Mathematics of Quantum Computation and Quantum Technology: 1st Edition (Hardback) book cover

Mathematics of Quantum Computation and Quantum Technology

1st Edition

Edited by Louis Kauffman, Samuel J. Lomonaco

Chapman and Hall/CRC

624 pages | 249 B/W Illus.

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Hardback: 9781584888994
pub: 2007-09-19
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Description

Research and development in the pioneering field of quantum computing involve just about every facet of science and engineering, including the significant areas of mathematics and physics. Based on the firm understanding that mathematics and physics are equal partners in the continuing study of quantum science, Mathematics of Quantum Computation and Quantum Technology explores the rapid mathematical advancements made in this field in recent years.

Novel Viewpoints on Numerous Aspects of Quantum Computing and Technology

Edited by a well-respected team of experts, this volume compiles contributions from specialists across various disciplines. It contains four main parts, beginning with topics in quantum computing that include quantum algorithms and hidden subgroups, quantum search, algorithmic complexity, and quantum simulation. The next section covers quantum technology, such as mathematical tools, quantum wave functions, superconducting quantum computing interference devices (SQUIDs), and optical quantum computing. The section on quantum information deals with error correction, cryptography, entanglement, and communication. The final part explores topological quantum computation, knot theory, category algebra, and logic.

The Tools You Need to Tackle the Next Generation of Quantum Technology

This book facilitates both the construction of a common quantum language and the development of interdisciplinary quantum techniques, which will aid efforts in the pursuit of the ultimate goal-a "real" scalable quantum computer.

Table of Contents

PREFACE

QUANTUM COMPUTATION

Quantum Hidden Subgroup Algorithms: An Algorithmic Toolkit

Samuel J. Lomonaco and Louis H. Kauffman

A Realization Scheme for Quantum Multi-Object Search

Zijian Diao, Goong Chen, and Peter Shiue

On Interpolating between Quantum and Classical Complexity Classes

J. Maurice Rojas

Quantum Algorithms for Hamiltonian Simulation

Dominic W. Berry, Graeme Ahokas, Richard Cleve, and Barry C. Sanders

QUANTUM TECHNOLOGY

New Mathematical Tools for Quantum Technology

C. Bracher, M. Kleber, and T. Kramer

The Probabilistic Nature of Quantum Mechanics

Leon Cohen

Superconducting Quantum Computing Devices

Zhigang Zhang and Goong Chen

Nondeterministic Logic Gates in Optical Quantum Computing

Federico M. Spedalieri, Jonathan P. Dowling, and Hwang Lee

QUANTUM INFORMATION

Exploiting Entanglement in Quantum Cryptographic Probes

Howard E. Brandt

Nonbinary Stabilizer Codes

Pradeep Kiran Sarvepalli, Salah A. Aly, and Andreas Klappenecker

Accessible Information about Quantum States: An Open Optimization Problem

Jun Suzuki, Syed M. Assad, and Berthold-Georg Englert

Quantum Entanglement: Concepts and Criteria

Fu-li Li and M. Suhail Zubairy

Parametrizations of Positive Matrices with Applications

M. Tseng, H. Zhou, and V. Ramakrishna

QUANTUM TOPOLOGY, CATEGORICAL ALGEBRA, AND LOGIC

Quantum Computing and Quantum Topology

Louis H. Kauffman and Samuel J. Lomonaco

Temperley-Lieb Algebra: From Knot Theory to Logic and Computation via Quantum Mechanics

Samson Abramsky

Quantum Measurements without Sums

Bob Coecke and Dusko Pavlovic

APPENDIX

INDEX

About the Series

Chapman & Hall/CRC Applied Mathematics & Nonlinear Science

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
SCI040000
SCIENCE / Mathematical Physics
SCI057000
SCIENCE / Quantum Theory