Quantum Error Correction
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.
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TL;DR: In this article, the relation between error correction and the concept of two-dimensional topological order in many-body physics is reviewed. And the authors show that certain multiqubit entangled states are well protected from common forms of decoherence as the quantum information is hidden in inherently nonlocal degrees of freedom.
Abstract: It may seem inevitable that highly entangled quantum states are susceptible to disturbance through interaction with a decohering environment. However, certain multiqubit entangled states are well protected from common forms of decoherence as the quantum information is hidden in inherently nonlocal degrees of freedom. This review shows that this robustness is enabled by specific measurements on subsets of qubits, implementing a quantum version of an error correction process. Beginning with the basics, the latest understanding of the relation between this form of error correction and the concept of two-dimensional topological order in many-body physics is reviewed.
956 citations
TL;DR: This review presents strategies employed to construct quantum algorithms for quantum chemistry, with the goal that quantum computers will eventually answer presently inaccessible questions, for example, in transition metal catalysis or important biochemical reactions.
Abstract: One of the most promising suggested applications of quantum computing is solving classically intractable chemistry problems. This may help to answer unresolved questions about phenomena such as high temperature superconductivity, solid-state physics, transition metal catalysis, and certain biochemical reactions. In turn, this increased understanding may help us to refine, and perhaps even one day design, new compounds of scientific and industrial importance. However, building a sufficiently large quantum computer will be a difficult scientific challenge. As a result, developments that enable these problems to be tackled with fewer quantum resources should be considered important. Driven by this potential utility, quantum computational chemistry is rapidly emerging as an interdisciplinary field requiring knowledge of both quantum computing and computational chemistry. This review provides a comprehensive introduction to both computational chemistry and quantum computing, bridging the current knowledge gap. Major developments in this area are reviewed, with a particular focus on near-term quantum computation. Illustrations of key methods are provided, explicitly demonstrating how to map chemical problems onto a quantum computer, and how to solve them. The review concludes with an outlook on this nascent field.
954 citations
28 Apr 2016
TL;DR: The National Institute of Standards and Technology (NIST)'s current understanding about the status of quantum computing and post-quantum cryptography is shared, and NIST’s initial plan to move forward is outlined.
Abstract: In recent years, there has been a substantial amount of research on quantum computers – machines that exploit quantum mechanical phenomena to solve mathematical problems that are difficult or intractable for conventional computers. If large-scale quantum computers are ever built, they will be able to break many of the public-key cryptosystems currently in use. This would seriously compromise the confidentiality and integrity of digital communications on the Internet and elsewhere. The goal of post-quantum cryptography (also called quantum-resistant cryptography) is to develop cryptographic systems that are secure against both quantum and classical computers, and can interoperate with existing communications protocols and networks. This Internal Report shares the National Institute of Standards and Technology (NIST)’s current understanding about the status of quantum computing and post-quantum cryptography, and outlines NIST’s initial plan to move forward in this space. The report also recognizes the challenge of moving to new cryptographic infrastructures and therefore emphasizes the need for agencies to focus on crypto agility.
514 citations
ICFO – The Institute of Photonic Sciences1, Ludwig Maximilian University of Munich2, Max Planck Society3, University of Amsterdam4, ETH Zurich5, Free University of Berlin6, University of Geneva7, Technische Universität München8, University of Strathclyde9, Leibniz University of Hanover10, German National Metrology Institute11, University of Oxford12, Saarland University13
TL;DR: In this article, the authors present an updated summary of the roadmap of quantum technologies (QT) and present an overview of the current state-of-the-art quantum technologies.
Abstract: Within the last two decades, quantum technologies (QT) have made tremendous progress, moving from Nobel Prize award-winning experiments on quantum physics (1997: Chu, Cohen-Tanoudji, Phillips; 2001: Cornell, Ketterle, Wieman; 2005: Hall, Hansch-, Glauber; 2012: Haroche, Wineland) into a cross-disciplinary field of applied research. Technologies are being developed now that explicitly address individual quantum states and make use of the 'strange' quantum properties, such as superposition and entanglement. The field comprises four domains: quantum communication, where individual or entangled photons are used to transmit data in a provably secure way; quantum simulation, where well-controlled quantum systems are used to reproduce the behaviour of other, less accessible quantum systems; quantum computation, which employs quantum effects to dramatically speed up certain calculations, such as number factoring; and quantum sensing and metrology, where the high sensitivity of coherent quantum systems to external perturbations is exploited to enhance the performance of measurements of physical quantities. In Europe, the QT community has profited from several EC funded coordination projects, which, among other things, have coordinated the creation of a 150-page QT Roadmap (http://qurope.eu/h2020/qtflagship/roadmap2016). This article presents an updated summary of this roadmap.
443 citations
TL;DR: Gate set tomography is used to completely characterize operations on a trapped-Yb+-ion qubit and it is demonstrated with greater than 95% confidence that they satisfy a rigorous threshold for FTQEC (diamond norm ≤6.7 × 10−4).
Abstract: Quantum information processors promise fast algorithms for problems inaccessible to classical computers. But since qubits are noisy and error-prone, they will depend on fault-tolerant quantum error correction (FTQEC) to compute reliably. Quantum error correction can protect against general noise if—and only if—the error in each physical qubit operation is smaller than a certain threshold. The threshold for general errors is quantified by their diamond norm. Until now, qubits have been assessed primarily by randomized benchmarking, which reports a different error rate that is not sensitive to all errors, and cannot be compared directly to diamond norm thresholds. Here we use gate set tomography to completely characterize operations on a trapped-Yb+-ion qubit and demonstrate with greater than 95% confidence that they satisfy a rigorous threshold for FTQEC (diamond norm ≤6.7 × 10−4). Quantum computation will depend on fault-tolerant error correction, which requires the chance for errors to occur to be below a certain threshold. Here the authors use gate set tomography as a means to rigorously characterize error rates of single-qubit operations of a qubit encoded in a trapped ion.
372 citations