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

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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.