Showing papers on "Quantum error correction published in 2013"
TL;DR: For the first time, physicists will have to master quantum error correction to design and operate complex active systems that are dissipative in nature, yet remain coherent indefinitely.
Abstract: The performance of superconducting qubits has improved by several orders of magnitude in the past decade. These circuits benefit from the robustness of superconductivity and the Josephson effect, and at present they have not encountered any hard physical limits. However, building an error-corrected information processor with many such qubits will require solving specific architecture problems that constitute a new field of research. For the first time, physicists will have to master quantum error correction to design and operate complex active systems that are dissipative in nature, yet remain coherent indefinitely. We offer a view on some directions for the field and speculate on its future.
2,013 citations
TL;DR: The basic aspects of quantum error correction and fault-tolerance are examined largely through detailed examples, which are more relevant to experimentalists today and in the near future.
Abstract: Quantum error correction (QEC) and fault-tolerant quantum computation represent one of the most vital theoretical aspects of quantum information processing. It was well known from the early developments of this exciting field that the fragility of coherent quantum systems would be a catastrophic obstacle to the development of large-scale quantum computers. The introduction of quantum error correction in 1995 showed that active techniques could be employed to mitigate this fatal problem. However, quantum error correction and fault-tolerant computation is now a much larger field and many new codes, techniques, and methodologies have been developed to implement error correction for large-scale quantum algorithms. In response, we have attempted to summarize the basic aspects of quantum error correction and fault-tolerance, not as a detailed guide, but rather as a basic introduction. The development in this area has been so pronounced that many in the field of quantum information, specifically researchers who are new to quantum information or people focused on the many other important issues in quantum computation, have found it difficult to keep up with the general formalisms and methodologies employed in this area. Rather than introducing these concepts from a rigorous mathematical and computer science framework, we instead examine error correction and fault-tolerance largely through detailed examples, which are more relevant to experimentalists today and in the near future.
625 citations
TL;DR: It is demonstrated that decoherence can be mitigated by environmental monitoring, and the foundation of quantum feedback approaches based on Bayesian statistics is validated, suggesting a new means of implementing 'quantum steering’—the harnessing of action at a distance to manipulate quantum states through measurement.
Abstract: The length of time that a quantum system can exist in a superposition state is determined by how strongly it interacts with its environment. This interaction entangles the quantum state with the inherent fluctuations of the environment. If these fluctuations are not measured, the environment can be viewed as a source of noise, causing random evolution of the quantum system from an initially pure state into a statistical mixture--a process known as decoherence. However, by accurately measuring the environment in real time, the quantum system can be maintained in a pure state and its time evolution described by a 'quantum trajectory' determined by the measurement outcome. Here we use weak measurements to monitor a microwave cavity containing a superconducting quantum bit (qubit), and track the individual quantum trajectories of the system. In this set-up, the environment is dominated by the fluctuations of a single electromagnetic mode of the cavity. Using a near-quantum-limited parametric amplifier, we selectively measure either the phase or the amplitude of the cavity field, and thereby confine trajectories to either the equator or a meridian of the Bloch sphere. We perform quantum state tomography at discrete times along the trajectory to verify that we have faithfully tracked the state of the quantum system as it diffuses on the surface of the Bloch sphere. Our results demonstrate that decoherence can be mitigated by environmental monitoring, and validate the foundation of quantum feedback approaches based on Bayesian statistics. Moreover, our experiments suggest a new means of implementing 'quantum steering'--the harnessing of action at a distance to manipulate quantum states through measurement.
388 citations
TL;DR: A time-energy uncertainty relation is derived for open quantum systems undergoing a general, completely positive, and trace preserving evolution which provides a bound to the quantum speed limit.
Abstract: Bounds to the speed of evolution of a quantum system are of fundamental interest in quantum metrology, quantum chemical dynamics, and quantum computation. We derive a time-energy uncertainty relation for open quantum systems undergoing a general, completely positive, and trace preserving evolution which provides a bound to the quantum speed limit. When the evolution is of the Lindblad form, the bound is analogous to the Mandelstam-Tamm relation which applies in the unitary case, with the role of the Hamiltonian being played by the adjoint of the generator of the dynamical semigroup. The utility of the new bound is exemplified in different scenarios, ranging from the estimation of the passage time to the determination of precision limits for quantum metrology in the presence of dephasing noise.
375 citations
TL;DR: A Margolus-Levitin-type bound on the minimal evolution time of an arbitrarily driven open quantum system is derived and it is shown that non-Markovian effects can speed up quantum evolution and therefore lead to a smaller quantum speed limit time.
Abstract: We derive a Margolus-Levitin-type bound on the minimal evolution time of an arbitrarily driven open quantum system. We express this quantum speed limit time in terms of the operator norm of the nonunitary generator of the dynamics. We apply these results to the damped Jaynes-Cummings model and demonstrate that the corresponding bound is tight. We further show that non-Markovian effects can speed up quantum evolution and therefore lead to a smaller quantum speed limit time.
367 citations
TL;DR: This work demonstrates the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time using an autonomous feedback scheme that combines continuous drives along with a specifically engineered coupling between the two-qubit register and a dissipative reservoir.
Abstract: An entangled Bell state of two superconducting quantum bits can be stabilized for an arbitrary time using an autonomous feedback scheme, that is, one that does not require a complicated external error-correcting feedback loop. Entangled states are a key resource in fundamental quantum physics, quantum cryptography and quantum computation. It has been generally assumed that the creation of such states requires the avoidance of contact with a dissipative environment, and minimization of decoherence. Some studies have shown, however, that dissipative interactions can be used to preserve coherence, and in this issue of Nature two groups demonstrate this principle for continuously driven physical systems. Lin et al. use engineered dissipation to deterministically produce and stabilize entanglement between two trapped-ion qubits, independent of their initial state. Shankar et al. use an autonomous feedback scheme to counteract decoherence and demonstrate the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time. This approach may be applied to a broad range of experimental systems to achieve desired quantum dynamics or steady states. Quantum error correction codes are designed to protect an arbitrary state of a multi-qubit register from decoherence-induced errors1, but their implementation is an outstanding challenge in the development of large-scale quantum computers. The first step is to stabilize a non-equilibrium state of a simple quantum system, such as a quantum bit (qubit) or a cavity mode, in the presence of decoherence. This has recently been accomplished using measurement-based feedback schemes2,3,4,5. The next step is to prepare and stabilize a state of a composite system6,7,8. Here we demonstrate the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time. Our result is achieved using an autonomous feedback scheme that combines continuous drives along with a specifically engineered coupling between the two-qubit register and a dissipative reservoir. Similar autonomous feedback techniques have been used for qubit reset9, single-qubit state stabilization10, and the creation11 and stabilization6 of states of multipartite quantum systems. Unlike conventional, measurement-based schemes, the autonomous approach uses engineered dissipation to counteract decoherence12,13,14,15, obviating the need for a complicated external feedback loop to correct errors. Instead, the feedback loop is built into the Hamiltonian such that the steady state of the system in the presence of drives and dissipation is a Bell state, an essential building block for quantum information processing. Such autonomous schemes, which are broadly applicable to a variety of physical systems, as demonstrated by the accompanying paper on trapped ion qubits16, will be an essential tool for the implementation of quantum error correction.
334 citations
TL;DR: It is shown that two different quantum gates, originating from two distinct paths in Hilbert space, yield non-equivalent transformations when applied in different orders, providing evidence for the non-Abelian character of the implemented holonomic quantum operations.
Abstract: Microwave stimulation of a superconducting artificial three-level atom is used to demonstrate high-fidelity, non-Abelian geometric transformations, the results of which depend on the order in which they are performed. Geometric phases are acquired whenever a quantum system evolves along a path. If the system contains degenerate energy levels, these can take the form of matrix-valued geometric transformations called non-Abelian holonomies. It has been proposed that such holonomies could be exploited for noise-resilient quantum computation. The authors realize non-Abelian holonomic quantum operations on a single superconducting artificial three-level atom. In combination with a non-trivial two-qubit gate, the results may suggest a route to universal holonomic quantum computing. The geometric aspects of quantum mechanics are emphasized most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a path in Hilbert space, that is, the space of quantum states of the system. The geometric phase is determined only by the shape of this path1,2,3 and is, in its simplest form, a real number. However, if the system has degenerate energy levels, then matrix-valued geometric state transformations, known as non-Abelian holonomies—the effect of which depends on the order of two consecutive paths—can be obtained4. They are important, for example, for the creation of synthetic gauge fields in cold atomic gases5 or the description of non-Abelian anyon statistics6,7. Moreover, there are proposals8,9 to exploit non-Abelian holonomic gates for the purposes of noise-resilient quantum computation. In contrast to Abelian geometric operations10, non-Abelian ones have been observed only in nuclear quadrupole resonance experiments with a large number of spins, and without full characterization of the geometric process and its non-commutative nature11,12. Here we realize non-Abelian non-adiabatic holonomic quantum operations13,14 on a single, superconducting, artificial three-level atom15 by applying a well-controlled, two-tone microwave drive. Using quantum process tomography, we determine fidelities of the resulting non-commuting gates that exceed 95 per cent. We show that two different quantum gates, originating from two distinct paths in Hilbert space, yield non-equivalent transformations when applied in different orders. This provides evidence for the non-Abelian character of the implemented holonomic quantum operations. In combination with a non-trivial two-quantum-bit gate, our method suggests a way to universal holonomic quantum computing.
330 citations
TL;DR: In this article, the authors proposed a new hardware-efficient paradigm for universal quantum computation which is based on encoding, protecting and manipulating quantum information in a quantum harmonic oscillator, and they considered two schemes.
Abstract: We present a new hardware-efficient paradigm for universal quantum computation which is based on encoding, protecting and manipulating quantum information in a quantum harmonic oscillator. This proposal exploits multi-photon driven dissipative processes to encode quantum information in logical bases composed of Schrodinger cat states. More precisely, we consider two schemes. In a first scheme, a two-photon driven dissipative process is used to stabilize a logical qubit basis of two-component Schrodinger cat states. While such a scheme ensures a protection of the logical qubit against the photon dephasing errors, the prominent error channel of single-photon loss induces bit-flip type errors that cannot be corrected. Therefore, we consider a second scheme based on a four-photon driven dissipative process which leads to the choice of four-component Schrodinger cat states as the logical qubit. Such a logical qubit can be protected against single-photon loss by continuous photon number parity measurements. Next, applying some specific Hamiltonians, we provide a set of universal quantum gates on the encoded qubits of each of the two schemes. In particular, we illustrate how these operations can be rendered fault-tolerant with respect to various decoherence channels of participating quantum systems. Finally, we also propose experimental schemes based on quantum superconducting circuits and inspired by methods used in Josephson parametric amplification, which should allow to achieve these driven dissipative processes along with the Hamiltonians ensuring the universal operations in an efficient manner.
315 citations
TL;DR: The Random Access Majorana Memory (RAMM) as discussed by the authors is a scalable circuit that can perform a joint parity measurement on Majorana fermions belonging to a selection of topological qubits.
Abstract: Majorana fermions hold promise for quantum computation, because their non-Abelian braiding statistics allows for topologically protected operations on quantum information. Topological qubits can be constructed from pairs of well-separated Majoranas in networks of nanowires. The coupling to a superconducting charge qubit in a transmission line resonator (transmon) permits braiding of Majoranas by external variation of magnetic fluxes. We show that readout operations can also be fully flux controlled, without requiring microscopic control over tunnel couplings. We identify the minimal circuit that can perform the initialization-braiding-measurement steps required to demonstrate non-Abelian statistics. We introduce the Random Access Majorana Memory (RAMM), a scalable circuit that can perform a joint parity measurement on Majoranas belonging to a selection of topological qubits. Such multiqubit measurements allow for the efficient creation of highly entangled states and simplify quantum error correction protocols by avoiding the need for ancilla qubits.
309 citations
01 Sep 2013
TL;DR: In this article, the authors introduce the concept of quantum error correction for quantum information processing and fault tolerance for holonomic quantum computation, including quantum dynamical decoupling and quantum convolutional codes.
Abstract: Prologue Preface Part I. Background: 1. Introduction to decoherence and noise in open quantum systems Daniel Lidar and Todd Brun 2. Introduction to quantum error correction Dave Bacon 3. Introduction to decoherence-free subspaces and noiseless subsystems Daniel Lidar 4. Introduction to quantum dynamical decoupling Lorenza Viola 5. Introduction to quantum fault tolerance Panos Aliferis Part II. Generalized Approaches to Quantum Error Correction: 6. Operator quantum error correction David Kribs and David Poulin 7. Entanglement-assisted quantum error-correcting codes Todd Brun and Min-Hsiu Hsieh 8. Continuous-time quantum error correction Ognyan Oreshkov Part III. Advanced Quantum Codes: 9. Quantum convolutional codes Mark Wilde 10. Non-additive quantum codes Markus Grassl and Martin Rotteler 11. Iterative quantum coding systems David Poulin 12. Algebraic quantum coding theory Andreas Klappenecker 13. Optimization-based quantum error correction Andrew Fletcher Part IV. Advanced Dynamical Decoupling: 14. High order dynamical decoupling Zhen-Yu Wang and Ren-Bao Liu 15. Combinatorial approaches to dynamical decoupling Martin Rotteler and Pawel Wocjan Part V. Alternative Quantum Computation Approaches: 16. Holonomic quantum computation Paolo Zanardi 17. Fault tolerance for holonomic quantum computation Ognyan Oreshkov, Todd Brun and Daniel Lidar 18. Fault tolerant measurement-based quantum computing Debbie Leung Part VI. Topological Methods: 19. Topological codes Hector Bombin 20. Fault tolerant topological cluster state quantum computing Austin Fowler and Kovid Goyal Part VII. Applications and Implementations: 21. Experimental quantum error correction Dave Bacon 22. Experimental dynamical decoupling Lorenza Viola 23. Architectures Jacob Taylor 24. Error correction in quantum communication Mark Wilde Part VIII. Critical Evaluation of Fault Tolerance: 25. Hamiltonian methods in QEC and fault tolerance Eduardo Novais, Eduardo Mucciolo and Harold Baranger 26. Critique of fault-tolerant quantum information processing Robert Alicki References Index.
306 citations
TL;DR: Here, a time-resolved, continuous parity measurement of two superconducting qubits is performed using the cavity in a three-dimensional circuit quantum electrodynamics architecture and phase-sensitive parametric amplification to produce entanglement by parity measurement reaching 88 per cent fidelity to the closest Bell state.
Abstract: A time-resolved, continuous parity measurement of two superconducting qubits in a three-dimensional circuit quantum electrodynamics architecture is reported; by further implementing feedback control, entanglement is generated ‘on demand’. In quantum computing, parity measurement projects a register of qubits to a state with an even or odd total number of excitations. Despite numerous proposals, realizing a parity meter that creates entanglement for both even and odd measurement results has remained an outstanding challenge. Here Leonardo DiCarlo and colleagues report the realization of a time-resolved, continuous parity measurement of two superconducting qubits in a three-dimensional circuit quantum electrodynamics architecture. By further implementing feedback control, entanglement generation can be achieved deterministically, or 'on demand'. The results provide key ingredients for active quantum error correction in the solid state. The stochastic evolution of quantum systems during measurement is arguably the most enigmatic feature of quantum mechanics. Measuring a quantum system typically steers it towards a classical state, destroying the coherence of an initial quantum superposition and the entanglement with other quantum systems. Remarkably, the measurement of a shared property between non-interacting quantum systems can generate entanglement, starting from an uncorrelated state. Of special interest in quantum computing is the parity measurement1, which projects the state of multiple qubits (quantum bits) to a state with an even or odd number of excited qubits. A parity meter must discern the two qubit-excitation parities with high fidelity while preserving coherence between same-parity states. Despite numerous proposals for atomic2, semiconducting1,3,4,5,6,7 and superconducting qubits8,9, realizing a parity meter that creates entanglement for both even and odd measurement results has remained an outstanding challenge. Here we perform a time-resolved, continuous parity measurement of two superconducting qubits using the cavity in a three-dimensional circuit quantum electrodynamics10,11 architecture and phase-sensitive parametric amplification12. Using postselection, we produce entanglement by parity measurement reaching 88 per cent fidelity to the closest Bell state. Incorporating the parity meter in a feedback-control loop, we transform the entanglement generation from probabilistic to fully deterministic, achieving 66 per cent fidelity to a target Bell state on demand. These realizations of a parity meter and a feedback-enabled deterministic measurement protocol provide key ingredients for active quantum error correction in the solid state13,14,15.
TL;DR: The derivation establishes a hierarchy of information quantities that can be used to investigate information theoretic tasks in the quantum domain: the one-shot entropies most accurately describe an operational quantity, yet they tend to be difficult to calculate for large systems.
Abstract: We consider two fundamental tasks in quantum information theory, data compression with quantum side information, as well as randomness extraction against quantum side information. We characterize these tasks for general sources using so-called one-shot entropies. These characterizations-in contrast to earlier results-enable us to derive tight second-order asymptotics for these tasks in the i.i.d. limit. More generally, our derivation establishes a hierarchy of information quantities that can be used to investigate information theoretic tasks in the quantum domain: The one-shot entropies most accurately describe an operational quantity, yet they tend to be difficult to calculate for large systems. We show that they asymptotically agree (up to logarithmic terms) with entropies related to the quantum and classical information spectrum, which are easier to calculate in the i.i.d. limit. Our technique also naturally yields bounds on operational quantities for finite block lengths.
TL;DR: The demonstration of an entangled steady state of two qubits represents a step towards dissipative state engineering, dissipative quantum computation and dissipative phase transitions and engineered coupling to the environment may be applied to a broad range of experimental systems to achieve desired quantum dynamics or steady states.
Abstract: Engineered dissipation is used to deterministically produce and stabilize entanglement between two trapped-ion quantum bits, independently of their initial states; the entanglement is stabilized even in the presence of experimental noise and decoherence. Entangled states are a key resource in fundamental quantum physics, quantum cryptography and quantum computation. It has been generally assumed that the creation of such states requires the avoidance of contact with a dissipative environment, and minimization of decoherence. Some studies have shown, however, that dissipative interactions can be used to preserve coherence, and in this issue of Nature two groups demonstrate this principle for continuously driven physical systems. Lin et al. use engineered dissipation to deterministically produce and stabilize entanglement between two trapped-ion qubits, independent of their initial state. Shankar et al. use an autonomous feedback scheme to counteract decoherence and demonstrate the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time. This approach may be applied to a broad range of experimental systems to achieve desired quantum dynamics or steady states. Entangled states are a key resource in fundamental quantum physics, quantum cryptography and quantum computation1. Introduction of controlled unitary processes—quantum gates—to a quantum system has so far been the most widely used method to create entanglement deterministically2. These processes require high-fidelity state preparation and minimization of the decoherence that inevitably arises from coupling between the system and the environment, and imperfect control of the system parameters. Here we combine unitary processes with engineered dissipation to deterministically produce and stabilize an approximate Bell state of two trapped-ion quantum bits (qubits), independent of their initial states. Compared with previous studies that involved dissipative entanglement of atomic ensembles3 or the application of sequences of multiple time-dependent gates to trapped ions4, we implement our combined process using trapped-ion qubits in a continuous time-independent fashion (analogous to optical pumping of atomic states). By continuously driving the system towards the steady state, entanglement is stabilized even in the presence of experimental noise and decoherence. Our demonstration of an entangled steady state of two qubits represents a step towards dissipative state engineering, dissipative quantum computation and dissipative phase transitions5,6,7. Following this approach, engineered coupling to the environment may be applied to a broad range of experimental systems to achieve desired quantum dynamics or steady states. Indeed, concurrently with this work, an entangled steady state of two superconducting qubits was demonstrated using dissipation8.
TL;DR: This work encoding in a single cavity mode, together with a protection protocol, significantly reduces the error rate due to photon loss and describes in detail how to implement these operations in a circuit quantum electrodynamics system.
Abstract: We propose to encode a quantum bit of information in a superposition of coherent states of an oscillator, with four different phases. Our encoding in a single cavity mode, together with a protection protocol, significantly reduces the error rate due to photon loss. This protection is ensured by an efficient quantum error correction scheme employing the nonlinearity provided by a single physical qubit coupled to the cavity. We describe in detail how to implement these operations in a circuit quantum electrodynamics system. This proposal directly addresses the task of building a hardware-efficient quantum memory and can lead to important shortcuts in quantum computing architectures.
TL;DR: The deterministic teleportation process succeeds with order unit probability for any input state, as it prepares maximally entangled two-qubit states as a resource and distinguish all Bell states in a single two- qubit measurement with high efficiency and high fidelity.
Abstract: Engineered macroscopic quantum systems based on superconducting electronic circuits are attractive for experimentally exploring diverse questions in quantum information science. At the current state of the art, quantum bits (qubits) are fabricated, initialized, controlled, read out and coupled to each other in simple circuits. This enables the realization of basic logic gates, the creation of complex entangled states and the demonstration of algorithms or error correction. Using different variants of low-noise parametric amplifiers, dispersive quantum non-demolition single-shot readout of single-qubit states with high fidelity has enabled continuous and discrete feedback control of single qubits. Here we realize full deterministic quantum teleportation with feed-forward in a chip-based superconducting circuit architecture. We use a set of two parametric amplifiers for both joint two-qubit and individual qubit single-shot readout, combined with flexible real-time digital electronics. Our device uses a crossed quantum bus technology that allows us to create complex networks with arbitrary connecting topology in a planar architecture. The deterministic teleportation process succeeds with order unit probability for any input state, as we prepare maximally entangled two-qubit states as a resource and distinguish all Bell states in a single two-qubit measurement with high efficiency and high fidelity. We teleport quantum states between two macroscopic systems separated by 6 mm at a rate of 10(4) s(-1), exceeding other reported implementations. The low transmission loss of superconducting waveguides is likely to enable the range of this and other schemes to be extended to significantly larger distances, enabling tests of non-locality and the realization of elements for quantum communication at microwave frequencies. The demonstrated feed-forward may also find application in error correction schemes.
TL;DR: This work demonstrates three-photon quantum operation of an integrated device containing three coupled interferometers, eight spatial modes and many classical and nonclassical interferences, and introduces a new scheme to verify quantum behaviour, using classically characterised device elements and hierarchies of photon correlation functions.
Abstract: Increasing the complexity of quantum photonic devices is essential for many optical information processing applications to reach a regime beyond what can be classically simulated, and integrated photonics has emerged as a leading platform for achieving this. Here we demonstrate three-photon quantum operation of an integrated device containing three coupled interferometers, eight spatial modes and many classical and nonclassical interferences. This represents a critical advance over previous complexities and the first on-chip nonclassical interference with more than two photonic inputs. We introduce a new scheme to verify quantum behaviour, using classically characterised device elements and hierarchies of photon correlation functions. We accurately predict the device’s quantum behaviour and show operation inconsistent with both classical and bi-separable quantum models. Such methods for verifying multiphoton quantum behaviour are vital for achieving increased circuit complexity. Our experiment paves the way for the next generation of integrated photonic quantum simulation and computing devices
TL;DR: In this article, the authors derived generalizations of the energy-time uncertainty relation for driven quantum systems using a geometric approach based on the Bures length between mixed quantum states, and obtained explicit expressions for the quantum speed limit time, valid for arbitrary initial and final quantum states and arbitrary unitary driving protocols.
Abstract: We derive generalizations of the energy–time uncertainty relation for driven quantum systems. Using a geometric approach based on the Bures length between mixed quantum states, we obtain explicit expressions for the quantum speed limit time, valid for arbitrary initial and final quantum states and arbitrary unitary driving protocols. Our results establish the fundamental limit on the rate of evolution of closed quantum systems.
TL;DR: A quantum receiver based on a novel adaptive measurement scheme and a high-bandwidth, high-detection-efficiency system for single-photon counting and an unconditionally discriminates between four nonorthogonal coherent states is presented.
Abstract: Researchers present a quantum receiver based on a novel adaptive measurement scheme and a high-bandwidth, high-detection-efficiency system for single-photon counting. The receiver unconditionally discriminates between four nonorthogonal coherent states with error probabilities 6 dB below the standard quantum limit for a wide range of input powers.
TL;DR: A general security analysis for TFQKD with binned measurements reveals a close connection with finite-dimensional QKD protocols and enables analysis of the effects of dark counts on the secure key size.
Abstract: We introduce a novel time-frequency quantum key distribution (TFQKD) scheme based on photon pairs entangled in these two conjugate degrees of freedom. The scheme uses spectral detection and phase modulation to enable measurements in the temporal basis by means of time-to-frequency conversion. This allows large-alphabet encoding to be implemented with realistic components. A general security analysis for TFQKD with binned measurements reveals a close connection with finite-dimensional QKD protocols and enables analysis of the effects of dark counts on the secure key size.
TL;DR: A way is shown to extend the techniques originally proposed in Demkowicz-Dobrza?ski et?al, so that they can be efficiently applied not only in the asymptotic but also in the finite number of particles regime, where quantum enhancement amounts to a constant factor improvement.
Abstract: Quantum metrology offers enhanced performance in experiments on topics such as gravitational wave-detection, magnetometry or atomic clock frequency calibration. The enhancement, however, requires a delicate tuning of relevant quantum features, such as entanglement or squeezing. For any practical application, the inevitable impact of decoherence needs to be taken into account in order to correctly quantify the ultimate attainable gain in precision. We compare the applicability and the effectiveness of various methods of calculating the ultimate precision bounds resulting from the presence of decoherence. This allows us to place a number of seemingly unrelated concepts into a common framework and arrive at an explicit hierarchy of quantum metrological methods in terms of the tightness of the bounds they provide. In particular, we show a way to extend the techniques originally proposed in Demkowicz-Dobrza?ski et?al (2012 Nature Commun. 3 1063), so that they can be efficiently applied not only in the asymptotic but also in the finite number of particles regime. As a result, we obtain a simple and direct method, yielding bounds that interpolate between the quantum enhanced scaling characteristic for a small number of particles and the asymptotic regime, where quantum enhancement amounts to a constant factor improvement. Methods are applied to numerous models, including noisy phase and frequency estimation, as well as the estimation of the decoherence strength itself.
TL;DR: In this article, the authors developed an experimental scheme based on a continuous-wave (cw) laser for generating arbitrary superpositions of photon number states, which are fully compatible with developed quantum teleportation and measurement-based quantum operations with cw lasers.
Abstract: We develop an experimental scheme based on a continuous-wave (cw) laser for generating arbitrary superpositions of photon number states. In this experiment, we successfully generate superposition states of zero to three photons, namely advanced versions of superpositions of two and three coherent states. They are fully compatible with developed quantum teleportation and measurement-based quantum operations with cw lasers. Due to achieved high detection efficiency, we observe, without any loss correction, multiple areas of negativity of Wigner function, which confirm strongly nonclassical nature of the generated states.
TL;DR: A protocol for testing a quantum computer using minimum quantum resources has been proposed and demonstrated and Alice can verify the result of a quantum computation that she has delegated to Bob without using a quantumComputer.
Abstract: Can Alice verify the result of a quantum computation that she has delegated to Bob without using a quantum computer? Now she can. A protocol for testing a quantum computer using minimum quantum resources has been proposed and demonstrated.
TL;DR: A quantum algorithm and a scalable quantum circuit design which approximates the solution of the Poisson equation on a grid with error e and produces a quantum state encoding the solution.
Abstract: The Poisson equation occurs in many areas of science and engineering. Here we focus on its numerical solution for an equation in d dimensions. In particular we present a quantum algorithm and a scalable quantum circuit design which approximates the solution of the Poisson equation on a grid with error e. We assume we are given a superposition of function evaluations of the right-hand side of the Poisson equation. The algorithm produces a quantum state encoding the solution. The number of quantum operations and the number of qubits used by the circuit is almost linear in d and polylog in e−1. We present quantum circuit modules together with performance guarantees which can also be used for other problems.
TL;DR: This work presents a scheme for linear optical quantum computing using time-bin-encoded qubits in a single spatial mode, providing a sufficient set of operations for universal quantum computing with the Knill-Laflamme-Milburn scheme.
Abstract: We present a scheme for linear optical quantum computing using time-bin-encoded qubits in a single spatial mode. We show methods for single-qubit operations and heralded controlled-phase (cphase) gates, providing a sufficient set of operations for universal quantum computing with the Knill-Laflamme-Milburn [Nature (London) 409, 46 (2001)] scheme. Our protocol is suited to currently available photonic devices and ideally allows arbitrary numbers of qubits to be encoded in the same spatial mode, demonstrating the potential for time-frequency modes to dramatically increase the quantum information capacity of fixed spatial resources. As a test of our scheme, we demonstrate the first entirely single spatial mode implementation of a two-qubit quantum gate and show its operation with an average fidelity of $0.84\ifmmode\pm\else\textpm\fi{}0.07$.
TL;DR: In this article, the authors presented deterministic schemes to construct universal quantum gates, that is, controlled-not, three-qubit Toffoli and Fredkin gates, between flying photon qubits and stationary electron-spin qubits assisted by quantum dots inside double-sided optical microcavities.
Abstract: We present some deterministic schemes to construct universal quantum gates, that is, controlled- not, three-qubit Toffoli, and Fredkin gates, between flying photon qubits and stationary electron-spin qubits assisted by quantum dots inside double-sided optical microcavities. The control qubit of our gates is encoded on the polarization of the moving single photon and the target qubits are encoded on the confined electron spins in quantum dots inside optical microcavities. Our schemes for these universal quantum gates on a hybrid system have some advantages. First, all the gates are accomplished with a success probability of 100$%$ in principle. Second, our schemes require no additional qubits. Third, the control qubits of the gates are easily manipulated and the target qubits are perfect for storage and processing. Fourth, the gates do not require that the transmission for the uncoupled cavity is balanceable with the reflectance for the coupled cavity, in order to get a high fidelity. Fifth, the devices for the three universal gates work in both the weak coupling and the strong coupling regimes, and they are feasible in experiment.
TL;DR: In this article, a coherent two-mode amplifier for photonic qubits coherently encoded across two optical modes is demonstrated, which enables a fivefold increase in the transmission fidelity of the polarization state of a single photon.
Abstract: Long-distance quantum communication is limited by optical absorption and scattering. A noiseless amplifier for photonic qubits coherently encoded across two optical modes is now demonstrated, which could combat this negative effect. The method enabled a fivefold increase in the transmission fidelity of the polarization state of a single photon. Photons are the best long-range carriers of quantum information, but the unavoidable absorption and scattering in a transmission channel places a serious limitation on viable communication distances. Signal amplification will therefore be an essential feature of quantum technologies, with direct applications to quantum communication, metrology and fundamental tests of quantum theory. Non-deterministic noiseless amplification of a single mode1,2,3,4,5 can circumvent the challenges related to amplifying a quantum signal, such as the no-cloning theorem6 and the minimum noise cost for deterministic quantum state amplification7. However, existing devices are not suitable for amplifying the fundamental optical quantum information carrier: a qubit coherently encoded across two optical modes. Here, we construct a coherent two-mode amplifier to demonstrate the first heralded noiseless linear amplification of a qubit encoded in the polarization state of a single photon. In doing so, we increase the transmission fidelity of a realistic qubit channel by up to a factor of five. Qubit amplifiers promise to extend the range of secure quantum communication8,9 and other quantum information science and technology protocols.
TL;DR: In this paper, a deterministic hyper-controlled-not (hyper-CNOT) gate operating in both the spatial mode and polarization DOF for a photon pair was proposed.
Abstract: To date, all work concerning the construction of quantum logic gates, an essential part of quantum computing, has focused on operating in one degree of freedom (DOF) for quantum systems. Here, we investigate the possibility of achieving scalable photonic quantum computing based on two DOFs for quantum systems. We construct a deterministic hyper-controlled-not (hyper-CNOT) gate operating in both the spatial mode and polarization DOFs for a photon pair simultaneously, using the giant optical Faraday rotation induced by a single-electron spin in a quantum dot inside a one-side optical microcavity as a result of cavity quantum electrodynamics. With this hyper-CNOT gate and linear optical elements, two-photon four-qubit cluster entangled states can be prepared and analyzed, which give an application to manipulate more information with less resources. We analyze the experimental feasibility of this hyper-CNOT gate and show that it can be implemented with current technology.
17 Jun 2013
TL;DR: In this paper, an attainable upper bound on the quantum speed limit of general physical processes based on quantum Fisher information has been presented, which allows one to tackle experimentally more realistic open-system dynamics.
Abstract: We present an attainable upper bound on the quantum speed limit of general physical processes based on the quantum Fisher information. This result allows one to tackle experimentally more realistic open-system dynamics.
TL;DR: In this paper, the decays of the quantum correlation as a function of the decoherence parameters were analyzed for the one-norm geometric quantum discord under Markovian local noise.
Abstract: Geometric quantum discord is a well-defined measure of quantum correlation if Schatten one-norm (trace norm) is adopted as a distance measure. Here, we analytically investigate the dynamical behavior of the one-norm geometric quantum discord under the effect of decoherence. By starting from arbitrary Bell-diagonal mixed states under Markovian local noise, we provide the decays of the quantum correlation as a function of the decoherence parameters. In particular, we show that the one-norm geometric discord exhibits the possibility of double sudden changes and freezing behavior during its evolution. For nontrivial Bell-diagonal states under simple Markovian channels, these are new features that are in contrast with the Schatten two-norm (Hilbert-Schmidt) geometric discord. The necessary and sufficient conditions for double sudden changes as well as their exact locations in terms of decoherence probabilities are provided. Moreover, we illustrate our results by investigating decoherence in quantum spin chains in the thermodynamic limit.
TL;DR: It is shown that high gate fidelity is possible, given recent dramatic experimental progress in superconducting circuits and photonic-crystal waveguides.
Abstract: We propose a new scheme for quantum computation using flying qubits---propagating photons in a one-dimensional waveguide interacting with matter qubits. Photon-photon interactions are mediated by the coupling to a four-level system, based on which photon-photon $\ensuremath{\pi}$-phase gates (controlled-not) can be implemented for universal quantum computation. We show that high gate fidelity is possible, given recent dramatic experimental progress in superconducting circuits and photonic-crystal waveguides. The proposed system can be an important building block for future on-chip quantum networks.