Showing papers on "Quantum error correction published in 2002"
TL;DR: This work shows how to achieve massively parallel gate operation in a large-scale quantum computer, based on techniques already demonstrated for manipulating small quantum registers, and uses the use of decoherence-free subspaces to do so.
Abstract: Among the numerous types of architecture being explored for quantum computers are systems utilizing ion traps, in which quantum bits (qubits) are formed from the electronic states of trapped ions and coupled through the Coulomb interaction. Although the elementary requirements for quantum computation have been demonstrated in this system, there exist theoretical and technical obstacles to scaling up the approach to large numbers of qubits. Therefore, recent efforts have been concentrated on using quantum communication to link a number of small ion-trap quantum systems. Developing the array-based approach, we show how to achieve massively parallel gate operation in a large-scale quantum computer, based on techniques already demonstrated for manipulating small quantum registers. The use of decoherence-free subspaces significantly reduces decoherence during ion transport, and removes the requirement of clock synchronization between the interaction regions.
1,469 citations
TL;DR: A superconducting tunnel junction circuit that behaves as a two-level atom that can be programmed with a series of microwave pulses and a projective measurement of the state can be performed by a pulsed readout subcircuit is designed and operated.
Abstract: We have designed and operated a superconducting tunnel junction circuit that behaves as a two-level atom: the "quantronium." An arbitrary evolution of its quantum state can be programmed with a series of microwave pulses, and a projective measurement of the state can be performed by a pulsed readout subcircuit. The measured quality factor of quantum coherence Qphi approximately 25,000 is sufficiently high that a solid-state quantum processor based on this type of circuit can be envisioned.
1,432 citations
TL;DR: This work proposes several methods for quantum key distribution (QKD) based on the generation and transmission of random distributions of coherent or squeezed states, and shows that they are secure against individual eavesdropping attacks.
Abstract: We propose several methods for quantum key distribution (QKD) based on the generation and transmission of random distributions of coherent or squeezed states, and we show that they are secure against individual eavesdropping attacks. These protocols require that the transmission of the optical line between Alice and Bob is larger than 50%, but they do not rely on "sub-shot-noise" features such as squeezing. Their security is a direct consequence of the no-cloning theorem, which limits the signal-to-noise ratio of possible quantum measurements on the transmission line. Our approach can also be used for evaluating various QKD protocols using light with Gaussian statistics.
1,130 citations
TL;DR: Recent theoretical and experimental advances suggest that cold atoms and individual photons may lead the way towards bigger and better quantum information processors, effectively building mesoscopic versions of 'Schrödinger's cat' from the bottom up.
Abstract: Quantum information processors exploit the quantum features of superposition and entanglement for applications not possible in classical devices, offering the potential for significant improvements in the communication and processing of information. Experimental realization of large-scale quantum information processors remains a long-term vision, as the required nearly pure quantum behaviour is observed only in exotic hardware such as individual laser-cooled atoms and isolated photons. But recent theoretical and experimental advances suggest that cold atoms and individual photons may lead the way towards bigger and better quantum information processors, effectively building mesoscopic versions of 'Schrodinger's cat' from the bottom up.
544 citations
TL;DR: How quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers is reviewed.
Abstract: Quantum theory has found a new field of application in the realm of information and computation during recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers. Some notable aspects of classical and quantum information theory will be addressed here. Quantum teleportation, dense coding, and quantum cryptography are discussed as examples of the impact of quanta on the transmission of information. Quantum logic gates and quantum algorithms are also discussed as instances of the improvement made possible in information processing by a quantum computer. Finally the authors provide some examples of current experimental realizations for quantum computers and future prospects.
534 citations
TL;DR: The quantum Zeno effect is recast in terms of an adiabatic theorem when the measurement is described as the dynamical coupling to another quantum system that plays the role of apparatus.
Abstract: The quantum Zeno effect is recast in terms of an adiabatic theorem when the measurement is described as the dynamical coupling to another quantum system that plays the role of apparatus. A few significant examples are proposed and their practical relevance discussed. We also focus on decoherence-free subspaces.
503 citations
TL;DR: The general principle for a quantum-signature scheme is proposed and investigated and can guarantee the unconditional security of the algorithm, mostly due to the correlation of the GHZ triplet states and the use of quantum one-time pads.
Abstract: The general principle for a quantum-signature scheme is proposed and investigated based on ideas from classical signature schemes and quantum cryptography. The suggested algorithm is implemented by a symmetrical quantum key cryptosystem and Greenberger-Horne-Zeilinger (GHZ) triplet states and relies on the availability of an arbitrator. We can guarantee the unconditional security of the algorithm, mostly due to the correlation of the GHZ triplet states and the use of quantum one-time pads.
370 citations
TL;DR: In this article, a teleportation scheme for a coherent-state qubit is developed and applied to gate operations, which is shown to be robust to detection inefficiency and can be used for universal quantum computation using optical coherent states.
Abstract: We study universal quantum computation using optical coherent states. A teleportation scheme for a coherent-state qubit is developed and applied to gate operations. This scheme is shown to be robust to detection inefficiency.
356 citations
TL;DR: It is obtained that any quantum process that begins with unentangled Gaussian states, performs only transformations generated by Hamiltonians that are quadratic in the canonical operators, and involves only measurements of canonical operators and suitable operations conditioned on these measurements can be simulated efficiently on a classical computer.
Abstract: We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum information. For a collection of harmonic oscillators, any quantum process that begins with unentangled Gaussian states, performs only transformations generated by Hamiltonians that are quadratic in the canonical operators, and involves only measurements of canonical operators (including finite losses) and suitable operations conditioned on these measurements can be simulated efficiently on a classical computer.
356 citations
TL;DR: A simple quantum network, based on the controlled-SWAP gate, is presented that can extract certain properties of quantum states without recourse to quantum tomography and is used as a basic building block for direct quantum estimations of both linear and nonlinear functionals of any density operator.
Abstract: We present a simple quantum network, based on the controlled-SWAP gate, that can extract certain properties of quantum states without recourse to quantum tomography. It can be used as a basic building block for direct quantum estimations of both linear and nonlinear functionals of any density operator. The network has many potential applications ranging from purity tests and eigenvalue estimations to direct characterization of some properties of quantum channels. Experimental realizations of the proposed network are within the reach of quantum technology that is currently being developed.
TL;DR: In this article, the authors studied the interaction of the thermal field and a quantum system composed of two qubits and found that such a chaotic field with minimal information can nevertheless entangle the qubits which are prepared initially in a separable state.
Abstract: A thermal field, which frequently appears in problems of decoherence, provides us with minimal information about the field. We study the interaction of the thermal field and a quantum system composed of two qubits and find that such a chaotic field with minimal information can nevertheless entangle the qubits which are prepared initially in a separable state. This simple model of a quantum register interacting with a noisy environment allows us to understand how memory of the environment affects the state of a quantum register.
TL;DR: An efficient and intuitive framework for universal quantum computation is presented that uses pairs of spin-1/2 particles to form logical qubits and a single physical interaction, Heisenberg exchange, to produce all gate operations.
Abstract: An efficient and intuitive framework for universal quantum computation is presented that uses pairs of spin-1/2 particles to form logical qubits and a single physical interaction, Heisenberg exchange, to produce all gate operations. Only two Heisenberg gate operations are required to produce a controlled $\ensuremath{\pi}$-phase shift, compared to nineteen for exchange-only proposals employing three spins. Evolved from well-studied decoherence-free subspaces, this architecture inherits immunity from collective decoherence mechanisms. The simplicity and adaptability of this approach should make it attractive for spin-based quantum computing architectures.
TL;DR: It is proved that one of two mixed states can be transformed into the other by single-qubit operations if and only if these states have equal values of all 18 invariants, which provides a complete description of nonlocal properties.
Abstract: Entanglement of two parts of a quantum system is a nonlocal property unaffected by local manipulations of these parts. It can be described by quantities invariant under local unitary transformations. Here we present, for a system of two qubits, a set of invariants which provides a complete description of nonlocal properties. The set contains 18 real polynomials of the entries of the density matrix. We prove that one of two mixed states can be transformed into the other by single-qubit operations if and only if these states have equal values of all 18 invariants. Corresponding local operations can be found efficiently. Without any of these 18 invariants the set is incomplete. Similarly, nonlocal, entangling properties of two-qubit unitary gates are invariant under single-qubit operations. We present a complete set of 3 real polynomial invariants of unitary gates. Our results are useful for optimization of quantum computations since they provide an effective tool to verify if and how a given two-qubit operation can be performed using exactly one elementary two-qubit gate, implemented by a basic physical manipulation (and arbitrarily many single-qubit gates).
PACS: 03.67-a; 03.67.Lx
TL;DR: An experimental demonstration of the power of feedback in quantum metrology, confirming the predicted superior performance of an adaptive homodyne technique for single-shot measurement of optical phase and underscore the importance of real-time feedback for reaching quantum limits in measurement and control.
Abstract: We present an experimental demonstration of the power of feedback in quantum metrology, confirming the predicted [H. M. Wiseman, Phys. Rev. Lett. 75, 4587 (1995)] superior performance of an adaptive homodyne technique for single-shot measurement of optical phase. For measurements performed on weak coherent states with no prior knowledge of the signal phase, adaptive homodyne estimation approaches closer to the intrinsic quantum uncertainty than any previous technique. Our results underscore the importance of real-time feedback for reaching quantum limits in measurement and control.
IBM1
TL;DR: It is shown that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant corresponds to a physical model of noninteracting fermions in one dimension.
Abstract: We show that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant [in Proceedings of the 33rd ACM Symposium on the Theory of Computing (2001), p. 114] corresponds to a physical model of noninteracting fermions in one dimension. We give an alternative proof of his result using the language of fermions and extend the result to noninteracting fermions with arbitrary pairwise interactions, where gates can be conditioned on outcomes of complete von Neumann measurements in the computational basis on other fermionic modes in the circuit. This last result is in remarkable contrast with the case of noninteracting bosons where universal quantum computation can be achieved by allowing gates to be conditioned on classical bits [E. Knill, R. Laflamme, and G. Milburn, Nature (London) 409, 46 (2001)].
TL;DR: In this article, the operation and tolerances of a quantum controlled-NOT gate for photonic qubits are described and a two-photon source is used for its demonstration.
Abstract: We describe the operation and tolerances of a nondeterministic, coincidence basis, quantum controlled-NOT gate for photonic qubits. It is constructed solely from linear optical elements and requires only a two-photon source for its demonstration. Its success probability is 1/9.
TL;DR: Interestingly, it is found that the nonadiabatic phase shift may be independent of the operation time under appropriate controllable conditions.
Abstract: We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal quantum gates. Physical implementation of this set of gates is designed for Josephson junctions and for NMR systems. Interestingly, we find that the nonadiabatic phase shift may be independent of the operation time under appropriate controllable conditions. A remarkable feature of the present nonadiabatic geometric gates is that there is no intrinsic limitation on the operation time.
TL;DR: In this article, the authors consider the problem of reversing quantum dynamics, with the goal of preserving an initial state's quantum entanglement or classical correlation with a reference system, and exhibit an approximate reversal operation, adapted to the initial density operator and the "noise" dynamics to be reversed.
Abstract: We consider the problem of reversing quantum dynamics, with the goal of preserving an initial state’s quantum entanglement or classical correlation with a reference system. We exhibit an approximate reversal operation, adapted to the initial density operator and the “noise” dynamics to be reversed. We show that its error in preserving either quantum or classical information is no more than twice that of the optimal reversal operation. Applications to quantum algorithms and information transmission are discussed.
TL;DR: The technique is applied to show the surprising result that there are languages for which quantum finite automata take exponentially more states than those of corresponding classical automata.
Abstract: We consider the possibility of encoding m classical bits into many fewer n quantum bits (qubits) so that an arbitrary bit from the original m bits can be recovered with good probability. We show that nontrivial quantum codes exist that have no classical counterparts. On the other hand, we show that quantum encoding cannot save more than a logarithmic additive factor over the best classical encoding. The proof is based on an entropy coalescence principle that is obtained by viewing Holevo's theorem from a new perspective.In the existing implementations of quantum computing, qubits are a very expensive resource. Moreover, it is difficult to reinitialize existing bits during the computation. In particular, reinitialization is impossible in NMR quantum computing, which is perhaps the most advanced implementation of quantum computing at the moment. This motivates the study of quantum computation with restricted memory and no reinitialization, that is, of quantum finite automata. It was known that there are languages that are recognized by quantum finite automata with sizes exponentially smaller than those of corresponding classical automata. Here, we apply our technique to show the surprising result that there are languages for which quantum finite automata take exponentially more states than those of corresponding classical automata.
TL;DR: Experimental realization shows that the structural resolution of today's pulse shapers is easily sufficient for pulse formation and the scaling of the system is favorable; sources for decoherence can be eliminated.
Abstract: A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated applying optimal control theory. The scaling of the system is favorable; sources for decoherence can be eliminated. A complete set of one- and two-quantum gates is presented for a specific molecule. Detailed analysis regarding experimental realization shows that the structural resolution of today's pulse shapers is easily sufficient for pulse formation.
TL;DR: In this article, the authors describe a protocol for continuously protecting unknown quantum states from decoherence that incorporates design principles from both quantum error correction and quantum feedback control, using continuous measurements and Hamiltonian operations.
Abstract: We describe a protocol for continuously protecting unknown quantum states from decoherence that incorporates design principles from both quantum error correction and quantum feedback control. Our protocol uses continuous measurements and Hamiltonian operations, which are weaker control tools than are typically assumed for quantum error correction. We develop a cost function appropriate for unknown quantum states and use it to optimize our state-estimate feedback. Using Monte Carlo simulations, we study our protocol for the three-qubit bit-flip code in detail and demonstrate that it can improve the fidelity of quantum states beyond what is achievable using quantum error correction when the time between quantum error-correction cycles is limited.
TL;DR: In this article, the authors proposed a scheme to implement the quantum random walk on a line and on a circle in an ion trap quantum computer and showed that the enhanced features of these walks could be observed experimentally.
Abstract: Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the variance on the line, and the mixing time on the circle increase quadratically faster in the quantum versions as compared to the classical versions. Here, we propose a scheme to implement the quantum random walk on a line and on a circle in an ion trap quantum computer. With current ion trap technology, the number of steps that could be experimentally implemented will be relatively small. However, we show how the enhanced features of these walks could be observed experimentally. In the limit of strong decoherence, the quantum random walk tends to the classical random walk. By measuring the degree to which the walk remains quantum, '' this algorithm could serve as an important benchmarking protocol for ion trap quantum computers.
TL;DR: In this paper, the authors propose an experimental realization of discrete quantum walks using neutral atoms trapped in optical lattices, and analyze the influence of possible imperfections in the experiment and investigate the transition from a quantum walk to the classical random walk.
Abstract: We propose an experimental realization of discrete quantum walks using neutral atoms trapped in optical lattices The quantum walk is taking place in position space and experimental implementation with present-day technology---even using existing setups---seems feasible We analyze the influence of possible imperfections in the experiment and investigate the transition from a quantum walk to the classical random walk for increasing errors and decoherence
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TL;DR: It is proved that Controlled-NOT plus any single-qubit real gate that does not preserve the computational basis and is not Hadamard (or its alike) are universal for quantum computing.
Abstract: What additional gates are needed for a set of classical universal gates to do universal quantum computation? We answer this question by proving that any single-qubit real gate suffices, except those that preserve the computational basis.
The result of Gottesman and Knill[quant-ph/9807006] implies that any quantum circuit involving only the Controlled-NOT and Hadamard gates can be efficiently simulated by a classical circuit. In contrast, we prove that Controlled-NOT plus any single-qubit real gate that does not preserve the computational basis and is not Hadamard (or its alike) are universal for quantum computing.
Previously only a ``generic'' gate, namely a rotation by an angle incommensurate with pi, is known to be sufficient in both problems, if only one single-qubit gate is added.
TL;DR: In this paper, it has been shown that any entangling two-qubit gate is universal for quantum computation, when assisted by one qubit gates, and a simple constructive procedure which is close to optimal and experimentally practical.
Abstract: Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-NOT, are universal when assisted by arbitrary one-qubit gates, it has only recently become clear precisely what class of two-qubit gates is universal in this sense. We present an elementary proof that any entangling two-qubit gate is universal for quantum computation, when assisted by one-qubit gates. A proof of this result for systems of arbitrary finite dimension has been provided by Brylinski and Brylinski; however, their proof relies on a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical.
TL;DR: Two-qubit logical gates are proposed on the basis of two atoms trapped in a cavity setup and commonly addressed by laser fields, which provides fidelity and a success rate very close to unity, suitable for performing quantum computation.
Abstract: Two-qubit logical gates are proposed on the basis of two atoms trapped in a cavity setup and commonly addressed by laser fields. Losses in the interaction by spontaneous transitions are efficiently suppressed by employing adiabatic transitions and the quantum Zeno effect. Dynamical and geometrical conditional phase gates are suggested. This method provides fidelity and a success rate of its gates very close to unity. Hence, it is suitable for performing quantum computation.
TL;DR: In this paper, the decay of the coherences of the quantum register is shown to strongly depend on the input states, and it is shown that this sensitivity is a characteristic of both types of coupling and not only of collective coupling.
Abstract: The dynamical evolution of a quantum register of arbitrary length coupled to an environment of arbitrary coherence length is predicted within a relevant model of decoherence. The results are reported for quantum bits (qubits) coupling individually to different environments (``independent decoherence'') and qubits interacting collectively with the same reservoir (``collective decoherence''). In both cases, explicit decoherence functions are derived for any number of qubits. The decay of the coherences of the register is shown to strongly depend on the input states: We show that this sensitivity is a characteristic of both types of coupling (collective and independent) and not only of the collective coupling, as has been reported previously. A nontrivial behavior (``recoherence'') is found in the decay of the off-diagonal elements of the reduced density matrix in the specific situation of independent decoherence. Our results lead to the identification of decoherence-free states in the collective decoherence limit. These states belong to subspaces of the system's Hilbert space that do not get entangled with the environment, making them ideal elements for the engineering of ``noiseless'' quantum codes. We also discuss the relations between decoherence of the quantum register and computational complexity based on the dynamical results obtained for the register density matrix.
TL;DR: In this article, higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation.
Abstract: We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas qubit-based quantum computation is adequate for analyses of quantum vs classical computation, in practice qubits are often realized in higher-dimensional systems by truncating all but two levels, thereby reducing the size of the precious Hilbert space. We develop natural qudit gates for universal quantum computation, and exploit the entire accessible Hilbert space. Mathematically, we give representations of the generalized Pauli group for qudits in coupled spin systems and harmonic oscillators, and include analyses of the qubit and the infinite-dimensional limits.
TL;DR: The proposed QC architecture is scalable since any two charge qubits can be effectively coupled by an experimentally accessible inductance, and an efficient and realizable QC scheme that requires only one two-bit operation to implement conditional gates.
Abstract: A goal of quantum information technology is to control the quantum state of a system, including its preparation, manipulation, and measurement. However, scalability to many qubits and controlled connectivity between any selected qubits are two of the major stumbling blocks to achieve quantum computing (QC). Here we propose an experimental method, using Josephson charge qubits, to efficiently solve these two central problems. The proposed QC architecture is scalable since any two charge qubits can be effectively coupled by an experimentally accessible inductance. More importantly, we formulate an efficient and realizable QC scheme that requires only one (instead of two or more) two-bit operation to implement conditional gates.