Quantum Computation and Quantum Error Prevention

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Table of Contents

   Preface

1. Chapter 1 - Introduction
   1. Introduction
   2. An Introduction to Quantum Computation
   3. Bits and qubits: An Introduction
   4. Obstacles to Building a Reliable Quantum Computer
2. Chapter 2 - Qubits and Collections of Qubits
   1. Introduction
   2. Qubit States
   3. Qubit Gates
   4. The Pauli Matrices
   5. States of Many Qubits
   6. Quantum Gates for Many Qubits
   7. Measurement
3. Chapter 3 - Physics of Quantum Information
   1. Introduction
   2. Schrodinger’s Equation
   3. Density Matrix for Pure States
   4. Measurements Revisited
   5. Density Matrix for a Mixed State
   6. Expectation Values
4. Chapter 4 - Entanglement
   1. Introduction
   2. Entangled Pure States
   3. Entangled Mixed States
   4. Extensions and Open Problems
5. Chapter 5 - Quantum Information: Basic Principles and Simple Examples
   1. Introduction
   2. No Cloning!
   3. Uncertainty Principle
   4. Quantum Dense Coding
   5. Teleporting a Quantum State
   6. QKD: BB84
6. Chapter 6 - Quantum Computation
   1. Quantum Computation Basics
   2. Deutsch-Josza Algorithm
   3. Simon’s Algorithm
   4. Shor’s Algorithm
   5. Grover’s Algorithm
7. Chapter 7 - Experiments
8. Chapter 8 - Noise in Quantum Systems
   1. Introduction
   2. SMR Representation or Operator-Sum Representation
   3. Physics Behind the Noise and Completely Positive Maps
   4. Notes
9. Chapter 9 - Conclusions
   1. What have we learned?

Appendices

1. Appendix A - Basic Probability Concepts
2. Appendix B - Complex Numbers
3. Appendix C - Vectors and Linear Algebra
   1. Vectors
   2. Linear Algebra: Matrices
   3. More Dirac Notation
   4. Transformations
   5. Eigenvalues and Eigenvectors
   6. Tensor Products
4. Appendix D - Group Theory
   1. Introduction
   2. Definitions and Examples
   3. Comparing Groups: Homomorphisms and Isomorphisms
   4. Infinite Order Groups: Lie Groups
   5. More Representation Theory
5. Appendix E - Density Operator: Extensions
   1. Introduction
   2. An N-dimensional Generalization of the Polarization Vector
   3. The Density Matrix for Two Qubits
6. Appendix F - NOTES and CREDITS

Index

Index

Bibliography

Bibliography

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Much of this material is based upon work supported by the National Science Foundation under Grant No. 0545798. However, any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.