Showing papers on "Quantum error correction published in 2006"
TL;DR: A generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection, is described.
Abstract: We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multimode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.
653 citations
TL;DR: It is demonstrated in straightforward calculations that even under ideally weak noise the relaxation of bipartite open quantum systems contains elements not previously encountered in quantum noise physics.
Abstract: We demonstrate in straightforward calculations that even under ideally weak noise the relaxation of bipartite open quantum systems contains elements not previously encountered in quantum noise physics. While additivity of decay rates is known to be generic for decoherence of a single system, we demonstrate that it breaks down for bipartite coherence of even the simplest composite systems.
588 citations
TL;DR: These codes implement the whole Clifford group of unitary operations in a fully topological manner and without selective addressing of qubits, which allows them to extend their application also to quantum teleportation, dense coding, and computation with magic states.
Abstract: We construct a class of topological quantum codes to perform quantum entanglement distillation. These codes implement the whole Clifford group of unitary operations in a fully topological manner and without selective addressing of qubits. This allows us to extend their application also to quantum teleportation, dense coding, and computation with magic states.
580 citations
TL;DR: It is shown that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry, recasting the problem of finding quantum circuits as a geometric problem.
Abstract: Quantum computers hold great promise for solving interesting computational problems, but it remains a challenge to find efficient quantum circuits that can perform these complicated tasks. Here we show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms or to prove limitations on the power of quantum computers.
494 citations
TL;DR: A fully general approach to the security analysis of continuous-variable quantum key distribution (CV-QKD) is presented, and Gaussian attacks are shown to be optimal against all collective eavesdropping strategies.
Abstract: A fully general approach to the security analysis of continuous-variable quantum key distribution (CV-QKD) is presented. Provided that the quantum channel is estimated via the covariance matrix of the quadratures, Gaussian attacks are shown to be optimal against all collective eavesdropping strategies. The proof is made strikingly simple by combining a physical model of measurement, an entanglement-based description of CV-QKD, and a recent powerful result on the extremality of Gaussian states [M. M. Wolf, Phys. Rev. Lett. 96, 080502 (2006)10.1103/PhysRevLett.96.080502].
461 citations
TL;DR: In three dimensions, this work provides evidence, in the form a simple mean field theory, that the Hamiltonian gives rise to a system which is self-correcting, robust to noise without external intervening quantum error-correction procedures.
Abstract: The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general notion of quantum error correction known as operator quantum error correction. In standard quantum error-correcting codes, one requires the ability to apply a procedure which exactly reverses on the error-correcting subspace any correctable error. In contrast, for operator error-correcting subsystems, the correction procedure need not undo the error which has occurred, but instead one must perform corrections only modulo the subsystem structure. This does not lead to codes which differ from subspace codes, but does lead to recovery routines which explicitly make use of the subsystem structure. Here we present two examples of such operator error-correcting subsystems. These examples are motivated by simple spatially local Hamiltonians on square and cubic lattices. In three dimensions we provide evidence, in the form a simple mean field theory, that our Hamiltonian gives rise to a system which is self-correcting. Such a system will be a natural high-temperature quantum memory, robust to noise without external intervening quantum error-correction procedures.
455 citations
TL;DR: A new version of the quantum threshold theorem is proved that applies to concatenation of a quantum code that corrects only one error, and this theorem is used to derive arigorous lower bound on the quantum accuracy threshold e0, the best lower bound that has been rigorously proven so far.
Abstract: We prove a new version of the quantum threshold theorem that applies to concatenationof a quantum code that corrects only one error, and we use this theorem to derive arigorous lower bound on the quantum accuracy" threshold e0. Our proof also appliesto concatenation of higher-distance codes, and to noise models that allow faults to becorrelated in space and in time. The proof uses new criteria for assessing the accuracy" offault-tolerant circuits, which are particularly conducive to the inductive analysis of recur-sire simulations. Our lower bound on the threshold, e0 ≥ 2.73 × 10-5 for an adversarialindependent stochastic noise model, is derived from a computer-assisted combinatorialanaly sis; it is the best lower bound that has been rigorously proven so far.
440 citations
TL;DR: The entanglement-assisted quantum codes described do not require the dual-containing constraint necessary for standard quantum error–correcting codes, thus allowing us to “quantize” all of classical linear coding theory.
Abstract: We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard quantum error-correcting codes, thus allowing us to "quantize" all of classical linear coding theory. In particular, efficient modern classical codes that attain the Shannon capacity can be made into entanglement-assisted quantum codes attaining the hashing bound (closely related to the quantum capacity). For systems without large amounts of shared entanglement, these codes can also be used as catalytic codes, in which a small amount of initial entanglement enables quantum communication.
410 citations
TL;DR: In this paper, entangled trinary quantum systems (qutrits) were used for quantum key distribution and two identical keys were obtained with a qutrit error rate of approximately 10% using an Ekert-type protocol.
Abstract: We produce two identical keys using, for the first time, entangled trinary quantum systems (qutrits) for quantum key distribution The advantage of qutrits over the normally used binary quantum systems is an increased coding density and a higher security margin The qutrits are encoded into the orbital angular momentum of photons, namely Laguerre–Gaussian modes with azimuthal index l + 1, 0 and −1, respectively The orbital angular momentum is controlled with phase holograms In an Ekert-type protocol the violation of a three-dimensional Bell inequality verifies the security of the generated keys A key is obtained with a qutrit error rate of approximately 10%
403 citations
TL;DR: It is shown that, for convenient trap-surface distances of a few microm, strong coupling between the cavity and ensemble qubit can be achieved and coherence properties of molecular ensemble quantum bits are investigated.
Abstract: We investigate a hybrid quantum circuit where ensembles of cold polar molecules serve as long-lived quantum memories and optical interfaces for solid state quantum processors. The quantum memory realized by collective spin states (ensemble qubit) is coupled to a high-Q stripline cavity via microwave Raman processes. We show that, for convenient trap-surface distances of a few microm, strong coupling between the cavity and ensemble qubit can be achieved. We discuss basic quantum information protocols, including a swap from the cavity photon bus to the molecular quantum memory, and a deterministic two qubit gate. Finally, we investigate coherence properties of molecular ensemble quantum bits.
377 citations
TL;DR: For the Bennett-Brassard 1984 (BB84) protocol, it is shown that if the efficiency mismatch between 0 and 1 detectors for some value of the control parameter gets large enough, Eve can construct a successful faked-states attack causing a quantum bit error rate lower than 11%.
Abstract: We suggest a type of attack on quantum cryptosystems that exploits variations in detector efficiency as a function of a control parameter accessible to an eavesdropper. With gated single-photon detectors, this control parameter can be the timing of the incoming pulse. When the eavesdropper sends short pulses using the appropriate timing so that the two gated detectors in Bob's setup have different efficiencies, the security of quantum key distribution can be compromised. Specifically, we show for the Bennett-Brassard 1984 (BB84) protocol that if the efficiency mismatch between 0 and 1 detectors for some value of the control parameter gets large enough (roughly 15:1 or larger), Eve can construct a successful faked-states attack causing a quantum bit error rate lower than 11%. We also derive a general security bound as a function of the detector sensitivity mismatch for the BB84 protocol. Experimental data for two different detectors are presented, and protection measures against this attack are discussed.
TL;DR: A fault-tolerant one-way quantum computer on cluster states in three dimensions using methods of topological error correction resulting from a link between cluster states and surface codes is described.
TL;DR: A novel protocol for a quantum repeater that enables long-distance quantum communication through realistic, lossy photonic channels by incorporating active purification of arbitrary errors at each step of the protocol using only two qubits at each repeater station.
Abstract: We describe a novel protocol for a quantum repeater that enables long-distance quantum communication through realistic, lossy photonic channels. Contrary to previous proposals, our protocol incorporates active purification of arbitrary errors at each step of the protocol using only two qubits at each repeater station. Because of these minimal physical requirements, the present protocol can be realized in simple physical systems such as solid-state single photon emitters. As an example, we show how nitrogen-vacancy color centers in diamond can be used to implement the protocol, using the nuclear and electronic spin to form the two qubits.
TL;DR: This paper constitutes the first successful experience of applying formal methods and satisfiability to quantum logic synthesis, thus synthesizing in principle arbitrary multi-output Boolean functions with quantum gate library.
Abstract: This paper proposes an approach to optimally synthesize quantum circuits by symbolic reachability analysis, where the primary inputs and outputs are basis binary and the internal signals can be nonbinary in a multiple-valued domain. The authors present an optimal synthesis method to minimize quantum cost and some speedup methods with nonoptimal quantum cost. The methods here are applicable to small reversible functions. Unlike previous works that use permutative reversible gates, a lower level library that includes nonpermutative quantum gates is used here. The proposed approach obtains the minimum cost quantum circuits for Miller gate, half adder, and full adder, which are better than previous results. This cost is minimum for any circuit using the set of quantum gates in this paper, where the control qubit of 2-qubit gates is always basis binary. In addition, the minimum quantum cost in the same manner for Fredkin, Peres, and Toffoli gates is proven. The method can also find the best conversion from an irreversible function to a reversible circuit as a byproduct of the generality of its formulation, thus synthesizing in principle arbitrary multi-output Boolean functions with quantum gate library. This paper constitutes the first successful experience of applying formal methods and satisfiability to quantum logic synthesis
TL;DR: An experiment is proposed which demonstrates the undoing of a weak continuous measurement of a solid-state qubit, so that any unknown initial state is fully restored.
Abstract: We propose an experiment which demonstrates the undoing of a weak continuous measurement of a solid-state qubit, so that any unknown initial state is fully restored. The undoing procedure has only a finite probability of success because of the nonunitary nature of quantum measurement, though it is accompanied by a clear experimental indication of whether or not the undoing has been successful. The probability of success decreases with increasing strength of the measurement, reaching zero for a traditional projective measurement. Measurement undoing (``quantum undemolition'') may be interpreted as a kind of quantum eraser, in which the information obtained from the first measurement is erased by the second measurement, which is an essential part of the undoing procedure. The experiment can be realized using quantum dot (charge) or superconducting (phase) qubits.
TL;DR: In this article, a general principle of quantum interference for quantum system is proposed, and based on this a new type of computing machine, the duality computer, is proposed that may outperform in principle both classical computer and the quantum computer.
Abstract: In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself. A quantum system considered here can be any quantum system: a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer, the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer, it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented: the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.
TL;DR: In this paper, the authors describe a procedure for splitting quantum information into two or more parts so that if and only if the recipients cooperate, the original qubit can be reconstructed, using W-type entangled states as the quantum channel.
Abstract: We describe a procedure for splitting quantum information into two or more parts so that if and only if the recipients cooperate, the original qubit can be reconstructed. Our scheme uses W-type entangled states as the quantum channel and thus the scheme is robust against decoherence. We illustrate the procedure in the ion-trap system, but the idea can also be realized in other systems.
TL;DR: An experimental benchmark of operational control methods in quantum information processors extended up to 12 qubits is presented and universal control of this large Hilbert space is implemented using two complementary approaches and their accuracy and scalability are discussed.
Abstract: In this Letter, we present an experimental benchmark of operational control methods in quantum information processors extended up to 12 qubits. We implement universal control of this large Hilbert space using two complementary approaches and discuss their accuracy and scalability. Despite decoherence, we were able to reach a 12-coherence state (or a 12-qubit pseudopure cat state) and decode it into an 11 qubit plus one qutrit pseudopure state using liquid state nuclear magnetic resonance quantum information processors.
TL;DR: It is shown that an arbitrarily long quantum computation can be executed with high reliability in D spatial dimensions, if the perturbation is sufficiently weak and decays with the distance r between the qubits faster than 1/r(D).
Abstract: We prove a new version of the quantum accuracy threshold theorem that applies to non-Markovian noise with algebraically decaying spatial correlations. We consider noise in a quantum computer arising from a perturbation that acts collectively on pairs of qubits and on the environment, and we show that an arbitrarily long quantum computation can be executed with high reliability in D spatial dimensions, if the perturbation is sufficiently weak and decays with the distance r between the qubits faster than 1/r^D.
TL;DR: The results show that the presence of redundancy divides information about the system into three parts: classical ( redundant); purely quantum; and the borderline, undifferentiated or "nonredundant," information.
Abstract: We lay a comprehensive foundation for the study of redundant information storage in decoherence processes. Redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects. We consider two ensembles of states for a model universe consisting of one system and many environments: the first consisting of arbitrary states, and the second consisting of "singly branching" states consistent with a simple decoherence model. Typical states from the random ensemble do not store information about the system redundantly, but information stored in branching states has a redundancy proportional to the environment's size. We compute the specific redundancy for a wide range of model universes, and fit the results to a simple first-principles theory. Our results show that the presence of redundancy divides information about the system into three parts: classical (redundant); purely quantum; and the borderline, undifferentiated or "nonredundant," information.
TL;DR: This Letter analyzes two different sequences of laser pulses implementing a controlled-NOT quantum gate operation using quantum process tomography to assess the performance of the gates for different experimental realizations and demonstrate the advantage of amplitude-shaped laser pulses over simple square pulses.
Abstract: A crucial building block for quantum information processing with trapped ions is a controlled-NOT quantum gate. In this Letter, two different sequences of laser pulses implementing such a gate operation are analyzed using quantum process tomography. Fidelities of up to 92.6(6)% are achieved for single-gate operations and up to 83.4(8)% for two concatenated gate operations. By process tomography we assess the performance of the gates for different experimental realizations and demonstrate the advantage of amplitude-shaped laser pulses over simple square pulses. We also investigate whether the performance of concatenated gates can be inferred from the analysis of the single gates.
TL;DR: In this paper, the authors present a new approach to scalable quantum computing called a "qubus computer" which realizes qubit measurement and quantum gates through interacting qubits with a quantum communication bus mode.
Abstract: We present here a new approach to scalable quantum computing—a 'qubus computer'—which realizes qubit measurement and quantum gates through interacting qubits with a quantum communication bus mode. The qubits could be 'static' matter qubits or 'flying' optical qubits, but the scheme we focus on here is particularly suited to matter qubits. There is no requirement for direct interaction between the qubits. Universal two-qubit quantum gates may be effected by schemes which involve measurement of the bus mode, or by schemes where the bus disentangles automatically and no measurement is needed. In effect, the approach integrates together qubit degrees of freedom for computation with quantum continuous variables for communication and interaction.
TL;DR: This work shows how to boost the counterfactual inference probability to unity, thereby beating the random guessing limit and implementing Grover's search algorithm with an all-optical approach, and can eliminate errors induced by decoherence.
Abstract: Reset your perceptions for a foray into the quantum world. Counterfactual computation has been proposed as a logical consequence of quantum mechanics. Using appropriate algorithms, the theory goes, it should be possible to infer the outcome of a quantum computation without actually running the computer. Hosten et al. now report experimental confirmation that this does indeed happen. Their all-optical quantum computer was prepared in a superposition of interacting with and not interacting with an algorithm, and they obtained information about the result even when the photon did not interact with the algorithm. Surprisingly, the counterfactual approach worked better than randomly guessing the solution. It should be possible to use a similar approach in other systems, including the trapped ions popular in quantum computing architecture. The logic underlying the coherent nature of quantum information processing often deviates from intuitive reasoning, leading to surprising effects. Counterfactual computation constitutes a striking example: the potential outcome of a quantum computation can be inferred, even if the computer is not run1. Relying on similar arguments to interaction-free measurements2 (or quantum interrogation3), counterfactual computation is accomplished by putting the computer in a superposition of ‘running’ and ‘not running’ states, and then interfering the two histories. Conditional on the as-yet-unknown outcome of the computation, it is sometimes possible to counterfactually infer information about the solution. Here we demonstrate counterfactual computation, implementing Grover's search algorithm with an all-optical approach4. It was believed that the overall probability of such counterfactual inference is intrinsically limited1,5, so that it could not perform better on average than random guesses. However, using a novel ‘chained’ version of the quantum Zeno effect6, we show how to boost the counterfactual inference probability to unity, thereby beating the random guessing limit. Our methods are general and apply to any physical system, as illustrated by a discussion of trapped-ion systems. Finally, we briefly show that, in certain circumstances, counterfactual computation can eliminate errors induced by decoherence.
Book•
15 Nov 2006
TL;DR: In this paper, the Schmidt decomposition is used to decompose entanglement into two types of entropies: Renyi and Tsallis Entropies and Renyi entropy.
Abstract: Foreword.- Section 1 Qubits: Quantum state purity.- The representation of qubits.- Stokes parameters.- Single-qubit gates.- The double-slit experiment.- The Mach-Zehnder interferometer.- Multiple qubits.- Section 2 Measurements and quantum operations: The von Neumann classification of processes.- The Pauli classification of measurements.- Maximal measurements and expectation values.- The Lueders rule and non-selective measurements.- Reduced statistical operators.- General operations.- Positive operator valued measures.- Section 3 Quantum non-locality and interferometry: Hidden variables and state completeness.- Von Neumann's 'no-go' theorem.- The Einstein-Podolsky-Rosen argument.- Gleason's theorem.- Bell inequalities.- Interferometric complementarity.- The Franson interferometer.- Two-qubit quantum gates.- Section 4 Classical information and communication: Communication channels.- Shannon entropy.- Renyi entropy.- Coding.- Error correction.- Data compression.- Communication complexity.- Section 5 Quantum information: Quantum entropy.- Quantum relative and conditional entropies.- Quantum mutual information.- Coherent information.- Quantum Renyi and Tsallis entropies.- Section 6 Quantum entanglement: Basic definitions.- The Schmidt decomposition.- Special bases and decompositions.- Stokes parameters and entanglement.- Partial transpose and reduction criteria.- The 'fundamental postulate'.- Entanglement monotones.- Distillation and bound entanglement.- Entanglement and majorization.- Concurrence.- Entanglement witnesses.- Entanglement as a resource.- The thermodynamic analogy.- Information and the foundations of physics.- The geometry of entanglement.- Creating entangled states of light.- Section 7 Entangled multipartite systems.- Stokes and correlation tensors.- N-tangle.- Generalized Schmidt decomposition.- Lorentz-group isometries.- Entanglement classes.- Algebraic invariants of multipartite systems.- Three-qubit states and residual tangle.- Three-qubit quantum logic gates.- States of higher qubit number.- Section 8 Quantum state and process estimation.- Quantum state tomography.- Quantum process tomography.- Direct estimation methods.- Section 9 Quantum communication: Quantum channels.- Channel capacities.- Holevo's theorem.- Discrimination of quantum states.- The no-cloning theorem.- Basic quantum channels.- The GHJW theorem.- Quantum dense coding.- Quantum teleportation.- Entanglement swapping.- Entanglement purification.- Quantum data compression.- Quantum communication complexity.- Section 10 Quantum decoherence and its mitigation: Quantum decoherence.- Decoherence and mixtures.- Decoherence-free subspaces.- Quantum coding, error detection and correction.- The 9-qubit Shor code.- Stabilizer codes.- Concatenation of quantum codes.- Section 11 Quantum broadcasting, copying and deleting: Quantum broadcasting.- Quantum copying.- Quantum deleting.- Landauer's principle.- Section 12 Quantum key distribution: Cryptography.- QKD systems.- The BB84 (four-state) protocol.- The E91 (Ekert) protocol.- The B92 (two-state) protocol.- The 6-state protocol.- Eavesdropping.- Security proofs.- Section 13 Classical and quantum computing: Classical computing.- Deterministic Turing machines.- Probabilistic Turing machines.- Multi-tape Turing machines . 13.5 Quantum Turing machines.- Quantum computational complexity.- Fault-tolerant quantum computing.- The KLM proposal.- Section 14 Quantum algorithms: The Deutsch-Jozsa algorithm.- The Grover search algorithm.- The Shor factoring algorithm.- The Simon algorithm.- Appendix A Mathematical elements: Boolean algebra and Galois fields.- Random variables.- Hilbert space.- The standard quantum formalism.- Dirac notation.- Groups o
TL;DR: In this paper, the authors investigated the quantum dynamics of two coupled superconducting qubits under microwave irradiation and found that with the qubits operated at the charge codegeneracy point, the quantum evolution of the system can be described by an effective Hamiltonian.
Abstract: We investigate the quantum dynamics of a system of two coupled superconducting qubits under microwave irradiation. We find that, with the qubits operated at the charge codegeneracy point, the quantum evolution of the system can be described by an effective Hamiltonian which has the form of two coupled qubits with tunable coupling between them. This Hamiltonian can be used for experimental tests on macroscopic entanglement and for implementing quantum gates.
TL;DR: In this paper, stabilizer codes are used to produce a constant energy gap against one-local and two-local noise, and the corresponding fault-tolerant universal Hamiltonians are four-and six-local, respectively.
Abstract: Recently, there has been growing interest in using adiabatic quantum computation as an architecture for experimentally realizable quantum computers. One of the reasons for this is the idea that the energy gap should provide some inherent resistance to noise. It is now known that universal quantum computation can be achieved adiabatically using two-local Hamiltonians. The energy gap in these Hamiltonians scales as an inverse polynomial in the number of quantum gates being simulated. Here we present stabilizer codes which can be used to produce a constant energy gap against one-local and two-local noise. The corresponding fault-tolerant universal Hamiltonians are four-local and six-local, respectively, which are the optimal result achievable within this framework.
TL;DR: These quantum circuits for the Schur transform provide explicit efficient methods for solving such diverse problems as estimating the spectrum of a density operator, quantum hypothesis testing, and communicating without a shared reference frame.
Abstract: The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient {size poly[n,d,log(1/epsilon)] for accuracy epsilon} quantum circuits for the Schur transform, which is the change of basis between the computational and the Schur bases. Our circuits provide explicit efficient methods for solving such diverse problems as estimating the spectrum of a density operator, quantum hypothesis testing, and communicating without a shared reference frame. We thus render tractable a large series of methods for extracting resources from quantum systems and for numerous quantum information protocols.
TL;DR: In this article, the Operator Quantum Error Correction formalism was introduced, which is a new scheme for the error correction of quantum operations that incorporates the known techniques, i.e., the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method, as special cases.
Abstract: This paper is an expanded and more detailed version of the work [1] in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known techniques -- i.e. the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method -- as special cases, and relies on a generalized mathematical framework for noiseless subsystems that applies to arbitrary quantum operations. We also discuss a number of examples and introduce the notion of "unitarily noiseless subsystems".
Posted Content•
TL;DR: In this article, the complexity of a quantum analogue of the satisfiability problem is studied and a polynomial-time algorithm for the classical 2-SAT is presented, which is complete in the complexity class QMA with one-sided error.
Abstract: Complexity of a quantum analogue of the satisfiability problem is studied. Quantum k-SAT is a problem of verifying whether there exists n-qubit pure state such that its k-qubit reduced density matrices have support on prescribed subspaces. We present a classical algorithm solving quantum 2-SAT in a polynomial time. It generalizes the well-known algorithm for the classical 2-SAT. Besides, we show that for any k>=4 quantum k-SAT is complete in the complexity class QMA with one-sided error.
TL;DR: In this paper, the authors describe a method for implementing deterministic quantum gates between two spin qubits separated by centimeters, and show that when such a double-quantum-dot qubit is embedded in a superconducting microstrip cavity, the strong coupling regime of cavity quantum electrodynamics lies within reach.
Abstract: We describe a method for implementing deterministic quantum gates between two spin qubits separated by centimeters. Qubits defined by the singlet and triplet states of two exchange coupled quantum dots have recently been shown to possess long coherence times. When the effective nuclear fields in the two asymmetric quantum dots are different, total spin will no longer be a good quantum number and there will be a large electric dipole coupling between the two qubit states. We show that when such a double-quantum-dot qubit is embedded in a superconducting microstrip cavity, the strong coupling regime of cavity quantum electrodynamics lies within reach. Virtual photons in a common cavity mode could mediate coherent interactions between two distant qubits embedded in the same structure; the range of this two-qubit interaction is determined by the wavelength of the microwave transition.