Knots and Topological Quantum Computing

A quantum computer is a hypothetical device that exploits the principles of quantum mechanics to perform computations. Such computers 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 field of topological quantum computing is full of theoretical challenges, including the formulation and classification of quantum phases on the mathematical side and the search for topological phases of matter on the physical side. This conference 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.

Several non-technical articles on topological quantum computing have appeared recently: “Knotty Calculations” appeared in the Science News in 2003, “Dancing the Quantum Dream” appeared in the New Scientist in 2004, “Knots May Unleash Computer Power” appeared in The Mathematics Calendar in 2005 and “Computing with Quantum Knots” is the cover article of the April 2006 Scientific American. The link to this article: Computing with Quantum Knots

“A machine based on bizarre particles called anyons that represent a calculation as a set of braids in spacetime might be a shortcut to practical computing.” -- Graham Collins, in “Computing with Quantum Knots,” in Scientific American, April 2006.