Quantum Computing and Shor's Algorithm

The Universal Turing Machine described by Alan Turing in the mid 1930s
created a perspective by which we judge computational complexity,
decidability, and other foundational topics.  However, with the current
understanding of quantum mechanics, we know of some tasks which are
performed in the natural world and which cannot be simulated by a Turing
Machine.  Quantum computing is a method by which these processes can be
reproduced.

Despite this intellectual curiosity, the utility of quantum computing
was not demonstrated until Peter Shor developed an algorithm for
factoring large numbers in 1994.  Not only does this algorithm operate
in efficient time on a quantum computer, but it also impacts the area of
secure-key cryptography.

In this seminar, we will discuss the theoretical underpinnings of
quantum computing, the differences between this and the classical model
of computing, and Shor's Algorithm for the factoring of large numbers. 
The depth of the algorithmic analysis will depend on the group's
interest in the first two topics.