Mathematics of Quantum Computation and Quantum Technology

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 TechnologyEdited 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 TechnologyThis 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.

PREFACEQUANTUM COMPUTATION Quantum Hidden Subgroup Algorithms: An Algorithmic Toolkit Samuel J. Lomonaco and Louis H. KauffmanA Realization Scheme for Quantum Multi-Object Search Zijian Diao, Goong Chen, and Peter ShiueOn Interpolating between Quantum and Classical Complexity Classes J. Maurice RojasQuantum Algorithms for Hamiltonian Simulation Dominic W. Berry, Graeme Ahokas, Richard Cleve, and Barry C. SandersQUANTUM TECHNOLOGYNew Mathematical Tools for Quantum Technology C. Bracher, M. Kleber, and T. KramerThe Probabilistic Nature of Quantum Mechanics Leon CohenSuperconducting Quantum Computing Devices Zhigang Zhang and Goong ChenNondeterministic Logic Gates in Optical Quantum Computing Federico M. Spedalieri, Jonathan P. Dowling, and Hwang LeeQUANTUM INFORMATIONExploiting Entanglement in Quantum Cryptographic Probes Howard E. BrandtNonbinary Stabilizer Codes Pradeep Kiran Sarvepalli, Salah A. Aly, and Andreas KlappeneckerAccessible Information about Quantum States: An Open Optimization Problem Jun Suzuki, Syed M. Assad, and Berthold-Georg EnglertQuantum Entanglement: Concepts and Criteria Fu-li Li and M. Suhail ZubairyParametrizations of Positive Matrices with Applications M. Tseng, H. Zhou, and V. RamakrishnaQUANTUM TOPOLOGY, CATEGORICAL ALGEBRA, AND LOGIC Quantum Computing and Quantum Topology Louis H. Kauffman and Samuel J. LomonacoTemperley-Lieb Algebra: From Knot Theory to Logic and Computation via Quantum Mechanics Samson AbramskyQuantum Measurements without Sums Bob Coecke and Dusko PavlovicAPPENDIXINDEX