Non-Gaussian Methods for Quantum Error Correction PDF Download

Author: Dominik Hörndlein
Publisher:
ISBN:
Category :
Languages : en
Pages : 85

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Book Description

Author: Ivan Djordjevic
Publisher: Academic Press
ISBN: 0123854911
Category : Computers
Languages : en
Pages : 597

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Book Description
Quantum Information Processing and Quantum Error Correction is a self-contained, tutorial-based introduction to quantum information, quantum computation, and quantum error-correction. Assuming no knowledge of quantum mechanics and written at an intuitive level suitable for the engineer, the book gives all the essential principles needed to design and implement quantum electronic and photonic circuits. Numerous examples from a wide area of application are given to show how the principles can be implemented in practice. This book is ideal for the electronics, photonics and computer engineer who requires an easy- to-understand foundation on the principles of quantum information processing and quantum error correction, together with insight into how to develop quantum electronic and photonic circuits. Readers of this book will be ready for further study in this area, and will be prepared to perform independent research. The reader completed the book will be able design the information processing circuits, stabilizer codes, Calderbank-Shor-Steane (CSS) codes, subsystem codes, topological codes and entanglement-assisted quantum error correction codes; and propose corresponding physical implementation. The reader completed the book will be proficient in quantum fault-tolerant design as well. Unique Features Unique in covering both quantum information processing and quantum error correction - everything in one book that an engineer needs to understand and implement quantum-level circuits. Gives an intuitive understanding by not assuming knowledge of quantum mechanics, thereby avoiding heavy mathematics. In-depth coverage of the design and implementation of quantum information processing and quantum error correction circuits. Provides the right balance among the quantum mechanics, quantum error correction, quantum computing and quantum communication. Dr. Djordjevic is an Assistant Professor in the Department of Electrical and Computer Engineering of College of Engineering, University of Arizona, with a joint appointment in the College of Optical Sciences. Prior to this appointment in August 2006, he was with University of Arizona, Tucson, USA (as a Research Assistant Professor); University of the West of England, Bristol, UK; University of Bristol, Bristol, UK; Tyco Telecommunications, Eatontown, USA; and National Technical University of Athens, Athens, Greece. His current research interests include optical networks, error control coding, constrained coding, coded modulation, turbo equalization, OFDM applications, and quantum error correction. He presently directs the Optical Communications Systems Laboratory (OCSL) within the ECE Department at the University of Arizona. Provides everything an engineer needs in one tutorial-based introduction to understand and implement quantum-level circuits Avoids the heavy use of mathematics by not assuming the previous knowledge of quantum mechanics Provides in-depth coverage of the design and implementation of quantum information processing and quantum error correction circuits

Author: Daniel A. Lidar
Publisher: Cambridge University Press
ISBN: 0521897874
Category : Computers
Languages : en
Pages : 689

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Book Description
Focusing on methods for quantum error correction, this book is invaluable for graduate students and experts in quantum information science.

Author: Christopher Chamberland
Publisher:
ISBN:
Category : Quantum computing
Languages : en
Pages : 190

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Book Description
Quantum computers have the potential to solve several interesting problems in polynomial time for which no polynomial time classical algorithms have been found. However, one of the major challenges in building quantum devices is that quantum systems are very sensitive to noise arising from undesired interactions with the environment. Noise can lead to errors which can corrupt the results of the computation. Quantum error correction is one way to mitigate the effects of noise arising in quantum devices. With a plethora of quantum error correcting codes that can be used in various settings, one of the main challenges of quantum error correction is understanding how well various codes perform under more realistic noise models that can be observed in experiments. This thesis proposes a new decoding algorithm which can optimize threshold values of error correcting codes under different noise models. The algorithm can be applied to any Markovian noise model. Further, it is shown that for certain noise models, logical Clifford corrections can further improve a code's threshold value if the code obeys certain symmetries. Since gates and measurements cannot in general be performed with perfect precision, the operations required to perform quantum error correction can introduce more errors into the system thus negating the benefits of error correction. Fault-tolerant quantum computing is a way to perform quantum error correction with imperfect operations while retaining the ability to suppress errors as long as the noise is below a code's threshold. One of the main challenges in performing fault-tolerant error correction is the high resource requirements that are needed to obtain very low logical noise rates. With the use of flag qubits, this thesis develops new fault-tolerant error correction protocols that are applicable to arbitrary distance codes. Various code families are shown to satisfy the requirements of flag fault-tolerant error correction. We also provide circuits using a constant number of qubits for these codes. It is shown that the proposed flag fault-tolerant method uses fewer qubits than previous fault-tolerant error correction protocols. It is often the case that the noise afflicting a quantum device cannot be fully characterized. Further, even with some knowledge of the noise, it can be very challenging to use analytic decoding methods to improve the performance of a fault-tolerant scheme. This thesis presents decoding schemes using several state of the art machine learning techniques with a focus on fault-tolerant quantum error correction in regimes that are relevant to near term experiments. It is shown that even in low noise rate regimes and with no knowledge of the noise, noise can be further suppressed for small distance codes. Limitations of machine learning decoders as well as the classical resources required to perform active error correction are discussed. In many cases, gate times can be much shorter than typical measurement times of quantum states. Further, classical decoding of the syndrome information used in quantum error correction to compute recovery operators can also be much slower than gate times. For these reasons, schemes where error correction can be implemented in a frame (known as the Pauli frame) have been developed to avoid active error correction. In this thesis, we generalize previous Pauli frame schemes and show how Clifford frame error correction can be implemented with minimal overhead. Clifford frame error correction is necessary if the logical component of recovery operators were chosen from the Clifford group, but could also be used in randomized benchmarking schemes.

Author:
Publisher: ScholarlyEditions
ISBN: 1464963320
Category : Science
Languages : en
Pages : 13957

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Book Description
Issues in General Physics Research / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about General Physics Research. The editors have built Issues in General Physics Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General Physics Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General Physics Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Author: Daniel A. Lidar
Publisher: Cambridge University Press
ISBN: 1107433835
Category : Science
Languages : en
Pages : 689

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Book Description
Quantum computation and information is one of the most exciting developments in science and technology of the last twenty years. To achieve large scale quantum computers and communication networks it is essential not only to overcome noise in stored quantum information, but also in general faulty quantum operations. Scalable quantum computers require a far-reaching theory of fault-tolerant quantum computation. This comprehensive text, written by leading experts in the field, focuses on quantum error correction and thoroughly covers the theory as well as experimental and practical issues. The book is not limited to a single approach, but reviews many different methods to control quantum errors, including topological codes, dynamical decoupling and decoherence-free subspaces. Basic subjects as well as advanced theory and a survey of topics from cutting-edge research make this book invaluable both as a pedagogical introduction at the graduate level and as a reference for experts in quantum information science.

Author: Tomas Jochym-O'Connor
Publisher:
ISBN:
Category : Error-correcting codes (Information theory)
Languages : en
Pages : 220

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Book Description
Quantum error correction is the backbone of fault-tolerant quantum computation, a necessary requirement for any large scale quantum computer. The fault-tolerance threshold theorem has long been a target for experimental precision, allowing for the possibility of reducing logical error rates to arbitrarily low levels without excessive overhead. While there are many promising fault-tolerant architectures, the path towards the most practical fault-tolerant scheme is far from decided and may vary for differing physical models. This thesis proposes new schemes for universal fault-tolerant quantum computation in both the concatenated and topological code settings. Through the concatenation of two different error correcting codes, a set of universal fault-tolerant gates can be obtained without requiring the need for magic state distillation. A lower bound of $1.28 \times 10^{-3}$ for the fault-tolerance threshold under circuit level depolarizing noise is obtained. Additionally, stacked codes are proposed as a means to simulate the action of a 3D topological code in 2D, allowing for the application of a universal set of transversal operations. While fault-tolerant, unfortunately the scheme does not exhibit a threshold due to the decreasing pseudo-threshold with growing code distance, yet points to potential interesting avenues for fault-tolerant computation in 2D without distillation. One of the primary avenues to constructing fault-tolerant logical operations is through transversal operations. In this thesis, the set of single qubit logical gates that can be implemented transversally are characterized and determined to all belong to the Clifford hierarchy. Moreover, any diagonal two-qubit operation that can be applied transversally must belong to the same level of the Clifford hierarchy as the set of gates that can be implemented in the single-qubit case. The opposite to quantum error correction is privacy, where the output of a channel is disguised from its input. The two are fundamentally related through the complementary channel construction. This thesis presents a new class of private quantum channels, expanding the existing class beyond a seemingly fundamental restriction. This yields interesting insights into the structure of quantum information and the leaking of information to external environments. Additionally, the duality is only recovered when extending the complementary channel to sufficiently high environmental dimension. Finally, the error properties of bucket brigade quantum Random Access Memory (qRAM) are assessed. It is determined that using the bucket brigade qRAM architecture for the running of Grover's algorithm necessitates reducing the error rate of the individual components to exponentially small levels for an exponential sized memory. As such, fault-tolerant architectures will likely play an essential role in the construction of such computing primitives.

Author: Matthew Reed
Publisher: Lulu.com
ISBN: 1304084868
Category : Science
Languages : en
Pages : 384

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Book Description
Softcover version of 2013 Ph.D. thesis of Matthew David Reed presented to the Physics department of Yale University. Concerns the realization of quantum error correction in the circuit quantum electrodynamics architecture, a precursor to quantum computing.

Author: Doan Binh Trieu
Publisher: Forschungszentrum Jülich
ISBN: 3893366016
Category :
Languages : en
Pages : 189

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Book Description

Author: Alessio Serafini
Publisher: CRC Press
ISBN: 100092050X
Category : Science
Languages : en
Pages : 589

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Book Description
Quantum Continuous Variables introduces the theory of continuous variable quantum systems, from its foundations based on the framework of Gaussian states to modern developments, including its applications to quantum information and forthcoming quantum technologies. This book addresses the theory of Gaussian states, operations, and dynamics in great depth and breadth, through a novel approach that embraces both the Hilbert space and phase descriptions. The second edition of this book has been revised throughout, and updated to include new topics, such as boson sampling, coherent feedback, nonlinear control, as well as several new solved problems. The volume includes coverage of entanglement theory and quantum information protocols, and their connection with relevant experimental set-ups. General techniques for non-Gaussian manipulations also emerge as the treatment unfolds and are demonstrated with specific case studies. This book will be of interest to graduate students looking to familiarise themselves with the field, in addition to experienced researchers eager to enhance their understanding of its theoretical methods. It will also appeal to experimentalists searching for a rigorous but accessible treatment of the theory in the area. Features Provides the first systematic graduate-level textbook for the field of quantum continuous variables and includes 77 problems for the reader, with accompanying solutions Explores applications to entanglement theory, nonlocality, quantum technologies and quantum control Describes, in detail, a comprehensive list of experimental platforms where the formalism applies Alessio Serafini earned his PhD from the University of Salerno. He is currently a Professor at University College London. His research focuses mainly on quantum optics, quantum information with continuous variables, and the theory of quantum control.