[quantum-info] IQC Seminar May 24th, Greg Kuperberg

[Erin Cronin]

IQC Seminar

Friday, 24 May 2013 at 10:30AM
QNC 1506

Connections between quantum computing and quantum algebra
Greg Kuperberg
University of California, Davis

    Quantum computing and quantum algebra are two celebrated modern kindred areas of research. The pinata-smashing result in quantum computing (but not the first important result) was Shor's algorithm in 1994. The pinata-smashing result in quantum algebra (again, in hindsight not the first important result) was the Jones polynomial in 1984. In both fields, as well, one starts with something commutative and makes it non-commutative: probability and Turing machines in the case of quantum computing; coordinate rings and tensor products in the case of quantum algebra. However, the interaction between quantum algebra and quantum computing is subtle and has alternately been ignored and overplayed. I will discuss those connections that I understand: anyonic thoery and fault tolerance, specific quantum algorithms from quantum algebra, and hardness results.