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 qrealq scalable quantum computer.C8 Let S be a positive matrix. ... C9 While Eqn. (13.4) is intricate, there is a useful diagram (called a transmission line diagram) which keeps track of all the matrix products in it ac. ... We show that positive Toeplitz matrices are PPT states.

Title | : | Mathematics of Quantum Computation and Quantum Technology |

Author | : | Louis Kauffman, Samuel J. Lomonaco |

Publisher | : | CRC Press - 2007-09-19 |

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