Download or read book Calculations of Quantum Error Correction and Fault Tolerance Thresholds written by Jesse Fern and published by . This book was released on 2008 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantum Error Correction and Fault Tolerant Quantum Computing written by Frank Gaitan and published by CRC Press. This book was released on 2008-02-07 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was once widely believed that quantum computation would never become a reality. However, the discovery of quantum error correction and the proof of the accuracy threshold theorem nearly ten years ago gave rise to extensive development and research aimed at creating a working, scalable quantum computer. Over a decade has passed since this monumental accomplishment yet no book-length pedagogical presentation of this important theory exists. Quantum Error Correction and Fault Tolerant Quantum Computing offers the first full-length exposition on the realization of a theory once thought impossible. It provides in-depth coverage on the most important class of codes discovered to date—quantum stabilizer codes. It brings together the central themes of quantum error correction and fault-tolerant procedures to prove the accuracy threshold theorem for a particular noise error model. The author also includes a derivation of well-known bounds on the parameters of quantum error correcting code. Packed with over 40 real-world problems, 35 field exercises, and 17 worked-out examples, this book is the essential resource for any researcher interested in entering the quantum field as well as for those who want to understand how the unexpected realization of quantum computing is possible.
Download or read book Quantum Error Correction and Fault Tolerant Quantum Computing written by Frank Gaitan and published by CRC Press. This book was released on 2018-10-03 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was once widely believed that quantum computation would never become a reality. However, the discovery of quantum error correction and the proof of the accuracy threshold theorem nearly ten years ago gave rise to extensive development and research aimed at creating a working, scalable quantum computer. Over a decade has passed since this monumental accomplishment yet no book-length pedagogical presentation of this important theory exists. Quantum Error Correction and Fault Tolerant Quantum Computing offers the first full-length exposition on the realization of a theory once thought impossible. It provides in-depth coverage on the most important class of codes discovered to date—quantum stabilizer codes. It brings together the central themes of quantum error correction and fault-tolerant procedures to prove the accuracy threshold theorem for a particular noise error model. The author also includes a derivation of well-known bounds on the parameters of quantum error correcting code. Packed with over 40 real-world problems, 35 field exercises, and 17 worked-out examples, this book is the essential resource for any researcher interested in entering the quantum field as well as for those who want to understand how the unexpected realization of quantum computing is possible.
Download or read book An Accurate Analytical Framework for Computing Fault tolerance Thresholds Using the 7 1 3 Quantum Code written by Andrew J. Morten and published by . This book was released on 2005 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: In studies of the threshold for fault-tolerant quantum error-correction, it is generally assumed that the noise channel at all levels of error-correction is the depolarizing channel. The effects of this assumption on the threshold result are unknown. We address this problem by calculating the effective noise channel at all levels of error-correction specifically for the Steane [[7,1,3]] code, and we recalculate the threshold using the new noise channels. We present a detailed analytical framework for these calculations and run numerical simulations for comparison. We find that only X and Z failures occur with significant probability in the effective noise channel at higher levels of error-correction. We calculate that when changes in the noise channel are accounted for, the value of the threshold for the Steane [[7,1,3]] code increases by about 30 percent, from .00030 to .00039, when memory failures occur with one tenth the probability of all other failures. Furthermore, our analytical model provides a framework for calculating thresholds for systems where the initial noise channel is very different from the depolarizing channel, such as is the case for ion trap quantum computation.
Download or read book Quantum Error Correction written by Daniel A. Lidar and published by Cambridge University Press. This book was released on 2013-09-12 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on methods for quantum error correction, this book is invaluable for graduate students and experts in quantum information science.
Download or read book Quantum Computation with Topological Codes written by Keisuke Fujii and published by Springer. This book was released on 2015-12-15 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a self-consistent review of quantum computation with topological quantum codes. The book covers everything required to understand topological fault-tolerant quantum computation, ranging from the definition of the surface code to topological quantum error correction and topological fault-tolerant operations. The underlying basic concepts and powerful tools, such as universal quantum computation, quantum algorithms, stabilizer formalism, and measurement-based quantum computation, are also introduced in a self-consistent way. The interdisciplinary fields between quantum information and other fields of physics such as condensed matter physics and statistical physics are also explored in terms of the topological quantum codes. This book thus provides the first comprehensive description of the whole picture of topological quantum codes and quantum computation with them.
Download or read book Threshold Analysis with Fault tolerant Operations for Nonbinary Quantum Error Correcting Codes written by Aparna Kanungo and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum error correcting codes have been introduced to encode the data bits in extra redundant bits in order to accommodate errors and correct them. However, due to the delicate nature of the quantum states or faulty gate operations, there is a possibility of catastrophic spread of errors which might render the error correction techniques ineffective. Hence, in this thesis we concentrate on how various operations can be carried out fault-tolerantly so that the errors are not propagated in the same block. We prove universal fault-tolerance for nonbinary CSS codes. This thesis is focussed only on nonbinary quantum codes and all the results pertain to nonbinarycodes. Efficient error detection and correction techniques using fault-tolerant techniques can help as long as we ensure that the gate error probability is below a certain threshold. The calculation of this threshold is therefore important to see if quantum computations are realizable or not, even with fault-tolerant operations. We derive an expression to compute the gate error threshold for nonbinary quantum codes and test this result for different classes of codes, to get codes with best threshold results.
Download or read book Quantum Information Processing and Quantum Error Correction written by Ivan Djordjevic and published by Academic Press. This book was released on 2012-04-16 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Quantum Error Correction and Fault Tolerant Quantum Computing S written by Gaitan Frank Staff and published by . This book was released on 2007-10 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: It was once widely believed that quantum computation would never become a reality. However, the discovery of quantum error correction and the proof of the accuracy threshold theorem nearly ten years ago gave rise to extensive development and research aimed at creating a working, scalable quantum computer. Over a decade has passed since this monumental accomplishment yet no book-length pedagogical presentation of this important theory exists. Quantum Error Correction and Fault Tolerant Quantum Computing offers the first full-length exposition on the realization of a theory once thought impossible. It provides in-depth coverage on the most important class of codes discovered to date quantum stabilizer codes. It brings together the central themes of quantum error correction and fault-tolerant procedures to prove the accuracy threshold theorem for a particular noise error model. The author also includes a derivation of well-known bounds on the parameters of quantum error correcting code. Packed with over 40 real-world problems, 35 field exercises, and 17 worked-out examples, this book is the essential resource for any researcher interested in entering the quantum field as well as for those who want to understand how the unexpected realization of quantum computing is possible.
Download or read book Novel Methods in Quantum Error Correction written by Tomas Jochym-O'Connor and published by . This book was released on 2016 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction To Quantum Computation And Information written by Adriano Barenco and published by World Scientific. This book was released on 1998-10-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide a pedagogical introduction to the subjects of quantum information and quantum computation. Topics include non-locality of quantum mechanics, quantum computation, quantum cryptography, quantum error correction, fault-tolerant quantum computation as well as some experimental aspects of quantum computation and quantum cryptography. Only knowledge of basic quantum mechanics is assumed. Whenever more advanced concepts and techniques are used, they are introduced carefully. This book is meant to be a self-contained overview. While basic concepts are discussed in detail, unnecessary technical details are excluded. It is well-suited for a wide audience ranging from physics graduate students to advanced researchers.This book is based on a lecture series held at Hewlett-Packard Labs, Basic Research Institute in the Mathematical Sciences (BRIMS), Bristol from November 1996 to April 1997, and also includes other contributions.
Download or read book The Complexity of Noise written by Amit Hagar and published by Morgan & Claypool Publishers. This book was released on 2010 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum computers are hypothetical quantum information processing (QIP) devices that allow one to store, manipulate, and extract information while harnessing quantum physics to solve various computational problems and do so putatively more efficiently than any known classical counterpart (5). Physical objects as they are, QIP devices are subject to the laws of physics. No doubt, the application of these laws is error-free, but noise - be it external influences or hardware imprecisions - can sometimes cause a mismatch between what the QIP device is supposed to do and what it actually does. In recent years the elimination of noise that result from external disturbances or from imperfect gates has become the "holy grail" within the quantum computing community, and a worldwide quest for a large scale, fault-tolerant, and computationally superior QIP device is currently taking place. Whether such machines are possible is an exciting open question, yet the debate on their feasibility has been so far rather ideological in character (45) (66)(110) (162). Remarkably, philosophers of science have been mostly silent about it: common wisdom has it that philosophy should not intervene in what appears to be (and is also presented as) an engineering problem, and besides, the mathematics employed in the theory of fault-tolerant quantum error correction (FTQEC henceforth) is rather daunting. It turns out, however, that behind this technical veil the central issues at the heart of the debate are worthy of philosophical analysis and, moreover, bear strong similarities to the conceptual problems that have been saturating a field quite familiar to philosophers, namely the foundations of statistical mechanics (SM henceforth). Reconstructing the debate on FTQEC with statistical mechanical analogies, this book aims to introduce it to readership outside the quantum computing community, and to take preliminary steps towards making it less ideological and mor
Download or read book Practical Fault tolerant Quantum Computation written by Theodore J. Yoder and published by . This book was released on 2018 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the past two and a half decades, a subset of the physics community has been focused on building a new type of computer, one that exploits the superposition, interference, and entanglement of quantum states to compute faster than a classical computer on select tasks. Manipulating quantum systems requires great care, however, as they are quite sensitive to many sources of noise. Surpassing the limits of hardware fabrication and control, quantum error-correcting codes can reduce error-rates to arbitrarily low levels, albeit with some overhead. This thesis takes another look at several aspects of stabilizer code quantum error-correction to discover solutions to the practical problems of choosing a code, using it to correct errors, and performing fault-tolerant operations. Our first result looks at limitations on the simplest implementation of fault-tolerant operations, transversality. By defining a new property of stabilizer codes, the disjointness, we find transversal operations on stabilizer codes are limited to the Clifford hierarchy and thus are not universal for computation. Next, we address these limitations by designing non-transversal fault-tolerant operations that can be used to universally compute on some codes. The key idea in our constructions is that error-correction is performed at various points partway through the non-transversal operation (even at points when the code is not-necessarily still a stabilizer code) to catch errors before they spread. Since the operation is thus divided into pieces, we dub this pieceable fault-tolerance. In applying pieceable fault tolerance to the Bacon-Shor family of codes, we find an interesting tradeoff between space and time, where a fault-tolerant controlled-controlled-Z operation takes less time as the code becomes more asymmetric, eventually becoming transversal. Further, with a novel error-correction procedure designed to preserve the coherence of errors, we design a reasonably practical implementation of the controlled-controlled-Z operation on the smallest Bacon-Shor code. Our last contribution is a new family of topological quantum codes, the triangle codes, which operate within the limits of a 2-dimensional plane. These codes can perform all encoded Clifford operations within the plane. Moreover, we describe how to do the same for the popular family of surface codes, by relation to the triangle codes.
Download or read book New Methods in Quantum Error Correction and Fault tolerant Quantum Computing written by Christopher Chamberland and published by . This book was released on 2018 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Large scale Simulations of Error Prone Quantum Computation Devices written by Doan Binh Trieu and published by Forschungszentrum Jülich. This book was released on 2010 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Frontiers of Engineering written by National Academy of Engineering and published by National Academies Press. This book was released on 2019-02-28 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents papers on the topics covered at the National Academy of Engineering's 2018 US Frontiers of Engineering Symposium. Every year the symposium brings together 100 outstanding young leaders in engineering to share their cutting-edge research and innovations in selected areas. The 2018 symposium was held September 5-7 and hosted by MIT Lincoln Laboratory in Lexington, Massachusetts. The intent of this book is to convey the excitement of this unique meeting and to highlight innovative developments in engineering research and technical work.
Download or read book Quantum Computing written by National Academies of Sciences, Engineering, and Medicine and published by National Academies Press. This book was released on 2019-04-27 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics, the subfield of physics that describes the behavior of very small (quantum) particles, provides the basis for a new paradigm of computing. First proposed in the 1980s as a way to improve computational modeling of quantum systems, the field of quantum computing has recently garnered significant attention due to progress in building small-scale devices. However, significant technical advances will be required before a large-scale, practical quantum computer can be achieved. Quantum Computing: Progress and Prospects provides an introduction to the field, including the unique characteristics and constraints of the technology, and assesses the feasibility and implications of creating a functional quantum computer capable of addressing real-world problems. This report considers hardware and software requirements, quantum algorithms, drivers of advances in quantum computing and quantum devices, benchmarks associated with relevant use cases, the time and resources required, and how to assess the probability of success.
