Showing papers on "Quantum error correction published in 1999"
TL;DR: This work shows how GHZ states can be used to split quantum information into two parts so that both parts are necessary to reconstruct the original qubit.
Abstract: Secret sharing is a procedure for splitting a message into several parts so that no subset of parts is sufficient to read the message, but the entire set is. We show how this procedure can be implemented using Greenberger-Horne-Zeilinger (GHZ) states. In the quantum case the presence of an eavesdropper will introduce errors so that his presence can be detected. We also show how GHZ states can be used to split quantum information into two parts so that both parts are necessary to reconstruct the original qubit.
2,789 citations
TL;DR: In this article, a single-Cooper-pair box with a gate electrode was used to control the coherent quantum state evolution, which modifies the energies of the two charge states non-adiabatically, bringing them into resonance.
Abstract: 5-7 as a candidate for a quantum bit or 'qubit'—the basic component of a quantum computer. Here we report the observation of quantum oscillations in a single- Cooper-pair box. By applying a short voltage pulse via a gate electrode, we can control the coherent quantum state evolution: the pulse modifies the energies of the two charge states non- adiabatically, bringing them into resonance. The resulting state— a superposition of the two charge states—is detected by a tunnelling current through a probe junction. Our results demon- strate electrical coherent control of a qubit in a solid-state
2,172 citations
TL;DR: In this paper, a scheme that realizes controlled interactions between two distant quantum dot spins is proposed, where the effective long-range interaction is mediated by the vacuum field of a high finesse microcavity.
Abstract: The electronic spin degrees of freedom in semiconductors typically have decoherence times that are several orders of magnitude longer than other relevant time scales. A solid-state quantum computer based on localized electron spins as qubits is therefore of potential interest. Here, a scheme that realizes controlled interactions between two distant quantum dot spins is proposed. The effective long-range interaction is mediated by the vacuum field of a high finesse microcavity. By using conduction-band-hole Raman transitions induced by classical laser fields and the cavity-mode, parallel controlled-not operations, and arbitrary single qubit rotations can be realized.
1,702 citations
TL;DR: It is shown that single quantum bit operations, Bell-basis measurements and certain entangled quantum states such as Greenberger–Horne–Zeilinger (GHZ) states are sufficient to construct a universal quantum computer.
Abstract: Algorithms such as quantum factoring1 and quantum search2 illustrate the great theoretical promise of quantum computers; but the practical implementation of such devices will require careful consideration of the minimum resource requirements, together with the development of procedures to overcome inevitable residual imperfections in physical systems3,4,5 Many designs have been proposed, but none allow a large quantum computer to be built in the near future6 Moreover, the known protocols for constructing reliable quantum computers from unreliable components can be complicated, often requiring many operations to produce a desired transformation3,4,5,7,8 Here we show how a single technique—a generalization of quantum teleportation9—reduces resource requirements for quantum computers and unifies known protocols for fault-tolerant quantum computation We show that single quantum bit (qubit) operations, Bell-basis measurements and certain entangled quantum states such as Greenberger–Horne–Zeilinger (GHZ) states10—all of which are within the reach of current technology—are sufficient to construct a universal quantum computer We also present systematic constructions for an infinite class of reliable quantum gates that make the design of fault-tolerant quantum computers much more straightforward and methodical
1,604 citations
TL;DR: In this paper, a dynamical method for beating decoherence and dissipation in open quantum systems is proposed, which can be combined with the capability of retaining control over the effective dynamical evolution of the open quantum system.
Abstract: We propose a novel dynamical method for beating decoherence and dissipation in open quantum systems. We demonstrate the possibility of filtering out the effects of unwanted (not necessarily known) system-environment interactions and show that the noise-suppression procedure can be combined with the capability of retaining control over the effective dynamical evolution of the open quantum system. Implications for quantum information processing are discussed.
1,407 citations
TL;DR: In this article, an implementation of quantum logic gates via virtual vibrational excitations in an ion-trap quantum computer was proposed. But it is not yet feasible to implement quantum computation with ions whose vibrations are strongly coupled to a thermal reservoir.
Abstract: We propose an implementation of quantum logic gates via virtual vibrational excitations in an ion-trap quantum computer. Transition paths involving unpopulated vibrational states interfere destructively to eliminate the dependence of rates and revolution frequencies on vibrational quantum numbers. As a consequence, quantum computation becomes feasible with ions whose vibrations are strongly coupled to a thermal reservoir.
945 citations
TL;DR: In this paper, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field can be constructed using simple linear devices, such as beam splitters and phase shifters, together with squeezers and nonlinear devices such as Kerr-effect fibers and atoms in optical cavities.
Abstract: This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field might be constructed using simple linear devices such as beam splitters and phase shifters, together with squeezers and nonlinear devices such as Kerr-effect fibers and atoms in optical cavities. Such a device could in principle perform “floating point” computations. Problems of noise, finite precision, and error correction are discussed.
849 citations
TL;DR: A scheme is presented that allows entanglement purification over arbitrary long channels and tolerates errors on the percent level and requires a polynomial overhead in time, and an overhead in local resources that grows only logarithmically with the length of the channel.
Abstract: We study the use of entanglement purification for quantum communication over long distances. For distances much longer than the coherence length of a corresponding noisy quantum channel, the fidelity of transmission is usually so low that standard purification methods are not applicable. It is possible, however, to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping. This method can be much more efficient than schemes based on quantum error correction, as it makes explicit use of two-way classical communication. An important question is how the noise, introduced by imperfect local operations (that constitute the protocols of purification and the entanglement swapping), accumulates in such a compound channel, and how it can be kept below a certain noise level. To treat this problem, we first study the applicability and the efficiency of entanglement purification protocols in the situation of imperfect local operations. We then present a scheme that allows entanglement purification over arbitrary long channels and tolerates errors on the percent level. It requires a polynomial overhead in time, and an overhead in local resources that grows only logarithmically with the length of the channel.
660 citations
TL;DR: A quantum key distribution scheme in which small phase and amplitude modulations of cw light beams carry the key information and the presence of EPR-type correlations provides the quantum protection.
Abstract: We propose a quantum cryptographic scheme in which small phase and amplitude modulations of cw light beams carry the key information. The presence of Einstein-Podolsky-Rosen type correlations provides the quantum protection.
551 citations
Proceedings Article•
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TL;DR: This paper introduces quantum mechanics and shows how this can be used for computation in devices designed to carry out classical functions.
Abstract: As device structures get smaller quantum mechanical effects predominate. About twenty years ago it was shown that it was possible to redesign devices so that they could still carry out the same functions. Recently it has been shown that the processing speed of computers based on quantum mechanics is indeed far superior to their classical counterparts for some important applications. This paper introduces quantum mechanics and shows how this can be used for computation.
545 citations
Posted Content•
TL;DR: This work shows that a suitable notion of "number of errors" e makes sense for any quantum or classical system in the presence of arbitrary interactions, and proves the existence of large codes for both quantum and classical information.
Abstract: Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of errors'' e makes sense for any system in the presence of arbitrary environmental interactions. In fact, the notion is directly related to the lowest order in time with which uncorrectable errors are introduced, and this in turn is derived from a grading of the algebra generated by the interaction operators. As a result, e-error-correcting codes are effective at protecting quantum information without requiring the usual assumptions of independence and lack of correlation. We prove the existence of large codes for both quantum and classical information. By viewing error-correcting codes as subsystems, we relate codes to irreducible representations of certain operator algebras and show that noiseless subsystems are infinite-distance error-correcting codes. An explicit example involving collective interactions is discussed.
TL;DR: In this paper, the authors proposed a method to solve the PDE problem in the context of the PhysRevA journal, which can be found at http://prola.aps.org/ Copyright American Physical Society DOI : 10.1103/PhysRevA.59.4249
Abstract: Original article can be found at: http://prola.aps.org/ Copyright American Physical Society DOI : 10.1103/PhysRevA.59.4249
TL;DR: In this paper, the authors present a formulation of feedback in quantum systems in which the best estimates of the dynamical variables are obtained continuously from the measurement record, and fed back to control the system.
Abstract: We present a formulation of feedback in quantum systems in which the best estimates of the dynamical variables are obtained continuously from the measurement record, and fed back to control the system. We apply this method to the problem of cooling and confining a single quantum degree of freedom, and compare it to current schemes in which the measurement signal is fed back directly in the manner usually considered in existing treatments of quantum feedback. Direct feedback may be combined with feedback by estimation, and the resulting combination, performed on a linear system, is closely analogous to classical linear-quadratic-Gaussian control theory with residual feedback.
TL;DR: Quantum physics, a child of the early 20th century, is probably the most successful description of nature ever invented by man and has been applied to a wide range of phenomena as discussed by the authors.
Abstract: Quantum physics, a child of the early 20th century, is probably the most successful description of nature ever invented by man. The range of phenomena it has been applied to is enormous. It covers phenomena from the elementary-particle level all me way to the physics of the early universe. Many modern technologies would be impossible without quantum physics—witness, for example, that all information technologies are based on a quantum understanding of solids, particularly of semiconductors, or that the operation of lasers is based on a quantum understanding of atomic and molecular phenomena.
TL;DR: In this article, the authors proposed a two-level system with macroscopic quantum coherent states in a superconducting quantum interference loop, which can be decoupled from the environment.
Abstract: Quantum computers have the potential to outperform their classical counterparts in a qualitative manner, as demonstrated by algorithms1 which exploit the parallelism inherent in the time evolution of a quantum state. In quantum computers, the information is stored in arrays of quantum two-level systems (qubits), proposals for which include utilizing trapped atoms and photons2,4, magnetic moments in molecules5 and various solid-state implementations6,10. But the physical realization of qubits is challenging because useful quantum computers must overcome two conflicting difficulties: the computer must be scalable and controllable, yet remain almost completely detached from the environment during operation, in order to maximize the phase coherence time11. Here we report a concept for a solid-state ‘quiet’ qubit that can be efficiently decoupled from the environment. It is based on macroscopic quantum coherent states in a superconducting quantum interference loop. Our two-level system is naturally bistable, requiring no external bias: the two basis states are characterized by different macroscopic phase drops across a Josephson junction, which may be switched with minimal external contact.
TL;DR: In this article, the authors show how macroscopically distinct quantum superposition states (Schrodinger cat states) may be used as logical qubit encodings for the correction of spontaneous emission errors.
Abstract: We show how macroscopically distinct quantum superposition states (Schrodinger cat states) may be used as logical qubit encodings for the correction of spontaneous emission errors. Spontaneous emission causes a bit flip error, which is easily corrected by a standard error correction circuit. The method works arbitrarily well as the distance between the amplitudes of the superposed coherent states increases. [S1050-2947(99)06503-8].
TL;DR: In this paper, the authors considered the situation when the detector output is explicitly recorded that leads to the opposite effect: gradual purification of the double-dot density matrix, and derived a nonlinear Langevin equation for the random evolution of the density matrix which is reflected and caused by the stochastic detector output.
Abstract: We consider the continuous measurement of a double quantum dot by a weakly coupled detector (tunnel point contact nearby) While the conventional approach describes the gradual system decoherence due to the measurement, we study the situation when the detector output is explicitly recorded that leads to the opposite effect: gradual purification of the double-dot density matrix The nonlinear Langevin equation is derived for the random evolution of the density matrix which is reflected and caused by the stochastic detector output Gradual collapse, gradual purification, and the quantum Zeno effect are naturally described by the equation We also discuss the possible experiments to confirm the theory
TL;DR: In this paper, it was shown that if one can perform a restricted set of fast manipulations on a quantum system, one can implement a large class of dynamical evolutions by effectively removing or introducing selected Hamiltonians.
Abstract: We show that if one can perform a restricted set of fast manipulations on a quantum system, one can implement a large class of dynamical evolutions by effectively removing or introducing selected Hamiltonians. The procedure can be used to achieve universal noise-tolerant control based on purely unitary open-loop transformations of the dynamics. As a result, it is in principle possible to perform noise-protected universal quantum computation using no extra space resources.
TL;DR: The role of quantum entanglement is stressed and Grover's (1997) quantum search algorithm described in detail, and a review of the current experimental status of quantum computers is reviewed.
Abstract: The basic ideas of quantum computation are introduced by a brief discussion of Bennett (1973, 1982) and Fredkin's (1982, 1997) ideas of reversible computation. After some remarks about Deutsch's (1985) pioneering work on quantum complexity and Shor's (1996) factorisation algorithm, quantum logic gates, qubits and registers are discussed. The role of quantum entanglement is stressed and Grover's (1997) quantum search algorithm described in detail. The paper ends with a review of the current experimental status of quantum computers.
TL;DR: Although interference is intrinsically a classical wave phenomenon, the superposition principle which underlies all interference is also at the heart of quantum mechanics as mentioned in this paper, and it has been referred to as the only quantum mystery.
Abstract: Although interference is intrinsically a classical wave phenomenon, the superposition principle which underlies all interference is also at the heart of quantum mechanics. Feynman has referred to interference as really “the only mystery” of quantum mechanics. Furthermore, in some interference experiments we encounter the idea of quantum entanglement, which has also been described as really the only quantum mystery. Clearly interference confronts us with some quite basic questions of interpretation. Despite its long history, going back to Thomas Young at the beginning of the 19th century, optical interference still challenges our understanding, and the last word on the subject probably has not yet been written. With the development of experimental techniques for fast and sensitive measurements of light, it has become possible to carry out many of the Gedanken experiments whose interpretation was widely debated in the 1920s and 1930s in the course of the development of quantum mechanics. Although this article focuses entirely on experiments with light, interference has also been observed with many kinds of material particles like electrons, neutrons, and atoms. We particularly draw the reader’s attention to the beautiful experiments with neutron beams by Rauch and co-workers and others (see, for example, Badurek et al.,1988). Quantum optical interference effects are key topics of a recent book (Greenstein and Zajonc, 1997), an extended rather thorough review (Buzek and Knight, 1995) and an article in Physics Today(Greenberger et al.,1993).
TL;DR: A new measure of information in quantum mechanics is proposed which takes into account that for quantum systems the only features known before an experiment is performed are the probabilities for various events to occur.
Abstract: A new measure of information in quantum mechanics is proposed which takes into account that for quantum systems the only features known before an experiment is performed are the probabilities for various events to occur. The sum of the individual measures of information for mutually complementary observations is invariant under the choice of the particular set of complementary observations and conserved if there is no information exchange with an environment. That operational quantum information invariant results in $k$ bits of information for a system consisting of $k$ qubits.
TL;DR: A lower bound on the probability of decoding error for a quantum communication channel is presented, from which the strong converse to the quantum channel coding theorem is immediately shown.
Abstract: A lower bound on the probability of decoding error for a quantum communication channel is presented, from which the strong converse to the quantum channel coding theorem is immediately shown. The results and their derivations are mostly straightforward extensions of the classical counterparts which were established by Arimoto (1973), except that more careful treatment is necessary here due to the noncommutativity of operators.
TL;DR: The recovery operation is adapted to simultaneously correct errors and perform a useful measurement that drives the computation, which means that the difficulty of realizing a useful quantum computer need be only an order of magnitude larger than the logic device contained within it.
Abstract: Quantum computing1—the processing of information according to the fundamental laws of physics—offers a means to solve efficiently a small but significant set of classically intractable problems. Quantum computers are based on the controlled manipulation of entangled quantum states, which are extremely sensitive to noise and imprecision; active correction of errors must therefore be implemented without causing loss of coherence. Quantum error-correction theory2,3,4,5,6,7,8,9 has made great progress in this regard, by predicting error-correcting ‘codeword’ quantum states. But the coding is inefficient and requires many quantum bits10,11,12, which results in physically unwieldy fault-tolerant quantum circuits10,11,12,13,14,15,16,17,18. Here I report a general technique for circumventing the trade-off between the achieved noise tolerance and the scale-up in computer size that is required to realize the error correction. I adapt the recovery operation (the process by which noise is suppressed through error detection and correction) to simultaneously correct errors and perform a useful measurement that drives the computation. The result is that a quantum computer need be only an order of magnitude larger than the logic device contained within it. For example, the physical scale-up factor10,11 required to factorize a thousand-digit number is reduced from 1,500 to 22, while preserving the original tolerated gate error rate (10−5) and memory noise per bit (10−7). The difficulty of realizing a useful quantum computer is therefore significantly reduced.
TL;DR: In this paper, a general scheme for performing a simulation of the dynamics of one quantum system using another was presented, which was used to experimentally simulate the dynamic behavior of truncated quantum harmonic and anharmonic oscillators using nuclear magnetic resonance.
Abstract: We present a general scheme for performing a simulation of the dynamics of one quantum system using another. This scheme is used to experimentally simulate the dynamics of truncated quantum harmonic and anharmonic oscillators using nuclear magnetic resonance. We believe this to be the first explicit physical realization of such a simulation.
Journal Article•
TL;DR: The connection between fault-tolerant quantum computation and nonabelian quantum statistics in two spatial dimensions is explored and it is shown that if information is encoded in pairs of quasiparticles, then the Aharonov-Bohm interactions can be adequate for universal fault-Tolerance quantum computation.
Abstract: Following a suggestion of A. Kitaev, we explore the connection between fault-tolerant quantum computation and nonabelian quantum statistics in two spatial dimensions. A suitably designed spin system can support localized excitations (quasiparticles) that exhibit long-range nonabelian Aharonov-Bohm interactions. Quantum information encoded in the charges of the quasiparticles is highly resistant to decoherence, and can be reliably processed by carrying one quasiparticle around another. If information is encoded in pairs of quasiparticles, then the Aharonov-Bohm interactions can be adequate for universal fault-tolerant quantum computation.
TL;DR: A secure quantum identification system combining a classical identification procedure and quantum key distribution is proposed and each identification sequence is always used just once and sequences are ``refueled'' from a shared provably secret key transferred through the quantum channel.
Abstract: A secure quantum identification system combining a classical identification procedure and quantum key distribution is proposed. Each identification sequence is always used just once and sequences are ``refueled'' from a shared provably secret key transferred through the quantum channel. Two identification protocols are devised. The first protocol can be applied when legitimate users have an unjammable public channel at their disposal. The deception probability is derived for the case of a noisy quantum channel. The second protocol employs unconditionally secure authentication of information sent over the public channel, and thus can be applied even in the case when an adversary is allowed to modify public communications. An experimental realization of a quantum identification system is described.
TL;DR: In this article, it was shown that any unitary matrix can be realized as the S-matrix at a given energy by choosing appropriate (unique) boundary conditions at the vertices.
Abstract: In this article we continue our investigations of one particle quantum scattering theory for Schroedinger operators on a set of connected (idealized one-dimensional) wires forming a graph with an arbitrary number of open ends. The Hamiltonian is given as minus the Laplace operator with suitable linear boundary conditions at the vertices (the local Kirchhoff law). In ``Kirchhoff's rule for quantum wires'' [J. Phys. A: Math. Gen. 32, 595 - 630 (1999)] we provided an explicit algebraic expression for the resulting (on-shell) S-matrix in terms of the boundary conditions and the lengths of the internal lines and we also proved its unitarity. Here we address the inverse problem in the simplest context with one vertex only but with an arbitrary number of open ends. We provide an explicit formula for the boundary conditions in terms of the S-matrix at a fixed, prescribed energy. We show that any unitary $n\times n$ matrix may be realized as the S-matrix at a given energy by choosing appropriate (unique) boundary conditions. This might possibly be used for the design of elementary gates in quantum computing. As an illustration we calculate the boundary conditions associated to the unitary operators of some elementary gates for quantum computers and raise the issue whether in general the unitary operators associated to quantum gates should rather be viewed as scattering operators instead of time evolution operators for a given time associated to a quantum mechanical Hamiltonian.
TL;DR: An overview of quantum information processing is given, showing that the famous Shor speedup of integer factoring is just one of a host of important applications for qubits, including cryptography, counterfeit protection, channel capacity enhancement, distributed computing, and others.
TL;DR: In this paper, an approximate formula for the amplitude of Grover's quantum algorithm is derived. But this formula assumes that the phase matching condition is satisfied, which is not always the case.
TL;DR: In this article, a Markovian model for a quantum dynamical system with input and output channels and a feedback is described, and a multi-stage version of the theory of quantum measurement and statistical decisions applied to the optimal control problem is developed.