Fault-tolerant Quantum Computer Architectures Using Hierarchies of Quantum Error-correcting Codes PDF Download

Author: Andrew William Cross
Publisher:
ISBN:
Category :
Languages : en
Pages : 238

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Book Description
(cont.) The methods are applied to measure inner error-correcting code performance, as a first step toward elucidation of an effective fault-tolerant quantum computer architecture that uses no more than a physical, inner, and outer level of coding. Of the inner codes, the Golay code gives the highest pseudothreshold of 2 x 10-3. A comparison of logical error rate and overhead shows that the Bacon-Shor codes are competitive with Knill's C4/C6 scheme at a base error rate of 10−4.

Author: Frank Gaitan
Publisher: CRC Press
ISBN: 1420006681
Category : Computers
Languages : en
Pages : 312

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Book Description
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.

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: 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: Michael John George Vasmer
Publisher:
ISBN:
Category :
Languages : en
Pages : 163

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Book Description
Quantum computers are far more error-prone than their classical counterparts. Therefore, to build a quantum computer capable of running large-scale quantum algorithms, we must use the techniques of quantum error correction to ensure that the computer produces the correct output even when its components are unreliable. However, the resource requirements of building such a fault-tolerant quantum computer are currently prohibitive. Here, we examine the utility of using three-dimensional (3D) surface codes in a fault-tolerant quantum computer. This family of topological error-correcting codes is a generalization of the well-known 2D surface code to three spatial dimensions. We show that certain 3D surface codes have a transversal logical non-Clifford gate. In a quantum computing architecture, a non-Clifford gate is required to achieve computational universality. Transversal gates do not entangle qubits in different codes, so they are naturally fault tolerant because they do not spread errors. Next, we consider the problem of decoding 3D surface codes. In a quantum error-correcting code, we cannot observe the qubits directly, so we measure parity-check operators to gain information about the state of the code. Decoding is the problem of estimating what error has occurred given a list of unsatisfied parity checks. We observe that 3D surface codes offer asymmetric protection against bit-flip and phase-flip errors, but in both cases, we find that a threshold error rate exists below which we can suppress logical errors by increasing the size of the code. We use our results about logical gates and decoding to propose two fault-tolerant quantum computing architectures that utilize 3D surface codes. Finally, we compare the resource requirements of our architectures with the requirements of leading quantum computing architectures based on topological codes. We find that one of our architectures may be competitive with the leading architectures, depending on the properties of the physical systems used to build the qubits.

Author: Gaitan Frank Staff
Publisher:
ISBN: 9781420073454
Category :
Languages : en
Pages :

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Book Description
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.

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: Keisuke Fujii
Publisher: Springer
ISBN: 981287996X
Category : Science
Languages : en
Pages : 148

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Book Description
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.

Author: Tzvetan S. Metodi
Publisher: Springer Nature
ISBN: 3031017188
Category : Technology & Engineering
Languages : en
Pages : 147

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Book Description
Quantum computation may seem to be a topic for science fiction, but small quantum computers have existed for several years and larger machines are on the drawing table. These efforts have been fueled by a tantalizing property: while conventional computers employ a binary representation that allows computational power to scale linearly with resources at best, quantum computations employ quantum phenomena that can interact to allow computational power that is exponential in the number of "quantum bits" in the system. Quantum devices rely on the ability to control and manipulate binary data stored in the phase information of quantum wave functions that describe the electronic states of individual atoms or the polarization states of photons. While existing quantum technologies are in their infancy, we shall see that it is not too early to consider scalability and reliability. In fact, such considerations are a critical link in the development chain of viable device technologies capable of orchestrating reliable control of tens of millions quantum bits in a large-scale system. The goal of this lecture is to provide architectural abstractions common to potential technologies and explore the systemslevel challenges in achieving scalable, fault-tolerant quantum computation. The central premise of the lecture is directed at quantum computation (QC) architectural issues. We stress the fact that the basic tenet of large-scale quantum computing is reliability through system balance: the need to protect and control the quantum information just long enough for the algorithm to complete execution. To architectQCsystems, onemust understand what it takes to design and model a balanced, fault-tolerant quantum architecture just as the concept of balance drives conventional architectural design. For example, the register file depth in classical computers is matched to the number of functional units, the memory bandwidth to the cache miss rate, or the interconnect bandwidth matched to the compute power of each element of a multiprocessor. We provide an engineering-oriented introduction to quantum computation and provide an architectural case study based upon experimental data and future projection for ion-trap technology.We apply the concept of balance to the design of a quantum computer, creating an architecture model that balances both quantum and classical resources in terms of exploitable parallelism in quantum applications. From this framework, we also discuss the many open issues remaining in designing systems to perform quantum computation.

Author: K. R. Parthasarathy
Publisher: Narosa Publishing House
ISBN:
Category : Computers
Languages : en
Pages : 144

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Book Description
These notes are based on a course of about twenty lectures on quantum computation, quantum error correcting codes and information theory. The topics include a comparative description of the basic features of classical probability theory on finite sample spaces and quantum probability theory on finite dimensional complex Hilbert spaces, quantum gates and cicuits, simple examples of circuits arising from quantum teleportation, communication through EPR pairs and arithmetical computations on a quantum computer, more sophisticated examples of such circuits in the context of Fourier transform and phase estimation, a detailed account of the order finding algorithm as well as the celebrated Shor's algorithm for factorising a positive integer into its prime factors. There is a leisurely discussion of quantum error correcting codes with the Knill-Laflamme criterion for error correction and a number of examples of such codes whose construction is based on the Weyl commutation relations for finite abelian groups. The reader may find here a brief introduction to the basic ideas of classical information theory as developed by Shannon,properties of von Neumann's quantum entropy and relative entropy as well as a proof of Schumacher's noiseless quantum coding theorem. The Holevo bound for transmission of classical information through encoding by quantum states followed by measurements is derived. The only background assumed of the reader is linear algebra on finite dimensional complex vector spaces and elementary classical probability theory on finite sample spaces.These notes are aimed at mathematicians and computer scientists who are curious to know the mystery behind a quantum computer and the possibility of communicating information using the principles of elementary quantum theory.