Quantum Information Processing and Quantum Error Correction
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Quantum Information Processing and Quantum Error Correction

An Engineering Approach

1st Edition - April 16, 2012

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  • Author: Ivan Djordjevic
  • eBook ISBN: 9780123854926
  • Hardcover ISBN: 9780123854919

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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.

Key Features

  • 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

Readership

Communications engineers, computer engineers, electronic systems engineers and graduate engineers taking either a course in quantum information engineering or quantum error correcting coding

Table of Contents

  • Dedication

    Preface

    About the Author

    Chapter 1. Introduction

    1.1 Photon Polarization

    1.2 The Concept of the Qubit

    1.3 Spin-1/2 Systems

    1.4 Quantum Gates and Quantum Information Processing

    1.5 Quantum Teleportation

    1.6 Quantum Error Correction Concepts

    1.7 Quantum Key Distribution (QKD)

    1.8 Organization of the Book

    REFERENCES

    Chapter 2. Quantum Mechanics Fundamentals

    2.1 Introduction

    2.2 Eigenkets as Base Kets

    2.3 Matrix Representations

    2.4 Quantum Measurements, Commutators, and Pauli Operators

    2.5 Uncertainty Principle

    2.6 Density Operators

    2.7 Change of Basis

    2.8 Time Evolution – Schrödinger Equation

    2.9 Harmonic Oscillator

    2.10 Angular Momentum

    2.11 Spin-1/2 Systems

    2.12 Hydrogen-Like Atoms and Beyond

    2.13 Summary

    2.14 Problems

    REFERENCES

    Chapter 3. Quantum Circuits and Quantum Information Processing Fundamentals

    3.1 Single-Qubit Operations

    3.2 Two-Qubit Operations

    3.3 Generalization to N-Qubit Gates and Quantum Computation Fundamentals

    3.4 Qubit Measurement (Revisited)

    3.5 Universal Quantum Gates

    3.6 Quantum Teleportation

    3.7 Summary

    3.8 Problems

    REFERENCES

    Chapter 4. Introduction to Quantum Information Processing

    4.1 Superposition Principle and Quantum Parallelism

    4.2 No-Cloning Theorem

    4.3 Distinguishing Quantum States

    4.4 Quantum Entanglement

    4.5 Operator-Sum Representation

    4.6 Decoherence and Quantum Errors

    4.7 Conclusion

    4.8 Problems

    REFERENCES

    Chapter 5. Quantum Algorithms

    5.1 Quantum Parallelism (Revisited)

    5.2 Deutsch and Deutsch–Jozsa Algorithms

    5.3 Grover Search Algorithm

    5.4 Quantum Fourier Transform

    5.5 The Period of a Function and Shor Factoring Algorithm

    5.6 Simon’s Algorithm

    5.7 Classical/Quantum Computing Complexities and Turing Machines

    5.8 Summary

    5.9 Problems

    REFERENCES

    Chapter 6. Classical Error Correcting Codes

    6.1 Channel Coding Preliminaries

    6.2 Linear Block Codes

    6.3 Cyclic Codes

    6.4 Bose–Chaudhuri–Hocquenghem (BCH) Codes

    6.5 Reed–Solomon (RS) Codes, Concatenated Codes, and Product Codes

    6.6 Concluding Remarks

    6.7 Problems

    REFERENCES

    Chapter 7. Quantum Error Correction

    7.1 Pauli Operators (Revisited)

    7.2 Quantum Error Correction Concepts

    7.3 Quantum Error Correction

    7.4 Important Quantum Coding Bounds

    7.5 Quantum Operations (Superoperators) and Quantum Channel Models

    7.6 Summary

    7.7 Problems

    REFERENCES

    Chapter 8. Quantum Stabilizer Codes and Beyond

    8.1 Stabilizer Codes

    8.2 Encoded Operators

    8.3 Finite Geometry Interpretation

    8.4 Standard Form of Stabilizer Codes

    8.5 Efficient Encoding and Decoding

    8.6 Nonbinary Stabilizer Codes

    8.7 Subsystem Codes

    8.8 Entanglement-Assisted (EA) Quantum Codes

    8.9 Topological Codes

    8.10 Summary

    8.11 Problems

    REFERENCES

    Chapter 9. Entanglement-Assisted Quantum Error Correction

    9.1 Entanglement-Assisted Quantum Error Correction Principles

    9.2 Entanglement-Assisted Canonical Quantum Codes

    9.3 General Entanglement-Assisted Quantum Codes

    9.4 Encoding and Decoding for Entanglement-Assisted Quantum Codes

    9.5 Operator Quantum Error Correction Codes (Subsystem Codes)

    9.6 Entanglement-Assisted Operator Quantum Error Correction Coding (EA-OQECC)

    9.7 Summary

    9.8 Problems

    REFERENCES

    Chapter 10. Quantum Low-Density Parity-Check Codes

    10.1 Classical LDPC Codes

    10.2 Dual-Containing Quantum LDPC Codes

    10.3 Entanglement-Assisted Quantum LDPC Codes

    10.4 Iterative Decoding of Quantum LDPC Codes

    10.5 Summary

    10.6 Problems

    REFERENCES

    Chapter 11. Fault-Tolerant Quantum Error Correction and Fault-Tolerant Quantum Computing

    11.1 Fault Tolerance Basics

    11.2 Fault-Tolerant Quantum Computation Concepts

    11.3 Fault-Tolerant Quantum Error Correction

    11.4 Fault-Tolerant Quantum Computation

    11.5 Accuracy Threshold Theorem

    11.6 Summary

    11.7 Problems

    REFERENCES

    Chapter 12. Quantum Information Theory

    12.1 Entropy

    12.2 Holevo Information, Accessible Information, and Holevo Bound

    12.3 Data Compression

    12.4 Holevo–Schumacher–Westmoreland (HSW) Theorem

    12.5 Conclusion

    12.6 Problems

    REFERENCES

    Chapter 13. Physical Implementations of Quantum Information Processing

    13.1 Physical Implementation Basics

    13.2 Nuclear Magnetic Resonance (NMR) in Quantum Information Processing

    13.3 Trapped Ions in Quantum Information Processing

    13.4 Photonic Quantum Implementations

    13.5 Photonic Implementation of Quantum Relay

    13.6 Implementation of Quantum Encoders and Decoders

    13.7 Cavity Quantum Electrodynamics (CQED)-Based Quantum Information Processing

    13.8 Quantum Dots in Quantum Information Processing

    13.9 Summary

    13.10 Problems

    REFERENCES

    Abstract Algebra Fundamentals

    A.1 Groups

    A.2 Group Acting on the Set

    A.3 Group Mapping

    A.4 Fields

    A.5 Vector Spaces

    A.6 Character Theory

    A.7 Algebra of Finite Fields

    A.8 Metric Spaces

    A.9 Hilbert Space

    Index

Product details

  • No. of pages: 600
  • Language: English
  • Copyright: © Academic Press 2012
  • Published: April 16, 2012
  • Imprint: Academic Press
  • eBook ISBN: 9780123854926
  • Hardcover ISBN: 9780123854919

About the Author

Ivan Djordjevic

Ivan B. Djordjevic is a Professor of Electrical and Computer Engineering and Optical Sciences, Director of the Optical Communications Systems Laboratory and the Quantum Communications Laboratory, and co-Director of the Signal Processing and Coding Lab at the University of Arizona. He is a fellow of IEEE and the Optical Society. Prof. Djordjevic has authored or co-authored seven books and more than 530 journal and conference publications. He presently serves as a Senior Editor and member of the Editorial Board on the OSA/IEEE Journal of Optical Communications and Networking; the IOP Journal of Optics; IEEE Communications Letters; the Elsevier Physical Communication Journal, PHYCOM; Optical and Quantum Electronics; and Frequenz. As of August 2020, he holds 53 U.S. patents.

Affiliations and Expertise

Professor of Electrical and Computer Engineering and Optical Sciences, University of Arizona, Tucson, USA

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