Quantum information science and its contributions to mathematics : American Mathematical Society Short Course, January 3-4, 2009, Washington, DC
Quantum information science and its contributions to mathematics : American Mathematical Society Short Course, January 3-4, 2009, Washington, DC
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DOI：
10.1090/psapm/068
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发表时间：
2010-10
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影响因子：
--
通讯作者：
S. Lomonaco
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作者：
S. Lomonaco
本卷是基于2009年1月3日至4日在华盛顿，华盛顿特区举行的2009年AMS量子计算和量子信息短期课程上的讲座。本卷的第一部分由两篇论文组成，介绍了量子计算和量子信息新兴领域的许多重要主题，即：量子信息科学（QIS）。第一篇论文讨论了QIS中的许多基本概念，并以纠缠浓度的奇怪和反直觉现象结束。第二个介绍了量子纠错和容错，QIS的第一道防线量子退相干的调查。第二部分由四篇论文说明如何QIS研究目前有助于发展新的数学研究方向。第一篇论文说明了微分几何如何成为开发量子计算机编译器的基础研究工具。第二篇论文对量子拓扑和量子计算之间的许多联系进行了综述。最后两篇论文概述了量子结理论这一新兴领域，这是一个连接量子计算和结理论的跨学科研究领域。这两篇论文说明了令人惊讶的联系与一些其他领域的数学。在附录中，还为那些不熟悉量子力学的读者提供了一篇介绍性的综述文章。
This volume is based on lectures delivered at the 2009 AMS Short Course on Quantum Computation and Quantum Information, held January 3-4, 2009, in Washington, D.C. Part I of this volume consists of two papers giving introductory surveys of many of the important topics in the newly emerging field of quantum computation and quantum information, i.e., quantum information science (QIS). The first paper discusses many of the fundamental concepts in QIS and ends with the curious and counter-intuitive phenomenon of entanglement concentration. The second gives an introductory survey of quantum error correction and fault tolerance, QIS's first line of defence against quantum decoherence. Part II consists of four papers illustrating how QIS research is currently contributing to the development of new research directions in mathematics. The first paper illustrates how differential geometry can be a fundamental research tool for the development of compilers for quantum computers. The second paper gives a survey of many of the connections between quantum topology and quantum computation. The last two papers give an overview of the new and emerging field of quantum knot theory, an interdisciplinary research field connecting quantum computation and knot theory. These two papers illustrate surprising connections with a number of other fields of mathematics. In the appendix, an introductory survey article is also provided for those readers unfamiliar with quantum mechanics.