Showing papers on "Open quantum system published in 2000"
Book•
01 Jan 2000
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
Abstract: Part I Fundamental Concepts: 1 Introduction and overview 2 Introduction to quantum mechanics 3 Introduction to computer science Part II Quantum Computation: 4 Quantum circuits 5 The quantum Fourier transform and its application 6 Quantum search algorithms 7 Quantum computers: physical realization Part III Quantum Information: 8 Quantum noise and quantum operations 9 Distance measures for quantum information 10 Quantum error-correction 11 Entropy and information 12 Quantum information theory Appendices References Index
25,929 citations
IBM1
TL;DR: In information processing, as in physics, the classical world view provides an incomplete approximation to an underlying quantum reality that can be harnessed to break codes, create unbreakable codes, and speed up otherwise intractable computations.
Abstract: In information processing, as in physics, our classical world view provides an incomplete approximation to an underlying quantum reality. Quantum effects like interference and entanglement play no direct role in conventional information processing, but they can--in principle now, but probably eventually in practice--be harnessed to break codes, create unbreakable codes, and speed up otherwise intractable computations.
3,080 citations
IBM1
TL;DR: In this paper, the authors provide an overview of the common objectives of the investigations reported in the remain- der of this special issue and discuss the requirements for the physical implementation of quantum computation.
Abstract: After a brief introduction to the principles and promise of quantum information processing, the requirements for the physical implementation of quantum computation are discussed. These five requirements, plus two relating to the communication of quantum information, are extensively ex- plored and related to the many schemes in atomic physics, quantum optics, nuclear and electron magnetic resonance spectroscopy, superconducting electronics, and quantum-dot physics, for achiev- ing quantum computing. I. INTRODUCTION � The advent of quantum information processing, as an abstract concept, has given birth to a great deal of new thinking, of a very concrete form, about how to create physical computing devices that operate in the hitherto unexplored quantum mechanical regime. The efforts now underway to produce working laboratory devices that perform this profoundly new form of information pro- cessing are the subject of this book. In this chapter I provide an overview of the common objectives of the investigations reported in the remain- der of this special issue. The scope of the approaches, proposed and underway, to the implementation of quan- tum hardware is remarkable, emerging from specialties in atomic physics (1), in quantum optics (2), in nuclear (3) and electron (4) magnetic resonance spectroscopy, in su- perconducting device physics (5), in electron physics (6), and in mesoscopic and quantum dot research (7). This amazing variety of approaches has arisen because, as we will see, the principles of quantum computing are posed using the most fundamental ideas of quantum mechanics, ones whose embodiment can be contemplated in virtually every branch of quantum physics. The interdisciplinary spirit which has been fostered as a result is one of the most pleasant and remarkable fea- tures of this field. The excitement and freshness that has been produced bodes well for the prospect for discovery, invention, and innovation in this endeavor.
1,727 citations
TL;DR: Experimental evidence is presented that a superconducting quantum interference device (SQUID) can be put into a superposition of two magnetic-flux states: one corresponding to a few microamperes of current flowing clockwise, the other corresponding to the same amount ofCurrent flowing anticlockwise.
Abstract: In 1935, Schrodinger attempted to demonstrate the limitations of quantum mechanics using a thought experiment in which a cat is put in a quantum superposition of alive and dead states. The idea remained an academic curiosity until the 1980s when it was proposed that, under suitable conditions, a macroscopic object with many microscopic degrees of freedom could behave quantum mechanically, provided that it was sufficiently decoupled from its environment. Although much progress has been made in demonstrating the macroscopic quantum behaviour of various systems such as superconductors, nanoscale magnets, laser-cooled trapped ions, photons in a microwave cavity and C60 molecules, there has been no experimental demonstration of a quantum superposition of truly macroscopically distinct states. Here we present experimental evidence that a superconducting quantum interference device (SQUID) can be put into a superposition of two magnetic-flux states: one corresponding to a few microamperes of current flowing clockwise, the other corresponding to the same amount of current flowing anticlockwise.
1,066 citations
TL;DR: The preview of the field presented here suggests that important advances in the control of molecules and the capability of learning about molecular interactions may be reached through the application of emerging theoretical concepts and laboratory technologies.
Abstract: This review puts into perspective the present state and prospects for controlling quantum phenomena in atoms and molecules. The topics considered include the nature of physical and chemical control objectives, the development of possible quantum control rules of thumb, the theoretical design of controls and their laboratory realization, quantum learning and feedback control in the laboratory, bulk media influences, and the ability to utilize coherent quantum manipulation as a means for extracting microscopic information. The preview of the field presented here suggests that important advances in the control of molecules and the capability of learning about molecular interactions may be reached through the application of emerging theoretical concepts and laboratory technologies.
997 citations
TL;DR: In this article, the authors introduce quantum mechanics of classically chaotic systems, or quantum chaos for short, with experimental or numerical examples of microwave billiard experiments, initiated by the author and his group.
Abstract: This book introduces the quantum mechanics of classically chaotic systems, or quantum chaos for short. The author's philosophy has been to keep the discussion simple and to illustrate theory, wherever possible, with experimental or numerical examples. The microwave billiard experiments, initiated by the author and his group, play a major role in this respect. Topics covered include the various types of billiard experiment, random matrix theory, systems with periodic time dependences, the analogy between the dynamics of a one-dimensional gas with a repulsive interaction and spectral level dynamics, where an external parameter takes the role of time, scattering theory distributions and fluctuation, properties of scattering matrix elements, semiclassical quantum mechanics, periodic orbit theory, and the Gutzwiller trace formula. This book will be of great value to anyone working in quantum chaos.
912 citations
TL;DR: A nuclear magnetic resonance experiment is performed in which a conditional Berry phase is implemented, demonstrating a controlled phase shift gate, and suggests the possibility of an intrinsically fault-tolerant way of performing quantum gate operations.
Abstract: A significant development in computing has been the discovery that the computational power of quantum computers exceeds that of Turing machines. Central to the experimental realization of quantum information processing is the construction of fault-tolerant quantum logic gates. Their operation requires conditional quantum dynamics, in which one sub-system undergoes a coherent evolution that depends on the quantum state of another sub-system; in particular, the evolving sub-system may acquire a conditional phase shift. Although conventionally dynamic in origin, phase shifts can also be geometric. Conditional geometric (or 'Berry') phases depend only on the geometry of the path executed, and are therefore resilient to certain types of errors; this suggests the possibility of an intrinsically fault-tolerant way of performing quantum gate operations. Nuclear magnetic resonance techniques have already been used to demonstrate both simple quantum information processing and geometric phase shifts. Here we combine these ideas by performing a nuclear magnetic resonance experiment in which a conditional Berry phase is implemented, demonstrating a controlled phase shift gate.
668 citations
Journal Article•
TL;DR: In this paper, a short review of ideas in quantum information theory is presented at the level of advanced undergraduate knowledge, together with some useful tools for quantum mechanics of open systems and a new resource: quantum information.
Abstract: In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level of advanced undergraduate knowledge, together with some useful tools for quantum mechanics of open systems. In the second chapter I outline how classical information is represented in quantum systems and what this means for agents trying to extract information from these systems. The final chapter presents a new resource: quantum information. This resource has some bewildering applications which have been discovered in the last ten years, and continually presents us with unexpected insights into quantum theory and the universe.
The treatment is pedagogical and suitable for beginning graduates in the field.
635 citations
TL;DR: It is argued that the degrees of freedom of the human brain that relate to cognitive processes should be thought of as a classical rather than quantum system, i.e., that there is nothing fundamentally wrong with the current classical approach to neural network simulations.
Abstract: Based on a calculation of neural decoherence rates, we argue that the degrees of freedom of the human brain that relate to cognitive processes should be thought of as a classical rather than quantum system, i.e., that there is nothing fundamentally wrong with the current classical approach to neural network simulations. We find that the decoherence time scales ( approximately 10(-13)-10(-20) s) are typically much shorter than the relevant dynamical time scales ( approximately 10(-3)-10(-1) s), both for regular neuron firing and for kinklike polarization excitations in microtubules. This conclusion disagrees with suggestions by Penrose and others that the brain acts as a quantum computer, and that quantum coherence is related to consciousness in a fundamental way.
622 citations
TL;DR: A model for an ion trap quantum computer that combines scalability (a feature usually associated with solid state proposals) with the advantages of quantum optical systems (in particular, quantum control and long decoherence times) is proposed.
Abstract: Quantum computers require the storage of quantum information in a set of two-level systems (called qubits), the processing of this information using quantum gates and a means of final readout. So far, only a few systems have been identified as potentially viable quantum computer models--accurate quantum control of the coherent evolution is required in order to realize gate operations, while at the same time decoherence must be avoided. Examples include quantum optical systems (such as those utilizing trapped ions or neutral atoms, cavity quantum electrodynamics and nuclear magnetic resonance) and solid state systems (using nuclear spins, quantum dots and Josephson junctions). The most advanced candidates are the quantum optical and nuclear magnetic resonance systems, and we expect that they will allow quantum computing with about ten qubits within the next few years. This is still far from the numbers required for useful applications: for example, the factorization of a 200-digit number requires about 3,500 qubits, rising to 100,000 if error correction is implemented. Scalability of proposed quantum computer architectures to many qubits is thus of central importance. Here we propose a model for an ion trap quantum computer that combines scalability (a feature usually associated with solid state proposals) with the advantages of quantum optical systems (in particular, quantum control and long decoherence times).
TL;DR: An all optical implementation of quantum information processing with semiconductor macroatoms is proposed, allowing for a subpicosecond, decoherence-free, operation time scale in realistic semiconductor nanostructures.
Abstract: An all optical implementation of quantum information processing with semiconductor macroatoms is proposed. Our quantum hardware consists of an array of quantum dots and the computational degrees of freedom are energy-selected interband optical transitions. The quantum-computing strategy exploits exciton-exciton interactions driven by ultrafast multicolor laser pulses. Contrary to existing proposals based on charge excitations, our approach does not require time-dependent electric fields, thus allowing for a subpicosecond, decoherence-free, operation time scale in realistic semiconductor nanostructures.
TL;DR: A new approach to the implementation of quantum gates is proposed in which decoherence during the gate operations is strongly reduced by making use of an environment induced quantum Zeno effect that confines the dynamics effectively to a decoherent-free subspace.
Abstract: We propose a new approach to the implementation of quantum gates in which decoherence during the gate operations is strongly reduced. This is achieved by making use of an environment induced quantum Zeno effect that confines the dynamics effectively to a decoherence-free subspace.
TL;DR: In this paper, the authors proposed an alternative method for quantum feedback control, in which the sensors, controller, and actuators are quantum systems that interact coherently with the system to be controlled.
Abstract: In the conventional picture of quantum feedback control, sensors perform measurements on the system, a classical controller processes the results of the measurements, and actuators supply semiclassical potentials to alter the behavior of the quantum system. In this picture, the sensors tend to destroy coherence in the process of making measurements, and although the controller can use the actuators to act coherently on the quantum system, it is processing and feeding back classical information. This paper proposes an alternative method for quantum feedback control, in which the sensors, controller, and actuators are quantum systems that interact coherently with the system to be controlled. In this picture, the controller gets, processes, and feeds back quantum information. Controllers that operate using such quantum feedback loops can perform tasks such as entanglement transfer that are not possible using classical feedback. Necessary and sufficient conditions are presented for Hamiltonian quantum systems to be controllable and observable using both classical and quantum feedback.
TL;DR: In this paper, the authors introduce and discuss the problem of quantum feedback control in the context of established formulations of classical control theory, examining conceptual analogies and essential differences, and apply their methods to the particular case of switching the state of a particle in a double-well potential.
Abstract: We introduce and discuss the problem of quantum feedback control in the context of established formulations of classical control theory, examining conceptual analogies and essential differences. We describe the application of state-observer-based control laws, familiar in classical control theory, to quantum systems and apply our methods to the particular case of switching the state of a particle in a double-well potential.
TL;DR: In this article, the authors stress the fact that quantum theory does not need an interpretation other than being an algorithm for computing probabilities associated with macroscopic phenomena and measurements, and the wave function is not objective entity, it only gives the evolution of our probabilities for the outcomes potential experiments.
Abstract: Purpose of this article is to stress the fact that Quantum Theory does not need an interpretation other than being an algorithm for computing probabilities associated with macroscopic phenomena and measurements. It does not ''describ'' reality, and the wave function is not objective entity, it only gives the evolution of our probabilities for the outcomes potential experiments. (AIP) (c)
TL;DR: The phenomenon of electromagnetically induced quantum coherence is demonstrated between three confined electron subband levels in a quantum well which are almost equally spaced in energy.
Abstract: The phenomenon of electromagnetically induced quantum coherence is demonstrated between three confined electron subband levels in a quantum well which are almost equally spaced in energy Applying a strong coupling field, two-photon resonant with the 1-3 intersubband transition, produces a pronounced narrow transparency feature in the 1-2 absorption line This result can be understood in terms of all three states being simultaneously driven into "phase-locked" quantum coherence by a single coupling field We describe the effect theoretically with a density matrix method and an adapted linear response theory
TL;DR: Basic principles of quantum mechanics are introduced to explain where the power of quantum computers comes from and why it is difficult to harness and various approaches to exploiting the powerof quantum parallelism are explained.
Abstract: Richard Feynman's observation that certain quantum mechanical effects cannot be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used these quantum effects. This speculation proved justified when Peter Shor described a polynomial time quantum algorithm for factoring intergers.In quantum systems, the computational space increases exponentially with the size of the system, which enables exponential parallelism. This parallelism could lead to exponentially faster quantum algorithms than possible classically. The catch is that accessing the results, which requires measurement, proves tricky and requires new nontraditional programming techniques.The aim of this paper is to guide computer scientists through the barriers that separate quantum computing from conventional computing. We introduce basic principles of quantum mechanics to explain where the power of quantum computers comes from and why it is difficult to harness. We describe quantum cryptography, teleportation, and dense coding. Various approaches to exploiting the power of quantum parallelism are explained. We conclude with a discussion of quantum error correction.
TL;DR: A general technique that allows for an ideal transfer of quantum correlations between light fields and metastable states of matter is described, based on trapping quantum states of photons in coherently driven atomic media in which the group velocity is adiabatically reduced to zero.
Abstract: We describe a general technique that allows for an ideal transfer of quantum correlations between light fields and metastable states of matter. The technique is based on trapping quantum states of photons in coherently driven atomic media, in which the group velocity is adiabatically reduced to zero. We discuss possible applications such as quantum state memories, generation of squeezed atomic states, preparation of entangled atomic ensembles, quantum information processing, and quantum networking.
TL;DR: It is established that the equivalence of 2D contour dynamics to the dispersionless limit of the integrable Toda hierarchy constrained by a string equation underlies 2D quantum gravity.
Abstract: We establish the equivalence of 2D contour dynamics to the dispersionless limit of the integrable Toda hierarchy constrained by a string equation. Remarkably, the same hierarchy underlies 2D quantum gravity.
TL;DR: In this paper, basic quantum electrodynamics and quantum optics aspects in microstructures that exhibit a gap in the spectrum of the electromagnetic radiation they support, known as photonic crystals are reviewed.
Abstract: We review basic quantum electrodynamics and quantum optics aspects in microstructures that exhibit a gap in the spectrum of the electromagnetic radiation they support, known as photonic crystals. After a brief sketch of the properties of such materials we discuss the behaviour of few-level atoms or collections thereof with transition frequencies inside and in the vicinity of the gap. The discussion is cast in terms of a unified formalism which facilitates the comparison with standard cavity-atom physics.
TL;DR: In this article, the authors theoretically studied a double-quantum-dot hydrogen molecule in the GaAs conduction band as the basic elementary gate for a quantum computer, with the electron spins in the dots serving as qubits.
Abstract: We theoretically study a double-quantum-dot hydrogen molecule in the GaAs conduction band as the basic elementary gate for a quantum computer, with the electron spins in the dots serving as qubits. Such a two-dot system provides the necessary two-qubit entanglement required for quantum computation. We determine the excitation spectrum of two horizontally coupled quantum dots with two confined electrons, and study its dependence on an external magnetic field. In particular, we focus on the splitting of the lowest singlet and triplet states, the double occupation probability of the lowest states, and the relative energy scales of these states. We point out that at zero magnetic field it is difficult to have both a vanishing double occupation probability for a small error rate and a sizable exchange coupling for fast gating. On the other hand, finite magnetic fields may provide finite exchange coupling for quantum computer operations with small errors. We critically discuss the applicability of the envelope-function approach in the current scheme, and also the merits of various quantum-chemical approaches in dealing with few-electron problems in quantum dots, such as the Hartree-Fock self-consistent-field method, the molecular-orbital method, the Heisenberg model, and the Hubbard model. We also discuss a number of relevant issues in quantum dot quantum computing in the context of our calculations, such as the required design tolerance, spin decoherence, adiabatic transitions, magnetic-field control, and error correction.
TL;DR: A general scheme to perform universal, fault-tolerant quantum computation within decoherence-free subspaces (DFSs) is presented, and it is shown explicitly how to performs universal computation on clusters of the four-qubit DFS encoding one logical qubit each under spatially symmetric (collective) decoherentity.
Abstract: A general scheme to perform universal, fault-tolerant quantum computation within decoherence-free subspaces (DFSs) is presented. At most two-qubit interactions are required, and the system remains within the DFS throughout the entire implementation of a quantum gate. We show explicitly how to perform universal computation on clusters of the four-qubit DFS encoding one logical qubit each under spatially symmetric (collective) decoherence. Our results have immediate relevance to quantum computer implementations in which quantum logic is implemented through exchange interactions, such as the recently proposed spin-spin coupled quantum dot arrays and donor-atom arrays.
TL;DR: In this article, the authors describe two schemes to manipulate the electronic qubit states of trapped ions independent of the collective vibrational state of the ions, which enables simulation of nonlinear quantum systems including systems that exhibit phase transitions, and other semiclassical bifurcations.
Abstract: We describe two schemes to manipulate the electronic qubit states of trapped ions independent of the collective vibrational state of the ions. The first scheme uses an adiabatic method, and thus is intrinsically slow. The second scheme takes the opposite approach and uses fast pulses to produce an effective direct coupling between the electronic qubits. This last scheme enables the simulation of a number of nonlinear quantum systems including systems that exhibit phase transitions, and other semiclassical bifurcations. Quantum tunnelling and entangled states occur in such systems.
TL;DR: In this article, the authors describe a general strategy for implementing a conditional geometric phase between two spins, which is a universal gate for quantum computation, in that any unitary transformation can be implemented with arbitrary precision using only single-spin operations and conditional phase shifts.
Abstract: We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary transformation can be implemented with arbitrary precision using only single-spin operations and conditional phase shifts. Thus quantum geometrical phases can form the basis of any quantum computation. Moreover, as the induced conditional phase depends only on the geometry of the paths executed by the spins it is resilient to certain types of errors and offers the potential of a naturally fault-tolerant way of performing quantum computation.
TL;DR: It is shown that the universal set of quantum logic gates can be realized using solid-state quantum bits based on coherent electron transport in quantum wires using a proper design of two quantum wires coupled through a potential barrier.
Abstract: It is shown that the universal set of quantum logic gates can be realized using solid-state quantum bits based on coherent electron transport in quantum wires. The elementary quantum bits are realized with a proper design of two quantum wires coupled through a potential barrier. Numerical simulations show that (a) a proper design of the coupling barrier allows one to realize any one-qbit rotation and (b) Coulomb interaction between two qbits of this kind allows the implementation of the CNOT gate. These systems are based on a mature technology and seem to be integrable with conventional electronics.
Posted Content•
TL;DR: In this paper, the authors derived quantum analogues of Jarzynski's relations and discussed two applications, namely, a derivation of the law of entropy increase for general compound systems, and a preliminary analysis of heat transfer between two quantum systems at different temperatures.
Abstract: We derive quantum analogues of Jarzynski's relations, and discuss two applications, namely, a derivation of the law of entropy increase for general compound systems, and a preliminary analysis of heat transfer between two quantum systems at different temperatures. We believe that the derivation of the law of entropy increase is new and of importance.
TL;DR: In this paper, the authors use the Heisenberg picture to analyse quantum information processing and reveal that quantum information is transmitted through classical (i.e. decoherent) information channels.
Abstract: All information in quantum systems is, notwithstanding Bell9s theorem, localized. Measuring or otherwise interacting with a quantum system S has no effect on distant systems from which S is dynamically isolated, even if they are entangled with S . Using the Heisenberg picture to analyse quantum information processing makes this locality explicit, and reveals that under some circumstances (in particular, in Einstein–Podolsky–Rosen experiments and in quantum teleportation), quantum information is transmitted through ‘classical’ (i.e. decoherent) information channels.
Repository•
TL;DR: A collection of references (papers, books, preprints, book reviews, Ph. D. thesis, patents, web sites, etc.), sorted alphabetically and classified by subject, on foundations of quantum mechanics and quantum information can be found in this article.
Abstract: This is a collection of references (papers, books, preprints, book reviews, Ph. D. thesis, patents, web sites, 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.
TL;DR: The quantum algorithms that are presented could provide an exponential speedup over what can be achieved with a classical device, given a preparation of the equilibrium state.
Abstract: We address the question of how a quantum computer can be used to simulate experiments on quantum systems in thermal equilibrium. We present two approaches for the preparation of the equilibrium state on a quantum computer. For both approaches, we show that the output state of the algorithm, after long enough time, is the desired equilibrium. We present a numerical analysis of one of these approaches for small systems. We show how equilibrium (time-)correlation functions can be efficiently estimated on a quantum computer, given a preparation of the equilibrium state. The quantum algorithms that we present are hard to simulate on a classical computer. This indicates that they could provide an exponential speedup over what can be achieved with a classical device.