Elementary Tools for Quantum Computation: Fourier Transforms and
Hidden Subgroups

Alexander Russell
University of Connecticut

11:30am Friday, October 31, 2003
247 Cullinane Hall


ABSTRACT

We survey the current state of the art in quantum Fourier transforms
and solutions to the hidden subgroup problem, outlining several recent
advances in these areas. Following a brief introduction to quantum
computation, we discuss the problem of computing the quantum Fourier
transform over a finite group and describe a quantization of the
remarkable "separation of variables" technique of Rockmore, et
al. Following this, we describe the hidden subgroup problem and the
canonical quantum approach involving the Fourier transform. Here we
describe several recent advances including efficient reconstruction of
normal subgroups and efficient reconstruction of certain subgroups of
the affine groups.

Bio

Alex Russell was born in Philadelphia in 1969. He received a B.A. in
Mathematics and a B.A. in Computer Science from Cornell University in
1991. He attended the Massachusetts Institute of Technology from 1991
to 1996, receiving an S.M. in Electrical Engineering and Computer
Science in 1993 and a Ph.D. in Mathematics in 1996. He is currently an
associate professor at the University of Connecticut. His research
interests include complexity theory, cryptography, quantum
computation, combinatorics, and harmonic analysis.