Logic and Algebraic Structures in Quantum Computing

Arising from a special session held at the 2010 North American Annual Meeting of the Association for Symbolic Logic, this volume is an international cross-disciplinary collaboration with contributions from leading experts exploring connections across their respective fields. Themes range from philosophical examination of the foundations of physics and quantum logic, to exploitations of the methods and structures of operator theory, category theory, and knot theory in an effort to gain insight into the fundamental questions in quantum theory and logic. The book will appeal to researchers and students working in related fields, including logicians, mathematicians, computer scientists, and physicists. A brief introduction provides essential background on quantum mechanics and category theory, which, together with a thematic selection of articles, may also serve as the basic material for a graduate course or seminar.

Table of Contents

Chapter 1. Introduction
Chapter 2. A (very) brief tour of quantum mechanics, computation, and category theory
Chapter 3. Could logic be empirical? The Putnam-Kripke debate
Chapter 4. The essence of quantum theory for computers
Chapter 5. Fiber products of measures and quantum foundations
Chapter 6. Operational theories and categorical quantum mechanics
Chapter 7. Relating operator spaces via adjunctions
Chapter 8. Topos-based logic for quantum systems and bi-Heyting algebras
Chapter 9. The logic of quantum mechanics – Take II
Chapter 10. Reasoning about meaning in natural language with compact closed categories and Frobenius algebras
Chapter 11. Knot logic and topological quantum computing with Majorana fermions