Quantum Computation: A Grand Mathematical Challenge for the Twenty-First Century and the Millennium
About this Title
Samuel J. Lomonaco Jr., Editor
Publication: Proceedings of Symposia in Applied Mathematics
Publication Year: 2002; Volume 58
ISBNs: 978-0-8218-2084-1 (print); 978-0-8218-9273-2 (online)
This book presents written versions of the eight lectures given during the AMS Short Course held at the Joint Mathematics Meetings in Washington, D.C. The objective of this course was to share with the scientific community the many exciting mathematical challenges arising from the new field of quantum computation and quantum information science. The course was geared toward demonstrating the great breadth and depth of this mathematically rich research field. Interrelationships with existing mathematical research areas were emphasized as much as possible. Moreover, the course was designed so that participants with little background in quantum mechanics would, upon completion, be prepared to begin reading the research literature on quantum computation and quantum information science.
Based on audience feedback and questions, the written versions of the lectures have been greatly expanded, and supplementary material has been added. The book features an overview of relevant parts of quantum mechanics with an introduction to quantum computation, including many potential quantum mechanical computing devices; introduction to quantum algorithms and quantum complexity theory; in-depth discussion on quantum error correcting codes and quantum cryptography; and finally, exploration into diverse connections between quantum computation and various areas of mathematics and physics.
This book is the companion volume to Quantum Computation and Quantum Information, CONM/305, Volume 305 in the Contemporary Mathematics series.
Graduate students, research mathematicians, and physicists interested in quantum theory, computer science, information, communication, and circuits.
Table of Contents
Chapter I. An invitation to quantum computation
- Samuel J. Lomonaco, Jr. – A Rosetta Stone for quantum mechanics with an introduction to quantum computation [MR 1922894]
- Howard E. Brandt – Qubit devices [MR 1922895]
Chapter II. Quantum algorithms and quantum complexity theory
- Peter W. Shor – Introduction to quantum algorithms [MR 1922896]
- Samuel J. Lomonaco, Jr. – Shor’s quantum factoring algorithm [MR 1922897]
- Samuel J. Lomonaco, Jr. – Grover’s quantum search algorithm [MR 1922898]
- Umesh V. Vazirani – A survey of quantum complexity theory [MR 1922899]
Chapter III. Quantum error correcting codes and quantum cryptography
- Daniel Gottesman – An introduction to quantum error correction [MR 1922900]
- Samuel J. Lomonaco, Jr. – A talk on quantum cryptography: Or how Alice outwits Eve [MR 1922901]
Chapter IV. More mathematical connections
- Alexei Kitaev – Topological quantum codes and anyons [MR 1922902]
- Louis H. Kauffman – Quantum topology and quantum computing [MR 1922903]
- Samuel J. Lomonaco, Jr. – An entangled tale of quantum entanglement [MR 1922904]