Quantum Information Processing, Quantum Computing, and Quantum Error Correction

An Engineering Approach

2nd Edition - February 20, 2021
Imprint: Academic Press
Author: Ivan B. Djordjevic
Language: English
Paperback ISBN:
9 7 8 - 0 - 1 2 - 8 2 1 9 8 2 - 9
eBook ISBN:
9 7 8 - 0 - 1 2 - 8 2 1 9 8 7 - 4

The Second Edition of Quantum Information Processing, Quantum Computing, and Quantum Error Correction: An Engineering Approach presents a self-contained introduction to all aspec… Read more

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The Second Edition of Quantum Information Processing, Quantum Computing, and Quantum Error Correction: An Engineering Approach presents a self-contained introduction to all aspects of the area, teaching the essentials such as state vectors, operators, density operators, measurements, and dynamics of a quantum system. In additional to the fundamental principles of quantum computation, basic quantum gates, basic quantum algorithms, and quantum information processing, this edition has been brought fully up to date, outlining the latest research trends. These include:

Key topics include:

Quantum error correction codes (QECCs), including stabilizer codes, Calderbank-Shor-Steane (CSS) codes, quantum low-density parity-check (LDPC) codes, entanglement-assisted QECCs, topological codes, and surface codes
Quantum information theory, and quantum key distribution (QKD)
Fault-tolerant information processing and fault-tolerant quantum error correction, together with a chapter on quantum machine learning. Both quantum circuits- and measurement-based quantum computational models are described
The next part of the book is spent investigating physical realizations of quantum computers, encoders and decoders; including photonic quantum realization, cavity quantum electrodynamics, and ion traps
In-depth analysis of the design and realization of a quantum information processing and quantum error correction circuits

This fully up-to-date new edition will be of use to engineers, computer scientists, optical engineers, physicists and mathematicians.

Cover image
Title page
Table of Contents
Copyright
Dedication
Preface
About the Author
Chapter 1. Introduction
1.1. Photon Polarization
1.2. The Concept of Qubit
1.3. The Spin-1/2 Systems
1.4. Quantum Gates and QIP
1.5. Quantum Teleportation
1.6. Quantum Error Correction Concepts
1.7. Quantum Key Distribution
1.8. Organization of the Book
Chapter 2. Quantum Mechanics Fundamentals
2.1. Introduction
2.2. Eigenkets as Base Kets
2.3. Matrix Representations
2.4. Pauli Operators and Hadamard Gate
2.5. Density Operators
2.6. Quantum Measurements
2.7. Uncertainty Principle
2.8. Change of Basis
2.9. Time Evolution—Schrödinger Equation
2.10. Harmonic Oscillator
2.11. Angular Momentum
2.12. Spin-1/2 Systems
2.13. Hydrogen-Like Atoms and Beyond
2.14. Summary
2.15. Problems
Chapter 3. Quantum Circuits and Modules
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. Gottesman–Knill and Solovay–Kitaev Theorems
3.6. Universal Quantum Gates
3.7. Quantum Teleportation
3.8. Computation-in-place
3.9. Summary
3.10. Problems
Chapter 4. Quantum Information Processing Fundamentals
4.1. Quantum Information Processing Features
4.2. Superposition Principle, Quantum Parallelism, and QIP Basics
4.3. No-Cloning Theorem
4.4. Distinguishing the Quantum States
4.5. Quantum Entanglement
4.6. Operator-Sum Representation
4.7. Decoherence Effects, Depolarization, and Amplitude-Damping Channel Models
4.8. Quantum Computing Simulators
4.9. Summary
4.10. Problems
Chapter 5. Quantum Algorithms and Methods
5.1. Quantum Parallelism (Revisited)
5.2. Deutsch's, Deutsch–Jozsa, and Bernstein–Vazirani Algorithms
5.3. Grover Search Algorithm
5.4. Quantum Fourier Transform
5.5. The Period of a Function and Shor's Factoring Algorithm
5.6. Simon's Algorithm
5.7. Quantum Phase Estimation
5.8. Classical/Quantum Computing Complexities and Turing Machines
5.9. Adiabatic Quantum Computing
5.10. Variational Quantum Eigensolver
5.11. Summary
5.12. Problems
Chapter 6. Information Theory and Classical Error Correcting Codes
6.1. Classical Information Theory Fundamentals
6.2. Channel Coding Preliminaries
6.3. Linear Block Codes
6.4. Cyclic Codes
6.5. Bose–Chaudhuri–Hocquenghem Codes
6.6. Reed–Solomon Codes, Concatenated Codes, and Product Codes
6.7. Concluding Remarks
6.8. Problems
Chapter 7. Quantum Information Theory Fundamentals
7.1. Introductory Remarks
7.2. Von Neumann Entropy
7.3. Holevo Information, Accessible Information, and Holevo Bound
7.4. Data Compression and Schumacher's Noiseless Quantum Coding Theorem
7.5. Quantum Channels
7.6. Quantum Channel Coding and Holevo–Schumacher–Westmoreland Theorem
7.7. Summary
7.8. Problems
Chapter 8. Quantum Error Correction
8.1. Pauli Operators (Revisited)
8.2. Quantum Error Correction Concepts
8.3. Quantum Error Correction
8.4. Important Quantum Coding Bounds
8.5. Quantum Operations (Superoperators) and Quantum Channel Models
8.6. Summary
8.7. Problems
Chapter 9. Quantum Stabilizer Codes and Beyond
9.1. Stabilizer Codes
9.2. Encoded Operators
9.3. Finite Geometry Interpretation
9.4. Standard Form of Stabilizer Codes
9.5. Efficient Encoding and Decoding
9.6. Nonbinary Stabilizer Codes
9.7. Subsystem Codes
9.8. Topological Codes
9.9. Surface Codes
9.10. Entanglement-Assisted Quantum Codes
9.11. Summary
9.12. Problems
Chapter 10. Quantum LDPC 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. Spatially Coupled Quantum LDPC Codes
10.6. Summary
10.7. Problems
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. Surface Codes and Large-Scale Quantum Computing
11.7. Summary
11.8. Problems
Chapter 12. Cluster State-based Quantum Computing
12.1. Cluster States
12.2. Universality of Cluster State-based Quantum Computing
12.3. Cluster State Processing and One-way Quantum Computation
12.4. Physical Implementations
12.5. Summary
12.6. Problems
Chapter 13. Physical Implementations of Quantum Information Processing
13.1. Physical Implementation Basics
13.2. Nuclear Magnetic Resonance in Quantum Computing
13.3. Trapped Ions in Quantum Computing
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-Based Quantum Information Processing
13.8. Quantum Dots in Quantum Information Processing
13.9. Summary
13.10. Problems
Chapter 14. Quantum Machine Learning
14.1. Machine Learning Fundamentals
14.2. The Ising Model, Adiabatic Quantum Computing, and Quantum Annealing
14.3. Quantum Approximate Optimization Algorithm and Variational Quantum Eigensolver
14.4. Quantum Boosting
14.5. Quantum Random Access Memory
14.6. Quantum Matrix Inversion
14.7. Quantum Principal Component Analysis
14.8. Quantum Optimization-Based Clustering
14.9. Grover Algorithm-Based Global Quantum Optimization
14.10. Quantum K-Means
14.11. Quantum Support Vector Machine
14.12. Quantum Neural Networks
14.13. Summary
14.14. Problems
Chapter 15. Quantum Key Distribution
15.1. Cryptography Basics
15.2. QKD Basics
15.3. No-Cloning Theorem and Distinguishing of Quantum States
15.4. Discrete Variable QKD Protocols
15.5. QKD Security
15.6. The Decoy-State Protocols
15.7. Measurement Device-Independent QKD Protocols
15.8. Twin-Field QKD Protocols
15.9. Information Reconciliation and Privacy Amplification
15.10. Quantum Optics and Gaussian Quantum Information Theory
15.11. Continuous Variable QKD
15.12. Summary
15.13. Problems
Appendix. Abstract Algebra Fundamentals
Index

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