NSF/CBMS Regional Conference in the Mathematical Sciences-Knots and Topological Quantum Computing-Summer 2008

量子计算机是一种利用量子力学原理进行计算的假想设备。这种计算机利用原子和光的特殊性质而不是电子来进行计算，有可能超过数字计算机的速度，解决即使是当今最快的并行计算机也难以解决的问题。制造这种计算机的主要障碍之一是在不引入误差或失去相干性的情况下操纵相干量子态。1997年，Freedman和Kitaev提出了一种量子计算机的拓扑模型，该模型通过编码辫状结构中的信息来执行计算。这些计算机具有内置的抗退相干防御功能，并且提供了比迄今为止任何其他量子计算方案低许多数量级的错误率。2002年，Freedman、Kitaev、Wang和Larsen证明了拓扑量子计算机可以执行所谓的“量子位量子计算机”所能做的任何计算。在一系列的十场讲座中，王正汉将涵盖拓扑量子计算领域的理论基础，过去十年取得的进展以及未来的挑战。此外，Ara Basmajian将会做一系列关于结点及其不变量的相关讲座。这次会议和由此产生的专著将使感兴趣的研究人员能够在这个令人兴奋的研究领域还处于起步阶段时就参与其中。它将引起物理学家、计算机科学家、数学家、理论家和实践者的兴趣。没有结理论，量子计算或量子物理的背景将被假设。将提供旅费，以减少参加者的开支。特别鼓励高级本科生、研究生、初级教师、妇女、少数民族和残疾人参与和申请支持。

A quantum computer is a hypothetical device that exploits the principles of quantum mechanics to perform computations. Such computers use the special properties of atoms and light rather than electronics to carry out calculations and have the potential to surpass the speed of digital computers and solve problems that are intractable even for today's fastest parallel machines. One of the main obstacles in building such computers is in manipulating coherent quantum states without introducing errors or losing coherence. In 1997, Freedman and Kitaev proposed a topological model of a quantum computer that performs computations by encoding information in the configurations of braids. These computers have a built-in defense against decoherence and offer the promise of error rates many orders of magnitude lower than any other quantum computation scheme to date. In 2002, Freedman, Kitaev, Wang and Larsen proved that a topological quantum computer can perform any computation that a so-called "qubit quantum computer" can do. In a series of ten lectures, Zhenghan Wang will cover the theoretical foundations of the field of topological quantum computing, the progress that has been made over the last decade, and the future challenges. In addition, Ara Basmajian will give a series of related lectures on knots and their invariants. The conference and the resulting monograph will enable interested researchers to get involved in this exciting area of research while it is still in its infancy. It will be of interest to physicists and computer scientists as well as to mathematicians, and to both theoreticians and practitioners. No background in knot theory, quantum computing, or quantum physics will be assumed. Travel funds will be available to deter the expenses of participants. Advanced undergraduates, graduate students, junior faculty, women, minorities, and persons with disabilities are especially encouraged to participate and to apply for support.