Notes for MA591 :

Preface

Table of Contents

Chapter 1. Tensor Product Space

· Hilbert Space

· Representation Theory

· Tensor Algebra

· Schmidt Decomposition and Singular Value Decomposition

Chapter 2. Basic Principles in Quantum Mechanics

· Copenhagen Interpretation

· Density Matrix and Its Statistical Meaning

· Entanglement

· Purification

Chapter 3. Quantum Computing Tools

· Quantum Computer

· Reversible Operations

· Logic Gates vs. Quantum Gates

· Circuits

· Hahn-Banach Theorem, II

· Applications of Entanglement – Dense Coding and Teleportation

Chapter 4. Computational Examples

· Deutsch Problem

· Bernstein-Vazirani Problem

· Simon Problem

· Unstructured Search Problem

· Constructing the Tofoli gate

Chapter 5. Applications

· RSA Encryption

· Quantum Fourier Transform

· Shor Factorization

· Solving Linear Algebra Problems

· Solving Ordinary Differential Equations

References