1st Edition
Quantum Error Correction and Fault Tolerant Quantum Computing
By Frank Gaitan
Copyright 2013
312 Pages
24 B/W Illustrations
by
CRC Press
312 Pages
24 B/W Illustrations
by
CRC Press
Also available as eBook on:
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... Read more
Introduction
Historical Background
Classical Error Correcting Codes
Using Quantum Systems to Store and Process Data
Quantum Error Correcting Codes-First Pass
Quantum Error Correcting Codes
Quantum Operations
Quantum Error Correcting Codes: Definitions
Example: Calderbank-Shor-Steane [7, 1, 3] Code
Quantum Stabilizer Codes
General Framework
Examples
Alternate Formulation: Finite Geometry
Concatenated Codes
Quantum Stabilizer Codes: Efficient Encoding and Decoding
Standard Form
Encoding
Decoding
Fault-Tolerant Quantum Computing
Fault-Tolerance
Error Correction
Encoded Operations in N(Qn) n N(S)
Measurement
Four-Qubit Interlude
Multi-Qubit Stabilizer Codes
Operations Outside N(Qn)-Toffoli Gate
Example: [5, 1, 3J] Code
Example: [4, 2, 2J] Code
Accuracy Threshold Theorem
Preliminaries
Threshold Analysis
Bounds on Quantum Error Correcting Codes
Quantum Hamming Bound
Quantum Gilbert-Varshamov Bound
Quantum Singleton Bound
Linear Programming Bounds for QECCs
Entanglement Purification and QECCs
Appendix A: Group Theory
Fundamental Notions
Group Action
Mapping Groups
Appendix B: Quantum Mechanics
States
Composite Systems
Observables
Dynamics
Measurement and State Preparation
Mixed States
References
Appendix
Historical Background
Classical Error Correcting Codes
Using Quantum Systems to Store and Process Data
Quantum Error Correcting Codes-First Pass
Quantum Error Correcting Codes
Quantum Operations
Quantum Error Correcting Codes: Definitions
Example: Calderbank-Shor-Steane [7, 1, 3] Code
Quantum Stabilizer Codes
General Framework
Examples
Alternate Formulation: Finite Geometry
Concatenated Codes
Quantum Stabilizer Codes: Efficient Encoding and Decoding
Standard Form
Encoding
Decoding
Fault-Tolerant Quantum Computing
Fault-Tolerance
Error Correction
Encoded Operations in N(Qn) n N(S)
Measurement
Four-Qubit Interlude
Multi-Qubit Stabilizer Codes
Operations Outside N(Qn)-Toffoli Gate
Example: [5, 1, 3J] Code
Example: [4, 2, 2J] Code
Accuracy Threshold Theorem
Preliminaries
Threshold Analysis
Bounds on Quantum Error Correcting Codes
Quantum Hamming Bound
Quantum Gilbert-Varshamov Bound
Quantum Singleton Bound
Linear Programming Bounds for QECCs
Entanglement Purification and QECCs
Appendix A: Group Theory
Fundamental Notions
Group Action
Mapping Groups
Appendix B: Quantum Mechanics
States
Composite Systems
Observables
Dynamics
Measurement and State Preparation
Mixed States
References
Appendix
Biography
Gaitan, Frank
