Showing papers on "Open quantum system published in 1998"
TL;DR: In this paper, a universal set of one-and two-quantum-bit gates for quantum computation using the spin states of coupled single-electron quantum dots is proposed, and the desired operations are effected by the gating of the tunneling barrier between neighboring dots.
Abstract: We propose an implementation of a universal set of one- and two-quantum-bit gates for quantum computation using the spin states of coupled single-electron quantum dots. Desired operations are effected by the gating of the tunneling barrier between neighboring dots. Several measures of the gate quality are computed within a recently derived spin master equation incorporating decoherence caused by a prototypical magnetic environment. Dot-array experiments that would provide an initial demonstration of the desired nonequilibrium spin dynamics are proposed.
5,801 citations
TL;DR: In this paper, the authors discuss the technique of stimulated Raman adiabatic passage (STIRAP), a method of using partially overlapping pulses (from pump and Stokes lasers) to produce complete population transfer between two quantum states of an atom or molecule.
Abstract: The authors discuss the technique of stimulated Raman adiabatic passage (STIRAP), a method of using partially overlapping pulses (from pump and Stokes lasers) to produce complete population transfer between two quantum states of an atom or molecule. The procedure relies on the initial creation of a coherence (a population-trapping state) with subsequent adiabatic evolution. The authors present the basic theory, with some extensions, and then describe examples of experimental utilization. They note some applications of the technique not only to preparation of selected states for reaction studies, but also to quantum optics and atom optics.
1,908 citations
TL;DR: It is shown that decoherence-free subspaces are stable to perturbations and, moreover, that universal quantum computation is possible within them.
Abstract: Decoherence in quantum computers is formulated within the semigroup approach The error generators are identified with the generators of a Lie algebra This allows for a comprehensive description which includes as a special case the frequently assumed spin-boson model A generic condition is presented for errorless quantum computation: decoherence-free subspaces are spanned by those states which are annihilated by all the generators It is shown that these subspaces are stable to perturbations and, moreover, that universal quantum computation is possible within them
1,561 citations
TL;DR: In this paper, the dynamics of a decohering two-level system driven by a suitable control Hamiltonian is studied, where the control procedure is implemented as a sequence of radio-frequency pulses that repetitively flip the state of the system, a technique that can be termed quantum ''bang-bang'' control after its classical analog.
Abstract: The dynamics of a decohering two-level system driven by a suitable control Hamiltonian is studied. The control procedure is implemented as a sequence of radio-frequency pulses that repetitively flip the state of the system, a technique that can be termed quantum ``bang-bang'' control after its classical analog. Decoherence introduced by the system's interaction with a quantum environment is shown to be washed out completely in the limit of continuous flipping and greatly suppressed provided the interval between the pulses is made comparable to the correlation time of the environment. The model suggests a strategy to fight against decoherence that complements existing quantum error-correction techniques.
1,241 citations
TL;DR: In this paper, quantum jump, Monte Carlo wave function, and quantum-trajectory methods are discussed and applied to a number of current problems in quantum optics, and relate them to ensemble descriptions.
Abstract: Dissipation, the irreversible loss of energy and coherence, from a microsystem is the result of coupling to a much larger macrosystem (or reservoir) that is so large that one has no chance of keeping track of all of its degrees of freedom. The microsystem evolution is then described by tracing over the reservoir states, which results in an irreversible decay as excitation leaks out of the initially excited microsystems into the outer reservoir environment. Earlier treatments of this dissipation used density matrices to describe an ensemble of microsystems, either in the Schr\"odinger picture with master equations, or in the Heisenberg picture with Langevin equations. The development of experimental techniques to study single quantum systems (for example, single trapped ions, or cavity-radiation-field modes) has stimulated the construction of theoretical methods to describe individual realizations conditioned on a particular observation record of the decay channel. These methods, variously described as quantum-jump, Monte Carlo wave function, and quantum-trajectory methods, are the subject of this review article. We discuss their derivation, apply them to a number of current problems in quantum optics, and relate them to ensemble descriptions.
1,232 citations
TL;DR: In this article, a common pattern underpinning quantum algorithms can be identified when quantum computation is viewed as multiparticle interference, and an explicit algorithm for generating any prescribed interference pattern with an arbitrary precision is provided.
Abstract: Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum computation is viewed as multiparticle interference. We use this approach to review (and improve) some of the existing quantum algorithms and to show how they are related to different instances of quantum phase estimation. We provide an explicit algorithm for generating any prescribed interference pattern with an arbitrary precision.
1,118 citations
TL;DR: The field of quantum error correction has developed spectacularly since its origin less than two years ago as discussed by the authors, and it can be classified into two categories: error correction and error correction.
Abstract: 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 uncontroll...
853 citations
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TL;DR: A general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity is provided, and a guide to the relevant literature is provided.
Abstract: The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime, is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii) A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler’s “spacetime foam” intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the Bekenstein-Hawking black-hole entropy. (v) Low-energy calculations, yielding n-point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.
851 citations
Book•
13 Mar 1998
TL;DR: In this paper, the authors present a survey of classical models of light experiments with Photons, as well as non-demolition experiments with light and non-quantum noise.
Abstract: Classical Models of Light Experiments with Photons Quantum Models of Light Basic Optical Components Photo-currents: Generation and Detection The Laser Quantum Noise: Basic Measurements Sub-Poissonian Light Squeezing Experiments Quantum Non-demolition Experiments Applications of Quantum Optics Summary and Outlook Appendices Index.
817 citations
TL;DR: In this article, it is shown that in high temperature ensemble quantum computation, it is possible to perform interesting physics simulations that have no known efficient classical algorithms, even though the model is less powerful than standard quantum computation in the presence of oracles.
Abstract: In standard quantum computation, the initial state is pure and the answer is determined by making a measurement of some of the bits in the computational basis. What can be accomplished if the initial state is a highly mixed state and the answer is determined by measuring the expectation of ${\ensuremath{\sigma}}_{z}$ on the first bit with bounded sensitivity? This is the situation in high temperature ensemble quantum computation. We show that in this model it is possible to perform interesting physics simulations that have no known efficient classical algorithms, even though the model is less powerful than standard quantum computation in the presence of oracles.
779 citations
24 Jun 1998
TL;DR: In this paper, a formalism describing the evolution of operators rather than states has proven extremely fruitful in understanding an important class of quantum operations, states used in error correction and certain communication protocols can be described by their stabilizer.
Abstract: Since Shor`s discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers--the difficulty of describing them on classical computers--also makes it difficult to describe and understand precisely what can be done with them. A formalism describing the evolution of operators rather than states has proven extremely fruitful in understanding an important class of quantum operations. States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. Even this simple group structure is sufficient to allow a rich range of quantum effects, although it falls short of the full power of quantum computation.
TL;DR: In this paper, a quantum algorithm using a bulk nuclear magnetic resonance technique was proposed to solve a purely mathematical problem in fewer steps than is possible classically, requiring fewer 'function calls' than a classical computer to determine the global properties of an unknown function.
Abstract: Quantum computers1,2,3,4,5 can in principle exploit quantum-mechanical effects to perform computations (such as factoring large numbers or searching an unsorted database) more rapidly than classical computers1,2,6,7,8. But noise, loss of coherence, and manufacturing problems make constructing large-scale quantum computers difficult9,10,11,12,13. Although ion traps and optical cavities offer promising experimental approaches14,15, no quantum algorithm has yet been implemented with these systems. Here we report the experimental realization of a quantum algorithm using a bulk nuclear magnetic resonance technique16,17,18, in which the nuclear spins act as ‘quantum bits’19. The nuclear spins are particularly suited to this role because of their natural isolation from the environment. Our simple quantum computer solves a purely mathematical problem in fewer steps than is possible classically, requiring fewer ‘function calls’ than a classical computer to determine the global properties of an unknown function.
TL;DR: In this paper, the authors reported an experimental implementation of full quantum teleportation over interatomic distances using liquid-state nuclear magnetic resonance (LMSNMR) using molecules of trichloroethylene.
Abstract: Quantum-mechanical systems have information processing capabilities1,2 that are not possible with classical devices. One example is quantum teleportation3, in which the quantum state of a system is transported from one location to another without moving through the intervening space. But although partial implementations4,5 of quantum teleportation over macroscopic distances have been achieved using optical systems, the final stage of the teleportation procedure — which allows the complete recovery of the original state — was omitted. Here we report an experimental implementation of full quantum teleportation over interatomic distances using liquid-state nuclear magnetic resonance. We achieve teleportation of the quantum state of a carbon nucleus to a hydrogen nucleus in molecules of trichloroethylene, by exploiting natural phase decoherence of the carbon nuclei. Such a teleportation scheme may be used as a subroutine in larger quantum computations, or for quantum communication.
TL;DR: This paper shows that this algorithm for exhaustive search can be implemented by replacing the W-H transform by almost any quantum mechanical operation, which leads to several new applications where it improves the number of steps by a square-root.
Abstract: A quantum computer has a clear advantage over a classical computer for exhaustive search The quantum mechanical algorithm for exhaustive search was originally derived by using subtle properties of a particular quantum mechanical operation called the Walsh-Hadamard (W-H) transform This paper shows that this algorithm can be implemented by replacing the W-H transform by almost any quantum mechanical operation This leads to several new applications where it improves the number of steps by a square root It also broadens the scope for implementation since it demonstrates quantum mechanical algorithms that can adapt to available technology
TL;DR: Wave function engineering techniques were used to monitor and control a nonstationary quantum mechanical state composed of a superposition of eigenstates to extend the concept of coherent control in semiconductors to the limit of a single quantum system in a zero-dimensional quantum dot.
Abstract: Picosecond optical excitation was used to coherently control the excitation in a single quantum dot on a time scale that is short compared with the time scale for loss of quantum coherence. The excitonic wave function was manipulated by controlling the optical phase of the two-pulse sequence through timing and polarization. Wave function engineering techniques, developed in atomic and molecular systems, were used to monitor and control a nonstationary quantum mechanical state composed of a superposition of eigenstates. The results extend the concept of coherent control in semiconductors to the limit of a single quantum system in a zero-dimensional quantum dot.
TL;DR: An overview of the research activities in the Quantum Optics Group at Caltech is presented with an emphasis on strong coupling in cavity QED which enables exploration of a new regime of nonlinear optics with single atoms and photons as mentioned in this paper.
Abstract: An important development in modern physics is the emerging capability for investigations of dynamical processes for open quantum systems in a regime of strong coupling for which individual quanta play a decisive role. Of particular significance in this context is research in cavity quantum electrodynamics which explores quantum dynamical processes for individual atoms strongly coupled to the electromagnetic field of a resonator. An overview of the research activities in the Quantum Optics Group at Caltech is presented with an emphasis on strong coupling in cavity QED which enables exploration of a new regime of nonlinear optics with single atoms and photons.
TL;DR: In this paper, it was shown that arbitrarily accurate quantum computation is possible provided that the error per operation is below a threshold value, i.e., it is possible to perform arbitrary quantum computations without decoherence and operational errors.
Abstract: Practical realization of quantum computers will require overcoming decoherence and operational errors, which lead to problems that are more severe than in classical computation. It is shown that arbitrarily accurate quantum computation is possible provided that the error per operation is below a threshold value.
TL;DR: In this article, the photon flux of a light beam has been measured using quantum non-demolition measurements of the light beam, which may open the way for applications such as noise-free information tapping in optical telecommunications.
Abstract: Quantum non-demolition measurements are designed to circumvent the limitations imposed by Heisenberg's uncertainty principle when performing repeated measurements of quantum states Recent progress in quantum optics has enabled the experimental realization of quantum non-demolition measurements of the photon flux of a light beam This achievement bears on fundamental issues about the ultimate sensitivity of measurements, and may open the way for applications such as noise-free information tapping in optical telecommunications
TL;DR: In this article, it was shown that a quantum-mechanical Turing machine can be used to implement a non-trivial fast quantum search algorithm, which can be conducted faster than a comparable search on a classical computer.
Abstract: In 1982 Feynman1 observed that quantum-mechanical systems have an information-processing capability much greater than that of corresponding classical systems, and could thus potentially be used to implement a new type of powerful computer. Three years later Deutsch2 described a quantum-mechanical Turing machine, showing that quantum computers could indeed be constructed. Since then there has been extensive research in this field, but although the theory is fairly well understood, actually building a quantum computer has proved extremely difficult. Only two methods have been used to demonstrate quantum logic gates: ion traps3,4 and nuclear magnetic resonance (NMR)5,6. NMR quantum computers have recently been used to solve a simple quantum algorithm—the two-bit Deutsch problem7,8. Here we show experimentally that such a computer can be used to implement a non-trivial fast quantum search algorithm initially developed by Grover9,10, which can be conducted faster than a comparable search on a classical computer.
TL;DR: In this paper, the authors derived the canonical distribution in the sense that, at sufficiently large and typical time, the (instantaneous) quantum mechanical expectation value of an arbitrary operator of the subsystem is almost equal to the desired canonical expectation value.
Abstract: Derivation of the canonical (or Boltzmann) distribution based only on quantum dynamics is discussed. Consider a closed system which consists of a mutually interacting subsystem and a heat bath, and assume that the whole system is initially in a pure state (which can be far from equilibrium) with small energy fluctuation. Under the ``hypothesis of equal weights for eigenstates,'' we derive the canonical distribution in the sense that, at sufficiently large and typical time, the (instantaneous) quantum mechanical expectation value of an arbitrary operator of the subsystem is almost equal to the desired canonical expectation value. We present a class of examples in which the above derivation can be rigorously established without any unproven hypotheses.
Book•
04 Mar 1998
TL;DR: Theory of Coherent Transport as mentioned in this paper, single-electron tunneling, and dissipative quantum systems are discussed in detail in Section 2.2.1.3.
Abstract: Theory of Coherent Transport. Quantization of Transport. Single-Electron Tunneling. Dissipative Quantum Systems. Driven Quantum Systems. Chaos, Coherence, and Dissipation. Indexes.
TL;DR: In this paper, a nonlinear stochastic Schrodinger equation for pure states describing non-Markovian diffusion of quantum trajectories and compatible with non-markovian master equations is presented, providing an unraveling of the evolution of any quantum system coupled to a finite or infinite number of harmonic oscillators.
Abstract: A nonlinear stochastic Schr\"odinger equation for pure states describing non-Markovian diffusion of quantum trajectories and compatible with non-Markovian master equations is presented. This provides an unraveling of the evolution of any quantum system coupled to a finite or infinite number of harmonic oscillators without any approximation. Its power is illustrated by several examples, including measurementlike situations, dissipation, and quantum Brownian motion. Some examples treat this environment phenomenologically as an infinite reservoir with fluctuations of arbitrary correlation. In other examples the environment consists of a finite number of oscillators. In such a quasiperiodic case we see the reversible decay of a macroscopic quantum-superposition (``Schr\"odinger cat''). Finally, our description of open systems is compatible with different positions of the ``Heisenberg cut'' between system and environment.
TL;DR: It is shown that the time evolution of the wave function of a quantum–mechanical many–particle system can be simulated precisely and efficiently on a quantum computer, and that ultimately the simulation of quantum field theory might be possible on large quantum computers.
Abstract: We show that the time evolution of the wave function of a quantum–mechanical many–particle system can be simulated precisely and efficiently on a quantum computer. The time needed for such a simulation is comparable to the time of a conventional simulation of the corresponding classical system, a performance which can9t be expected from any classical simulation of a quantum system. We then show how quantities of interest, like the energy spectrum of a system, can be obtained. We also indicate that ultimately the simulation of quantum field theory might be possible on large quantum computers.
TL;DR: In this article, a scheme to create a macroscopic ''Schr''odinger-cat state formed by two interacting Bose condensates was proposed, which can be seen as an example of quantum atom optics at work.
Abstract: We propose a scheme to create a macroscopic ``Schr\"odinger-cat'' state formed by two interacting Bose condensates. In analogy with quantum optics, where the control and engineering of quantum states can be maintained to a large extent, we consider the present scheme to be an example of quantum atom optics at work.
TL;DR: This work demonstrates the use of a NMR quantum computer based on the pyrimidine base cytosine, and the implementation of a quantum algorithm to solve Deutsch’s problem (distinguishing between constant and balanced functions).
Abstract: Quantum computing shows great promise for the solution of many difficult problems, such as the simulation of quantum systems and the factorization of large numbers. While the theory of quantum computing is fairly well understood, it has proved difficult to implement quantum computers in real physical systems. It has recently been shown that nuclear magnetic resonance (NMR) can be used to implement small quantum computers using the spin states of nuclei in carefully chosen small molecules. Here we demonstrate the use of a NMR quantum computer based on the pyrimidine base cytosine, and the implementation of a quantum algorithm to solve Deutsch’s problem (distinguishing between constant and balanced functions). This is the first successful implementation of a quantum algorithm on any physical system.
TL;DR: In this article, it was shown that quantum computation is possible with mixed states instead of pure states as inputs, by embedding within the mixed state a subspace that transforms like a pure state and that can be identified by labelling it based on logical (spin), temporal, or spatial degrees of freedom.
Abstract: We show that quantum computation is possible with mixed states instead of pure states as inputs. This is performed by embedding within the mixed state a subspace that transforms like a pure state and that can be identified by labelling it based on logical (spin), temporal, or spatial degrees of freedom. This permits quantum computation to be realized with bulk ensembles far from the ground state. Experimental results are presented for quantum gates and circuits implemented with liquid nuclear magnetic resonance techniques and verified by quantum state tomography.
TL;DR: In this paper, a constructive method for simulating small-scale quantum circuits by use of linear optical devices is presented, which relies on the representation of several quantum bits by a single photon and on the implementation of universal quantum gates using simple optical components (beam splitters, phase shifters, etc.).
Abstract: A constructive method for simulating small-scale quantum circuits by use of linear optical devices is presented. It relies on the representation of several quantum bits by a single photon, and on the implementation of universal quantum gates using simple optical components (beam splitters, phase shifters, etc.). This suggests that the optical realization of small quantum networks with present-day quantum optics technology is a reasonable goal. This technique could be useful for demonstrating basic concepts of simple quantum algorithms or error-correction schemes. The optical analog of a nontrivial three-bit quantum circuit is presented as an illustration.
TL;DR: The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution as discussed by the authors, and one ansatz to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action.
Abstract: The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation, quantum Regge calculus, and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.
TL;DR: This work provides algorithms that solve NP-complete and #P oracle problems by exploiting nonlinear quantum logic gates, and it is argued that virtually any deterministic non linear quantum theory will include such gates.
Abstract: If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve $\mathrm{NP}$-complete and # $P$ problems in polynomial time. We provide algorithms that solve $\mathrm{NP}$-complete and # $P$ oracle problems by exploiting nonlinear quantum logic gates. Using the Weinberg model as a simple example, the explicit construction of these gates is derived from the underlying physics. Nonlinear quantum algorithms are also presented using Polchinski type nonlinearities which do not allow for superluminal communication.