Showing papers on "Quantum error correction published in 2010"
TL;DR: In this paper, a pedagogical introduction to the physics of quantum noise and its connections to quantum measurement and quantum amplification is given, and the basics of weak continuous measurements are described.
Abstract: The topic of quantum noise has become extremely timely due to the rise of quantum information physics and the resulting interchange of ideas between the condensed matter and atomic, molecular, optical--quantum optics communities. This review gives a pedagogical introduction to the physics of quantum noise and its connections to quantum measurement and quantum amplification. After introducing quantum noise spectra and methods for their detection, the basics of weak continuous measurements are described. Particular attention is given to the treatment of the standard quantum limit on linear amplifiers and position detectors within a general linear-response framework. This approach is shown how it relates to the standard Haus-Caves quantum limit for a bosonic amplifier known in quantum optics and its application to the case of electrical circuits is illustrated, including mesoscopic detectors and resonant cavity detectors.
1,581 citations
TL;DR: A necessary and sufficient condition for the existence of nonzero quantum discord for any dimensional bipartite states is obtained, and a geometrical way of quantifying quantum discord is proposed.
Abstract: Quantum discord characterizes "nonclassicality" of correlations in quantum mechanics. It has been proposed as the key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. We obtain a necessary and sufficient condition for the existence of nonzero quantum discord for any dimensional bipartite states. This condition is easily experimentally implementable. Based on this, we propose a geometrical way of quantifying quantum discord. For two qubits this results in a closed form of expression for discord. We apply our results to the model of deterministic quantum computation with one qubit, showing that quantum discord is unlikely to be the reason behind its speedup.
1,101 citations
TL;DR: In this article, the authors proposed a universal quantum simulator for spin models with high-order Rydberg atoms, including higher order spin-liquid phases, which can be used to simulate other quantum systems with many-body interactions and strongly correlated ground states.
Abstract: A universal quantum simulator is a controlled quantum device that reproduces the dynamics of any other many-particle quantum system with short-range interactions. This dynamics can refer to both coherent Hamiltonian and dissipative open-system evolution. Here we propose that laser-excited Rydberg atoms in large-spacing optical or magnetic lattices provide an efficient implementation of a universal quantum simulator for spin models involving n-body interactions, including such of higher order. This would allow the simulation of Hamiltonians of exotic spin models involving n-particle constraints, such as the Kitaev toric code, colour code and lattice gauge theories with spin-liquid phases. In addition, our approach provides the ingredients for dissipative preparation of entangled states based on engineering n-particle reservoir couplings. The basic building blocks of our architecture are efficient and high-fidelity n-qubit entangling gates using auxiliary Rydberg atoms, including a possible dissipative time step through optical pumping. This enables mimicking the time evolution of the system by a sequence of fast, parallel and high-fidelity n-particle coherent and dissipative Rydberg gates. Building on recent experimental advances in controlling individual Rydberg atoms, theoretical work proposes a ‘Rydberg quantum simulator’. Such a system would be suitable for efficiently simulating other quantum systems with many-body interactions and strongly correlated ground states.
721 citations
TL;DR: Single-shot, projective measurement of a single nuclear spin in diamond is demonstrated using a quantum nondemolition measurement scheme, which allows real-time observation of an individual nuclear spin’s state in a room-temperature solid.
Abstract: Projective measurement of single electron and nuclear spins has evolved from a gedanken experiment to a problem relevant for applications in atomic-scale technologies like quantum computing Although several approaches allow for detection of a spin of single atoms and molecules, multiple repetitions of the experiment that are usually required for achieving a detectable signal obscure the intrinsic quantum nature of the spin's behavior We demonstrated single-shot, projective measurement of a single nuclear spin in diamond using a quantum nondemolition measurement scheme, which allows real-time observation of an individual nuclear spin's state in a room-temperature solid Such an ideal measurement is crucial for realization of, for example, quantum error correction protocols in a quantum register
585 citations
TL;DR: The area of quantum communication complexity is reviewed, and it is shown how it connects the foundational physics questions regarding non-locality with those of communication complexity studied in theoretical computer science.
Abstract: Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. Until recently the common notion of computing was based on classical mechanics, and did not take into account all the possibilities that physically-realizable computing devices offer in principle. The field gained momentum after Peter Shor developed an efficient algorithm for factoring numbers, demonstrating the potential computing powers that quantum computing devices can unleash. In this review we study the information counterpart of computing. It was realized early on by Holevo, that quantum bits, the quantum mechanical counterpart of classical bits, cannot be used for efficient transformation of information, in the sense that arbitrary k-bit messages can not be compressed into messages of k − 1 qubits. The abstract form of the distributed computing setting is called communication complexity. It studies the amount of information, in terms of bits or in our case qubits, that two spatially separated computing devices need to exchange in order to perform some computational task. Surprisingly, quantum mechanics can be used to obtain dramatic advantages for such tasks. We review the area of quantum communication complexity, and show how it connects the foundational physics questions regarding non-locality with those of communication complexity studied in theoretical computer science. The first examples exhibiting the advantage of the use of qubits in distributed information-processing tasks were based on non-locality tests. However, by now the field has produced strong and interesting quantum protocols and algorithms of its own that demonstrate that entanglement, although it cannot be used to replace communication, can be used to reduce the communication exponentially. In turn, these new advances yield a new outlook on the foundations of physics, and could even yield new proposals for experiments that test the foundations of physics.
572 citations
TL;DR: Deterministic production of three-qubit Greenberger–Horne–Zeilinger (GHZ) states with fidelity of 88 per cent is demonstrated, demonstrating the first step of basic quantum error correction, namely the encoding of a logical qubit into a manifold of GHZ-like states using a repetition code.
Abstract: Quantum entanglement, in which the states of two or more particles are inextricably linked, is a key requirement for quantum computation. In superconducting devices, two-qubit entangled states have been used to implement simple quantum algorithms. The availability of three-qubit states, which can be entangled in two fundamentally different ways (the GHZ and W states), would be a significant advance because they should make it possible to perform error correction and infer scalability to the higher numbers of qubits needed for a practical quantum-information-processing device. Two groups now report the generation of three-qubit entanglement. John Martinis and colleagues create and measure both GHZ and W-type states. Leonardo DiCarlo and colleagues generate the GHZ state and demonstrate the first step of basic quantum error correction by encoding a logical qubit into a manifold of GHZ-like states using a repetition code. Quantum entanglement is a key resource for technologies such as quantum communication and computation. A major question for solid-state quantum information processing is whether an engineered system can display the three-qubit entanglement necessary for quantum error correction. A positive answer to this question is now provided. A circuit quantum electrodynamics device has been used to demonstrate deterministic production of three-qubit entangled states and the first step of basic quantum error correction. Traditionally, quantum entanglement has been central to foundational discussions of quantum mechanics. The measurement of correlations between entangled particles can have results at odds with classical behaviour. These discrepancies grow exponentially with the number of entangled particles1. With the ample experimental2,3,4 confirmation of quantum mechanical predictions, entanglement has evolved from a philosophical conundrum into a key resource for technologies such as quantum communication and computation5. Although entanglement in superconducting circuits has been limited so far to two qubits6,7,8,9, the extension of entanglement to three, eight and ten qubits has been achieved among spins10, ions11 and photons12, respectively. A key question for solid-state quantum information processing is whether an engineered system could display the multi-qubit entanglement necessary for quantum error correction, which starts with tripartite entanglement. Here, using a circuit quantum electrodynamics architecture13,14, we demonstrate deterministic production of three-qubit Greenberger–Horne–Zeilinger (GHZ) states15 with fidelity of 88 per cent, measured with quantum state tomography. Several entanglement witnesses detect genuine three-qubit entanglement by violating biseparable bounds by 830 ± 80 per cent. We demonstrate the first step of basic quantum error correction, namely the encoding of a logical qubit into a manifold of GHZ-like states using a repetition code. The integration of this encoding with decoding and error-correcting steps in a feedback loop will be the next step for quantum computing with integrated circuits.
554 citations
Book•
21 Apr 2010TL;DR: The theory of quantum computation can be constructed from the abstract study of anyonic systems as discussed by the authors, which can be seen as a catch-all for several models of computation based on a theoretical ability to manufacture, manipulate and measure quan- tum states.
Abstract: The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones poly- nomial and arise in Witten-Chern-Simons theory. The braiding and fusion of anyonic excitations in quantum Hall electron liquids and 2D-magnets are modeled by modular functors, opening a new possi- bility for the realization of quantum computers. The chief advantage of anyonic computation would be physical error correction: An error rate scaling like e −αl , where l is a length scale, and α is some posi- tive constant. In contrast, the "presumptive" qubit-model of quantum computation, which repairs errors combinatorically, requires a fantas- tically low initial error rate (about 10 −4 ) before computation can be stabilized. Quantum computation is a catch-all for several models of computation based on a theoretical ability to manufacture, manipulate and measure quan- tum states. In this context, there are three areas where remarkable algo- rithms have been found: searching a data base (15), abelian groups (factor- ing and discrete logarithm) (19 ,27), and simulating physical systems (5 ,21). To this list we may add a fourth class of algorithms which yield approximate,
505 citations
TL;DR: In this article, the authors show that the discrete-time quantum walk is able to implement the same universal gate set and thus both discrete and continuous time quantum walks are computational primitives.
Abstract: A proof that continuous-time quantum walks are universal for quantum computation, using unweighted graphs of low degree, has recently been presented by A. M. Childs [Phys. Rev. Lett. 102, 180501 (2009)]. We present a version based instead on the discrete-time quantum walk. We show that the discrete-time quantum walk is able to implement the same universal gate set and thus both discrete and continuous-time quantum walks are computational primitives. Additionally, we give a set of components on which the discrete-time quantum walk provides perfect state transfer.
471 citations
Abstract: Dakic, Vedral, and Brukner [arXiv:1004.0190 (2010)] introduced a geometric measure of quantum discord and derived an explicit formula for any two-qubit state. This measure is significant in capturing quantum correlations from a geometric perspective. In this brief report, we evaluate the geometric measure of quantum discord for an arbitrary state and obtain an explicit and tight lower bound. Furthermore, we reveal an intrinsic feature of geometric measure of quantum discord by showing that it actually coincides with a simpler quantity based on von Neumann measurements.
457 citations
TL;DR: The time-dependent density matrix renormalization group with techniques from the theory of orthogonal polynomials are combined to provide an efficient method for simulating open quantum systems, including spin-boson models and their generalizations to multicomponent systems.
Abstract: Multicomponent quantum systems in strong interaction with their environment are receiving increasing attention due to their importance in a variety of contexts, ranging from solid state quantum information processing to the quantum dynamics of biomolecular aggregates. Unfortunately, these systems are difficult to simulate as the system-bath interactions cannot be treated perturbatively and standard approaches are invalid or inefficient. Here we combine the time-dependent density matrix renormalization group with techniques from the theory of orthogonal polynomials to provide an efficient method for simulating open quantum systems, including spin-boson models and their generalizations to multicomponent systems.
416 citations
TL;DR: The dynamics of different kinds of bipartite correlations in an all-optical experimental setup are investigated and quantum correlation is observed to be larger than classical correlation, which disproves the early conjecture that classical correlation is always greater than quantum correlation.
Abstract: It is well known that many operations in quantum information processing depend largely on a special kind of quantum correlation, that is, entanglement However, there are also quantum tasks that display the quantum advantage without entanglement Distinguishing classical and quantum correlations in quantum systems is therefore of both fundamental and practical importance In consideration of the unavoidable interaction between correlated systems and the environment, understanding the dynamics of correlations would stimulate great interest In this study, we investigate the dynamics of different kinds of bipartite correlations in an all-optical experimental setup The sudden change in behaviour in the decay rates of correlations and their immunity against certain decoherences are shown Moreover, quantum correlation is observed to be larger than classical correlation, which disproves the early conjecture that classical correlation is always greater than quantum correlation Our observations may be important for quantum information processing
TL;DR: In this paper, a platform based on spin qubits connected through arrays of nanoelectromechanical resonators is proposed to reconcile the conflicting requirements of information leakage in a quantum computer.
Abstract: In a quantum computer, the data carriers (or qubits) must be well isolated from their environment to avoid information leakage. At the same time they have to interact with one another to process information. A proposed platform based on spin qubits connected through arrays of nanoelectromechanical resonators should be able to reconcile these conflicting requirements.
TL;DR: A method to take into account the quantum decoherence effect in a surface hopping framework by evaluating the overlap between frozen Gaussian wavepackets, the time evolution of which is obtained in an approximate way.
Abstract: In this paper we set up a method called overlap decoherence correction (ODC) to take into account the quantum decoherence effect in a surface hopping framework. While keeping the standard surface hopping approach based on independent trajectories, our method allows to account for quantum decoherence by evaluating the overlap between frozen Gaussian wavepackets, the time evolution of which is obtained in an approximate way. The ODC scheme mainly depends on the parameter σ, which is the Gaussian width of the wavepackets. The performance of the ODC method is tested versus full quantum calculations on three model systems, and by comparison with full multiple spawning (FMS) results for the S(1)→S(0) decay in the azobenzene molecule.
Book•
31 May 2010TL;DR: In this paper, the authors describe the techniques that are likely to be used in implementing optical quantum information processors, including single photons and linear optics, optically controlled atoms and solid state systems, atomic ensembles, and optical continuous variables.
Abstract: Quantum information processing offers fundamental improvements over classical information processing, such as computing power, secure communication, and high-precision measurements. However, the best way to create practical devices is not yet known. This textbook describes the techniques that are likely to be used in implementing optical quantum information processors. After developing the fundamental concepts in quantum optics and quantum information theory, the book shows how optical systems can be used to build quantum computers according to the most recent ideas. It discusses implementations based on single photons and linear optics, optically controlled atoms and solid-state systems, atomic ensembles, and optical continuous variables. This book is ideal for graduate students beginning research in optical quantum information processing. It presents the most important techniques of the field using worked examples and over 120 exercises.
TL;DR: In this article, a superconducting chip containing a regular array of flux qubits, tunable interqubit inductive couplers, an XY-addressable readout system, on-chip programmable magnetic memory, and a sparse network of analog control lines has been studied.
Abstract: A superconducting chip containing a regular array of flux qubits, tunable interqubit inductive couplers, an XY-addressable readout system, on-chip programmable magnetic memory, and a sparse network of analog control lines has been studied. The architecture of the chip and the infrastructure used to control it were designed to facilitate the implementation of an adiabatic quantum optimization algorithm. The performance of an eight-qubit unit cell on this chip has been characterized by measuring its success in solving a large set of random Ising spin-glass problem instances as a function of temperature. The experimental data are consistent with the predictions of a quantum mechanical model of an eight-qubit system coupled to a thermal environment. These results highlight many of the key practical challenges that we have overcome and those that lie ahead in the quest to realize a functional large-scale adiabatic quantum information processor.
TL;DR: This article reviews the current state of quantum algorithms, focusing on algorithms with superpolynomial speedup over classical computation and, in particular, on problems with an algebraic flavor.
Abstract: Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article reviews the current state of quantum algorithms, focusing on algorithms with superpolynomial speedup over classical computation and, in particular, on problems with an algebraic flavor.
TL;DR: In this paper, the authors demonstrate a clock input state with spectroscopic sensitivity 3.0(8) dB beyond the standard quantum limit, and compare the resulting reduction of quantum projection noise with the concomitant reduction of coherence.
Abstract: We generate entangled states of an ensemble of $5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ $^{87}\mathrm{Rb}$ atoms by optical quantum nondemolition measurement. The resonator-enhanced measurement leaves the atomic ensemble, prepared in a superposition of hyperfine clock levels, in a squeezed spin state. By comparing the resulting reduction of quantum projection noise [up to 8.8(8) dB] with the concomitant reduction of coherence, we demonstrate a clock input state with spectroscopic sensitivity 3.0(8) dB beyond the standard quantum limit.
TL;DR: In this article, a superconducting circuit was used to investigate microwave photons trapped in a cavity, and the measurement answers the question: are there exactly N photons in the cavity?
Abstract: Quantum non-demolition (QND) measurements interrogate a quantum state without disturbing it. A QND scheme that uses a superconducting circuit to investigate microwave photons trapped in a cavity is now shown. The measurement answers the question: are there exactly N photons in the cavity?
18 Feb 2010
TL;DR: In this article, the system-reservoir dynamics of classical and quantum correlations in the decoherence phenomenon within a two-qubit composite system interacting with two independent environments are examined.
Abstract: We examine the system-reservoir dynamics of classical and quantum correlations in the decoherence phenomenon within a two-qubit composite system interacting with two independent environments. The most common noise channels (amplitude damping, phase damping, bit flip, bit-phase flip, and phase flip) are analyzed. By analytical and numerical analyses we find that, contrary to what is usually stated in the literature, decoherence may occur without entanglement between the system and the environment. We also show that, in some cases, the bipartite quantum correlation initially present in the system is completely evaporated and not transferred to the environments.
TL;DR: In this paper, the authors illustrate the power of the Positive Operator Valued Measures (POVM) concept on examples relevant to applications in quantum cryptography and give a brief introduction to the quantum theory of measurements, including generalized measurements.
Abstract: In quantum information processing and quantum computing protocols the carrier of information is a quantum system and information is encoded in the state of a quantum system. After processing the information it has to be read out what is equivalent to determining the final state of the system. When the possible final states are not orthogonal this is a highly nontrivial task that constitutes the general area of what is known as quantum state discrimination. It consists in finding measurement schemes that, according to some figure of merit, will determine the state of the system. Optimized measurement schemes often lead to generalized measurements (Positive Operator Valued Measures [POVMs]). In this tutorial review we illustrate the power of the POVM concept on examples relevant to applications in quantum cryptography. In order to keep the flow of the presentation we give a brief introduction to the quantum theory of measurements, including generalized measurements (POVMs), in the Appendices.
TL;DR: It turns out that due to a phenomenon similar to Anderson localization, exponentially small gaps appear close to the end of the adiabatic algorithm for large random instances of NP-complete problems, which implies that unfortunately, adiABatic quantum optimization fails: the system gets trapped in one of the numerous local minima.
Abstract: Understanding NP-complete problems is a central topic in computer science (NP stands for nondeterministic polynomial time). This is why adiabatic quantum optimization has attracted so much attention, as it provided a new approach to tackle NP-complete problems using a quantum computer. The efficiency of this approach is limited by small spectral gaps between the ground and excited states of the quantum computer’s Hamiltonian. We show that the statistics of the gaps can be analyzed in a novel way, borrowed from the study of quantum disordered systems in statistical mechanics. It turns out that due to a phenomenon similar to Anderson localization, exponentially small gaps appear close to the end of the adiabatic algorithm for large random instances of NP-complete problems. This implies that unfortunately, adiabatic quantum optimization fails: The system gets trapped in one of the numerous local minima.
TL;DR: In this article, the authors present an intrinsically stable, deterministic implementation of discrete quantum walks with single photons in space, and explore the quantum-to-classical transition by introducing tunable decoherence.
Abstract: Quantum walks have a host of applications, ranging from quantum computing to the simulation of biological systems. We present an intrinsically stable, deterministic implementation of discrete quantum walks with single photons in space. The number of optical elements required scales linearly with the number of steps. We measure walks with up to 6 steps and explore the quantum-to-classical transition by introducing tunable decoherence. Finally, we also investigate the effect of absorbing boundaries and show that decoherence significantly affects the probability of absorption.
TL;DR: A layered quantum computer architecture is developed, which is a systematic framework for tackling the individual challenges of developing a quantum computer while constructing a cohesive device design and finding that the quantum dot architecture could solve such problems on the timescale of days.
Abstract: We develop a layered quantum computer architecture, which is a systematic framework for tackling the individual challenges of developing a quantum computer while constructing a cohesive device design. We discuss many of the prominent techniques for implementing circuit-model quantum computing and introduce several new methods, with an emphasis on employing surface code quantum error correction. In doing so, we propose a new quantum computer architecture based on optical control of quantum dots. The timescales of physical hardware operations and logical, error-corrected quantum gates differ by several orders of magnitude. By dividing functionality into layers, we can design and analyze subsystems independently, demonstrating the value of our layered architectural approach. Using this concrete hardware platform, we provide resource analysis for executing fault-tolerant quantum algorithms for integer factoring and quantum simulation, finding that the quantum dot architecture we study could solve such problems on the timescale of days.
TL;DR: The three-spin qubit was designed to allow all operations for full qubit control to be tuned via nearest-neighbor exchange interaction as discussed by the authors, and the theory of the exchange-only qubit is developed and it is shown that initialization of only two spins suffices for operation.
Abstract: Initialization, two-spin coherent manipulation, and readout of a three-spin qubit are demonstrated using a few-electron triple quantum dot. The three-spin qubit is designed to allow all operations for full qubit control to be tuned via nearest-neighbor exchange interaction. Fast readout of charge states takes advantage of multiplexed reflectometry. Decoherence measured in a two-spin subspace is found to be consistent with predictions based on gate voltage noise with a uniform power spectrum. The theory of the exchange-only qubit is developed and it is shown that initialization of only two spins suffices for operation. Requirements for full multiqubit control using only exchange and electrostatic interactions are outlined.
TL;DR: In this paper, the authors show that qubit decoherence due to zero-temperature energy relaxation can be almost completely suppressed by using the quantum uncollapsing (measurement reversal) procedure.
Abstract: We show that qubit decoherence due to zero-temperature energy relaxation can be almost completely suppressed by using the quantum uncollapsing (measurement reversal) procedure. To protect a qubit state, a partial quantum measurement moves it toward the ground state, where it is kept during the storage period, while the second partial measurement restores the initial state. This procedure preferentially selects the cases without energy decay events. Stronger decoherence suppression requires smaller selection probability; a desired point in this trade-off can be chosen by varying the measurement strength. The experiment can be realized in a straightforward way using the superconducting phase qubit.
TL;DR: Borders are proved on the one-shot quantum capacity of an arbitrary channel, which allows us to compute the quantumcapacity of a channel with arbitrarily correlated noise, in the limit of asymptotically many uses of the channel.
Abstract: We study optimal rates for quantum communication over a single use of a channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. The corresponding capacity is often referred to as the one-shot quantum capacity. In this paper, we prove bounds on the one-shot quantum capacity of an arbitrary channel. This allows us to compute the quantum capacity of a channel with arbitrarily correlated noise, in the limit of asymptotically many uses of the channel. In the memoryless case, we explicitly show that our results reduce to known expressions for the quantum capacity.
TL;DR: In this paper, the authors describe a theoretical mechanism that may ensure high-fidelity entanglement of photons, and thus could be used to construct a practical quantum repeater The communication rate is shown to be a function of the maximum distance between any two adjacent quantum repeaters, rather than of the entire length of the network.
Abstract: Researchers describe a theoretical mechanism that may ensure high-fidelity entanglement of photons, and thus could be used to construct a practical quantum repeater The communication rate is shown to be a function of the maximum distance between any two adjacent quantum repeaters, rather than of the entire length of the network
TL;DR: Using a flow chart representation of quantum optomechanical dynamics, coherent quantum-noise-cancellation schemes are designed that can eliminate the backaction noise induced by radiation pressure at all frequencies and thus overcome the standard quantum limit of force sensing.
Abstract: Using a flow chart representation of quantum optomechanical dynamics, we design coherent quantum-noise-cancellation schemes that can eliminate the backaction noise induced by radiation pressure at all frequencies and thus overcome the standard quantum limit of force sensing. The proposed schemes can be regarded as novel examples of coherent feedforward quantum control.
TL;DR: The first experimental demonstration of quantum state tomography of two-qubit polarization states to take advantage of mutually unbiased bases is presented and improved state estimation as compared to standard measurement strategies is demonstrated.
Abstract: When used in quantum state estimation, projections onto mutually unbiased bases have the ability to maximize information extraction per measurement and to minimize redundancy. We present the first experimental demonstration of quantum state tomography of two-qubit polarization states to take advantage of mutually unbiased bases. We demonstrate improved state estimation as compared to standard measurement strategies and discuss how this can be understood from the structure of the measurements we use. We experimentally compared our method to the standard state estimation method for three different states and observe that the infidelity was up to 1.84 ± 0.06 times lower by using our technique than it was by using standard state estimation methods.
TL;DR: This work proposes an approach to quantum error correction based on coding and continuous syndrome readout via scattering of coherent probe fields, in which the usual steps of measurement and discrete restoration are replaced by direct physical processing of the probe beams and coherent feedback to the register qubits.
Abstract: We propose an approach to quantum error correction based on coding and continuous syndrome readout via scattering of coherent probe fields, in which the usual steps of measurement and discrete restoration are replaced by direct physical processing of the probe beams and coherent feedback to the register qubits. Our approach is well matched to physical implementations that feature solid-state qubits embedded in planar electromagnetic circuits, providing an autonomous and "on-chip" quantum memory design requiring no external clocking or control logic.