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
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
