Quantum Computing Fundamentals

Table of Contents

Preface

Part I Preparatory Material

Chapter 1: Introduction to Essential Linear Algebra

1.1 What Is Linear Algebra?

1.2 Some Basic Algebra

1.2.1 Groups, Rings, and Fields

1.3 Matrix Math

1.3.1 Matrix Addition and Multiplication

1.3.2 Matrix Transposition

1.3.3 Submatrix

1.3.4 Identity Matrix

1.3.5 Deeper Into the Matrix

1.4 Vectors and Vector Spaces

1.5 Set Theory

1.6 Summary

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Chapter 2: Complex Numbers

2.1 What Are Complex Numbers?

2.2 Algebra of Complex Numbers

2.3 Complex Numbers Graphically

2.4 Vector Representations of Complex Numbers

2.5 Pauli Matrices

2.5.1 Algebraic Properties of Pauli Matrices

2.6 Transcendental Numbers

2.7 Summary

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Chapter 3: Basic Physics for Quantum Computing

3.1 ...