method first proposed in this paper is a novel and reliable method for the design and synthesis of MIP.
Dubnikova, Faina; Tamburu, Carmen; Lifshitz, Assa
2016-09-29
The isomerization of o-quinolyl ↔ o-isoquinolyl radicals and their thermal decomposition were studied by quantum chemical methods, where potential energy surfaces of the reaction channels and their kinetics rate parameters were determined. A detailed kinetics scheme containing 40 elementary steps was constructed. Computer simulations were carried out to determine the isomerization mechanism and the distribution of reaction products in the decomposition. The calculated mole percent of the stable products was compared to the experimental values that were obtained in this laboratory in the past, using the single pulse shock tube. The agreement between the experimental and the calculated mole percents was very good. A map of the figures containing the mole percent's of eight stable products of the decomposition plotted vs T are presented. The fast isomerization of o-quinolyl → o-isoquinolyl radicals via the intermediate indene imine radical and the attainment of fast equilibrium between these two radicals is the reason for the identical product distribution regardless whether the reactant radical is o-quinolyl or o-isoquinolyl. Three of the main decomposition products of o-quinolyl radical, are those containing the benzene ring, namely, phenyl, benzonitrile, and phenylacetylene radicals. They undergo further decomposition mainly at high temperatures via two types of reactions: (1) Opening of the benzene ring in the radicals, followed by splitting into fragments. (2) Dissociative attachment of benzonitrile and phenyl acetylene by hydrogen atoms to form hydrogen cyanide and acetylene.
Robust dynamical decoupling for quantum computing and quantum memory.
Souza, Alexandre M; Alvarez, Gonzalo A; Suter, Dieter
2011-06-17
Dynamical decoupling (DD) is a popular technique for protecting qubits from the environment. However, unless special care is taken, experimental errors in the control pulses used in this technique can destroy the quantum information instead of preserving it. Here, we investigate techniques for making DD sequences robust against different types of experimental errors while retaining good decoupling efficiency in a fluctuating environment. We present experimental data from solid-state nuclear spin qubits and introduce a new DD sequence that is suitable for quantum computing and quantum memory.
Entropy, Topological Theories and Emergent Quantum Mechanics
Directory of Open Access Journals (Sweden)
D. Cabrera
2017-02-01
Full Text Available The classical thermostatics of equilibrium processes is shown to possess a quantum mechanical dual theory with a ﬁnite dimensional Hilbert space of quantum states. Speciﬁcally, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological ﬁeld theory is also discussed in the context of the approach of the emergence of quantum theory, where the concept of entropy plays a key role.
Quantum algorithms for computational nuclear physics
Directory of Open Access Journals (Sweden)
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.
Fun with supersymmetric quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Freedman, B.; Cooper, F.
1984-04-01
One reason for studying supersymmetric quantum mechanics is that there are a class of superpotentials W(x) which behave at large x as x/sup ..cap alpha../ for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpotentials to test various ideas about how to see if supersymmetry is broken in an arbitrary model. Recently, Witten proposed a topological invariant, the Witten index ..delta.. which counts the number of bosons minus the number of fermions having ground state energy zero. Since if supersymmetry is broken, the ground state energy cannot be zero, one expects if ..delta.. is not zero, SUSY is preserved and the theory is not a good candidate for a realistic model. In this study we evaluate ..delta.. for several examples, and show some unexpected peculiarities of the Witten index for certain choice of superpotentials W(x). We also discuss two other nonperturbative methods of studying supersymmetry breakdown. One involves relating supersymmetric quantum mechanics to a stochastic classical problem and the other involves considering a discrete (but not supersymmetric) version of the theory and studying its behavior as one removes the lattice cuttoff. In this survey we review the Hamiltonian and path integral approaches to supersymmetric quantum mechanics. We then discuss the related path integrals for the Witten Index and for stochastic processes and show how they are indications for supersymmetry breakdown. We then discuss a system where the superpotential W(x) has assymetrical values at +-infinity. We finally discuss nonperturbative strategies for studying supersymmetry breakdown based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed. 17 references.
Fu, Chien-wei; Lin, Thy-Hou
2017-01-01
As an important enzyme in Phase I drug metabolism, the flavin-containing monooxygenase (FMO) also metabolizes some xenobiotics with soft nucleophiles. The site of metabolism (SOM) on a molecule is the site where the metabolic reaction is exerted by an enzyme. Accurate prediction of SOMs on drug molecules will assist the search for drug leads during the optimization process. Here, some quantum mechanics features such as the condensed Fukui function and attributes from circular fingerprints (called Molprint2D) are computed and classified using the support vector machine (SVM) for predicting some potential SOMs on a series of drugs that can be metabolized by FMO enzymes. The condensed Fukui function fA− representing the nucleophilicity of central atom A and the attributes from circular fingerprints accounting the influence of neighbors on the central atom. The total number of FMO substrates and non-substrates collected in the study is 85 and they are equally divided into the training and test sets with each carrying roughly the same number of potential SOMs. However, only N-oxidation and S-oxidation features were considered in the prediction since the available C-oxidation data was scarce. In the training process, the LibSVM package of WEKA package and the option of 10-fold cross validation are employed. The prediction performance on the test set evaluated by accuracy, Matthews correlation coefficient and area under ROC curve computed are 0.829, 0.659, and 0.877 respectively. This work reveals that the SVM model built can accurately predict the potential SOMs for drug molecules that are metabolizable by the FMO enzymes. PMID:28072829
Correspondence Truth and Quantum Mechanics
Karakostas, Vassilios
2015-01-01
The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure of the theory allows truth-value assignment in conformity with the traditional conception of a correspondence theory of truth. Every proposition in classical mechanics is assigned a definite truth value, either 'true' or 'false', describing what is actually the case at a certain moment of time. Truth-value assignment in quantum mechanics, however, differs; it is known, by means of a variety of 'no go' theorems, that it is not possible to assign definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. In this respect, the Bub-Clifton 'uniqueness theorem' is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state...
Transfer of Learning in Quantum Mechanics
Singh, Chandralekha
2016-01-01
We investigate the difficulties that undergraduate students in quantum mechanics courses have in transferring learning from previous courses or within the same course from one context to another by administering written tests and conducting individual interviews. Quantum mechanics is abstract and its paradigm is very different from the classical one. A good grasp of the principles of quantum mechanics requires creating and organizing a knowledge structure consistent with the quantum postulates. Previously learned concepts such as the principle of superposition and probability can be useful in quantum mechanics if students are given opportunity to build associations between new and prior knowledge. We also discuss the need for better alignment between quantum mechanics and modern physics courses taken previously because semi-classical models can impede internalization of the quantum paradigm in more advanced courses.
Quantum localization of Classical Mechanics
Batalin, Igor A
2016-01-01
Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.
Quantum localization of classical mechanics
Batalin, Igor A.; Lavrov, Peter M.
2016-07-01
Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.
Quantum mechanics in phase space
DEFF Research Database (Denmark)
Hansen, Frank
1984-01-01
A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered....... Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations...
Universality of black hole quantum computing
Energy Technology Data Exchange (ETDEWEB)
Dvali, Gia [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Max-Planck-Institut fuer Physik, Muenchen (Germany); New York Univ., NY (United States). Center for Cosmology and Particle Physics; Gomez, Cesar [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM-CSIC; Luest, Dieter [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Max-Planck-Institut fuer Physik, Muenchen (Germany); Omar, Yasser [Instituto de Telecomunicacoes (Portugal). Physics of Information and Quantum Technologies Group; Lisboa Univ. (Portugal). Inst. Superior Tecnico; Richter, Benedikt [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Instituto de Telecomunicacoes (Portugal). Physics of Information and Quantum Technologies Group; Lisboa Univ. (Portugal). Inst. Superior Tecnico
2017-01-15
By analyzing the key properties of black holes from the point of view of quantum information, we derive a model-independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with quantum critical condensates, allowing the use of a common language to describe quantum computing in both systems. We analyze such quantum computing by allowing coupling to external modes, under the condition that the external influence must be soft-enough in order not to offset the basic properties of the system. We derive model-independent bounds on some crucial time-scales, such as the times of gate operation, decoherence, maximal entanglement and total scrambling. We show that for black hole type quantum computers all these time-scales are of the order of the black hole half-life time. Furthermore, we construct explicitly a set of Hamiltonians that generates a universal set of quantum gates for the black hole type computer. We find that the gates work at maximal energy efficiency. Furthermore, we establish a fundamental bound on the complexity of quantum circuits encoded on these systems, and characterize the unitary operations that are implementable. It becomes apparent that the computational power is very limited due to the fact that the black hole life-time is of the same order of the gate operation time. As a consequence, it is impossible to retrieve its information, within the life-time of a black hole, by externally coupling to the black hole qubits. However, we show that, in principle, coupling to some of the internal degrees of freedom allows acquiring knowledge about the micro-state. Still, due to the trivial complexity of operations that can be performed, there is no time advantage over the collection of Hawking radiation and subsequent decoding. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Compressed quantum computation using a remote five-qubit quantum computer
Hebenstreit, M.; Alsina, D.; Latorre, J. I.; Kraus, B.
2017-05-01
The notion of compressed quantum computation is employed to simulate the Ising interaction of a one-dimensional chain consisting of n qubits using the universal IBM cloud quantum computer running on log2(n ) qubits. The external field parameter that controls the quantum phase transition of this model translates into particular settings of the quantum gates that generate the circuit. We measure the magnetization, which displays the quantum phase transition, on a two-qubit system, which simulates a four-qubit Ising chain, and show its agreement with the theoretical prediction within a certain error. We also discuss the relevant point of how to assess errors when using a cloud quantum computer with a limited amount of runs. As a solution, we propose to use validating circuits, that is, to run independent controlled quantum circuits of similar complexity to the circuit of interest.
Counting Trees in Supersymmetric Quantum Mechanics
Cordova, Clay
2015-01-01
We study the supersymmetric ground states of the Kronecker model of quiver quantum mechanics. This is the simplest quiver with two gauge groups and bifundamental matter fields, and appears universally in four-dimensional N=2 systems. The ground state degeneracy may be written as a multi-dimensional contour integral, and the enumeration of poles can be simply phrased as counting bipartite trees. We solve this combinatorics problem, thereby obtaining exact formulas for the degeneracies of an infinite class of models. We also develop an algorithm to compute the angular momentum of the ground states, and present explicit expressions for the refined indices of theories where one rank is small.
Pointlessness and dangerousness of the postulates of quantum mechanics
Moret-Bailly, J
2001-01-01
The formalism of quantum mechanics produces spectacular results, but its rules, its parameters are empirical, either deduced from classical physics, or from experimental results rather than from the postulates. Thus, quantum mechanics is purely phenomenological; for instance, the computation of the eigenvalues of the energy is generally a simple interpolation in the discrete space of the quantum numbers. The attempts to show that quantum electrodynamics is more precise than classical electrodynamics are based on wrong computations. The lack of paradoxes in the classical theory, the appearance of classical, true interpretations of the wave-particle duality justify the criticism of Ehrenfest and Einstein. The obscurity of the quantum concepts leads to wrong conclusions that handicap the development of physics. Just as building a laser was considered absurd before the first maser worked, the concept of photon leads to deny a type of coherent Raman scattering necessary to understand some redshifts of spectra in a...
Quantum mechanics for applied physics and engineering
Fromhold, Albert T
2011-01-01
This excellent text, directed to upper-level undergraduates and graduate students in engineering and applied physics, introduces the fundamentals of quantum mechanics, emphasizing those aspects of quantum mechanics and quantum statistics essential to an understanding of solid-state theory. A heavy background in mathematics and physics is not required beyond basic courses in calculus, differential equations, and calculus-based elementary physics.The first three chapters introduce quantum mechanics (using the Schrödinger equations), quantum statistics, and the free-electron theory of metals. Ch
A Quantum Space Behind Simple Quantum Mechanics
Chew, Chuan Sheng; Payne, Jason
2016-01-01
In physics, we are supposed to learn from experiments what constitutes a good/correct theoretical/mathematical model of any physical concept, the physical space should not be an exception. The best picture of the physical space, in Newtonian physics, is given by the configuration space of a free particle. The space, as well as the phase space, can be constructed as a representation space of the relativity symmetry. Starting with the corresponding quantum symmetry, we illustrate the construction of a quantum space along the lines of the quantum phase space and demonstrate the retrieval of the classical picture as an approximation through the contraction of the (relativity) symmetry and the representations of it. The result suggests a picture of the physical space beyond that of a finite dimensional manifold.
Computer studies of multiple-quantum spin dynamics
Energy Technology Data Exchange (ETDEWEB)
Murdoch, J.B.
1982-11-01
The excitation and detection of multiple-quantum (MQ) transitions in Fourier transform NMR spectroscopy is an interesting problem in the quantum mechanical dynamics of spin systems as well as an important new technique for investigation of molecular structure. In particular, multiple-quantum spectroscopy can be used to simplify overly complex spectra or to separate the various interactions between a nucleus and its environment. The emphasis of this work is on computer simulation of spin-system evolution to better relate theory and experiment.
Computational electronics semiclassical and quantum device modeling and simulation
Vasileska, Dragica; Klimeck, Gerhard
2010-01-01
Starting with the simplest semiclassical approaches and ending with the description of complex fully quantum-mechanical methods for quantum transport analysis of state-of-the-art devices, Computational Electronics: Semiclassical and Quantum Device Modeling and Simulation provides a comprehensive overview of the essential techniques and methods for effectively analyzing transport in semiconductor devices. With the transistor reaching its limits and new device designs and paradigms of operation being explored, this timely resource delivers the simulation methods needed to properly model state-of
Efficient quantum circuits for one-way quantum computing.
Tanamoto, Tetsufumi; Liu, Yu-Xi; Hu, Xuedong; Nori, Franco
2009-03-13
While Ising-type interactions are ideal for implementing controlled phase flip gates in one-way quantum computing, natural interactions between solid-state qubits are most often described by either the XY or the Heisenberg models. We show an efficient way of generating cluster states directly using either the imaginary SWAP (iSWAP) gate for the XY model, or the sqrt[SWAP] gate for the Heisenberg model. Our approach thus makes one-way quantum computing more feasible for solid-state devices.
The emerging quantum the physics behind quantum mechanics
Pena, Luis de la; Valdes-Hernandez, Andrea
2014-01-01
This monograph presents the latest findings from a long-term research project intended to identify the physics behind Quantum Mechanics. A fundamental theory for quantum mechanics is constructed from first physical principles, revealing quantization as an emergent phenomenon arising from a deeper stochastic process. As such, it offers the vibrant community working on the foundations of quantum mechanics an alternative contribution open to discussion. The book starts with a critical summary of the main conceptual problems that still beset quantum mechanics. The basic consideration is then introduced that any material system is an open system in permanent contact with the random zero-point radiation field, with which it may reach a state of equilibrium. Working from this basis, a comprehensive and self-consistent theoretical framework is then developed. The pillars of the quantum-mechanical formalism are derived, as well as the radiative corrections of nonrelativistic QED, while revealing the underlying physi...
Quantum mechanics in complex systems
Hoehn, Ross Douglas
This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown
Potentiality, Actuality, and Quantum Mechanics
Directory of Open Access Journals (Sweden)
Boris Koznjak
2007-12-01
Full Text Available In this paper a possible interpretative value of Aristotle’s fundamental ontological doctrine of potentiality (δύναµις and actuality (ἐνέργεια is considered in the context of operationally undoubtedly the most successful but interpretatively still controversial theory of modern physics – quantum mechanics – especially regarding understanding the nature of the world, the phenomena of which it describes and predicts so successfully. In particular, beings of the atomic world are interpreted as real potential beings (δυνάµει ὄντα actualized by the measurement process in appropriate experimental arrangement, and the problem of actual beings (ἐνεργείᾳ ὄντα of the atomic world (better known as the measurement problem in quantum mechanics is considered in the context of Aristotle’s threefold requirement for the priority of actuality over potentiality – in time (χρόνος, definition or knowledge (λόγος, and substantiality (οὐσία.
Bridging classical and quantum mechanics
Haddad, D.; Seifert, F.; Chao, L. S.; Li, S.; Newell, D. B.; Pratt, J. R.; Williams, C.; Schlamminger, S.
2016-10-01
Using a watt balance and a frequency comb, a mass-energy equivalence is derived. The watt balance compares mechanical power measured in terms of the meter, the second, and the kilogram to electrical power measured in terms of the volt and the ohm. A direct link between mechanical action and the Planck constant is established by the practical realization of the electrical units derived from the Josephson and the quantum Hall effects. By using frequency combs to measure velocities and acceleration of gravity, the unit of mass can be realized from a set of three defining constants: the Planck constant h, the speed of light c, and the hyperfine splitting frequency of 133Cs.
Applications of Computer Simulations and Statistical Mechanics in Surface Electrochemistry
Rikvold, P A; Juwono, T; Robb, D T; Novotny, M A; 10.1007/978-0-387-49586-6_4
2009-01-01
We present a brief survey of methods that utilize computer simulations and quantum and statistical mechanics in the analysis of electrochemical systems. The methods, Molecular Dynamics and Monte Carlo simulations and quantum-mechanical density-functional theory, are illustrated with examples from simulations of lithium-battery charging and electrochemical adsorption of bromine on single-crystal silver electrodes.
Kochen-Specker Theorem as a Precondition for Quantum Computing
Nagata, Koji; Nakamura, Tadao
2016-12-01
We study the relation between the Kochen-Specker theorem (the KS theorem) and quantum computing. The KS theorem rules out a realistic theory of the KS type. We consider the realistic theory of the KS type that the results of measurements are either +1 or -1. We discuss an inconsistency between the realistic theory of the KS type and the controllability of quantum computing. We have to give up the controllability if we accept the realistic theory of the KS type. We discuss an inconsistency between the realistic theory of the KS type and the observability of quantum computing. We discuss the inconsistency by using the double-slit experiment as the most basic experiment in quantum mechanics. This experiment can be for an easy detector to a Pauli observable. We cannot accept the realistic theory of the KS type to simulate the double-slit experiment in a significant specific case. The realistic theory of the KS type can not depicture quantum detector. In short, we have to give up both the observability and the controllability if we accept the realistic theory of the KS type. Therefore, the KS theorem is a precondition for quantum computing, i.e., the realistic theory of the KS type should be ruled out.
Kochen-Specker Theorem as a Precondition for Quantum Computing
Nagata, Koji; Nakamura, Tadao
2016-08-01
We study the relation between the Kochen-Specker theorem (the KS theorem) and quantum computing. The KS theorem rules out a realistic theory of the KS type. We consider the realistic theory of the KS type that the results of measurements are either +1 or -1. We discuss an inconsistency between the realistic theory of the KS type and the controllability of quantum computing. We have to give up the controllability if we accept the realistic theory of the KS type. We discuss an inconsistency between the realistic theory of the KS type and the observability of quantum computing. We discuss the inconsistency by using the double-slit experiment as the most basic experiment in quantum mechanics. This experiment can be for an easy detector to a Pauli observable. We cannot accept the realistic theory of the KS type to simulate the double-slit experiment in a significant specific case. The realistic theory of the KS type can not depicture quantum detector. In short, we have to give up both the observability and the controllability if we accept the realistic theory of the KS type. Therefore, the KS theorem is a precondition for quantum computing, i.e., the realistic theory of the KS type should be ruled out.
Emergent quantum mechanics and emergent symmetries
Hooft, G. 't
2007-01-01
Quantum mechanics is ‘emergent’ if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present in the underlying deterministic system. Such
A Process Model of Quantum Mechanics
Sulis, William
2014-01-01
A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise through a non-uniform interpolation process. Standard non-relativistic quantum mechanics emerges under the limit of infinite information (the causal space grows to infinity) and infinitesimal scale (the separation between points goes to zero). The model has th...
Quantum tic-tac-toe: A teaching metaphor for superposition in quantum mechanics
Goff, Allan
2006-11-01
Quantum tic-tac-toe was developed as a metaphor for the counterintuitive nature of superposition exhibited by quantum systems. It offers a way of introducing quantum physics without advanced mathematics, provides a conceptual foundation for understanding the meaning of quantum mechanics, and is fun to play. A single superposition rule is added to the child's game of classical tic-tac-toe. Each move consists of a pair of marks subscripted by the number of the move ("spooky" marks) that must be placed in different squares. When a measurement occurs, one spooky mark becomes real and the other disappears. Quantum tic-tac-toe illustrates a number of quantum principles including states, superposition, collapse, nonlocality, entanglement, the correspondence principle, interference, and decoherence. The game can be played on paper or on a white board. A Web-based version provides a refereed playing board to facilitate the mechanics of play, making it ideal for classrooms with a computer projector.
Free spin quantum computation with semiconductor nanostructures
Zhang, W M; Soo, C; Zhang, Wei-Min; Wu, Yin-Zhong; Soo, Chopin
2005-01-01
Taking the excess electron spin in a unit cell of semiconductor multiple quantum-dot structure as a qubit, we can implement scalable quantum computation without resorting to spin-spin interactions. The technique of single electron tunnelings and the structure of quantum-dot cellular automata (QCA) are used to create a charge entangled state of two electrons which is then converted into spin entanglement states by using single spin rotations. Deterministic two-qubit quantum gates can also be manipulated using only single spin rotations with help of QCA. A single-short read-out of spin states can be realized by coupling the unit cell to a quantum point contact.
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.
The Application of SCC-DV-Xα Computational Method of Quantum Chemistry in Cement Chemistry
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
It has been explored why quantum chemistry is applied to the research field of cement chemistry. The fundamental theory of SCC-DV-Xα computational method of quantum chemistry is synopsized. The results obtained by computational quantum chemistry method in recent years of valence-bond structures and hydration activity of some cement clinker minerals, mechanical strength and stabilization of some hydrates are summarized and evaluated. Finally the prospects of the future application of quantum chemistry to cement chemistry are depicted.
Progress in theoretical quantum computing
Institute of Scientific and Technical Information of China (English)
2008-01-01
@@ Computing is perhaps one of the most distinguished features that differentiate humans from animals.Aside from counting numbers using fingers and toes,abacus was the first great computing machine of human civilization.
Energy Technology Data Exchange (ETDEWEB)
Whitaker, A [Department of Physics, Queen' s University, Belfast (United Kingdom)
2004-02-27
This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried's well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. To commence with general discussion of the new book, the authors recognise that the graduate student of today almost certainly has substantial experience of wave mechanics, and is probably familiar with the Dirac formalism. The new edition has been almost entirely rewritten; even at the level of basic text, it is difficult to trace sentences or paragraphs that have moved unscathed from one edition to the next. As well as the new topics, many of the old ones are discussed in much greater depth, and the general organisation is entirely different. As compared with the steady rise in level of the 1966 edition, the level of this book is fairly consistent throughout, and from the perspective of a beginning graduate student, I would estimate, a little tough. To sum up, Gottfried and Yan's book contains a vast amount of knowledge and understanding
Quantum Computation by Pairing Trapped Ultracold Ions
Institute of Scientific and Technical Information of China (English)
冯芒; 朱熙文; 高克林; 施磊
2001-01-01
Superpositional wavefunction oscillations for the implementation of quantum algorithms modify the desired interference required for the quantum computation. We propose a scheme with trapped ultracold ion-pairs beingqubits to diminish the detrimental effect of the wavefunction oscillations, which is applied to the two-qubitGrover's search. It can be also found that the qubits in our scheme are more robust against the decoherencecaused by the environment, and the model is scalable.
Entanglement and Quantum Computation: An Overview
Energy Technology Data Exchange (ETDEWEB)
Perez, R.B.
2000-06-27
This report presents a selective compilation of basic facts from the fields of particle entanglement and quantum information processing prepared for those non-experts in these fields that may have interest in an area of physics showing counterintuitive, ''spooky'' (Einstein's words) behavior. In fact, quantum information processing could, in the near future, provide a new technology to sustain the benefits to the U.S. economy due to advanced computer technology.