Project page: http://www.math.wm.edu/~ckli/quantum2.html
Topic description: One may see http://en.wikipedia.org/wiki/Quantum_computing for a basic introduction of quantum computing.
In NMR spectroscopy (a technology used in the construction of quantum computers), one needs to determine
min{||A - U*CU||: U unitary},
which is equivalent to finding
max{ Real(trace(CUA*U*)): U unitary},
for two n-by-n-matrices A and C. Usually, A and C are special matrices, and one may sometimes restrict the choice of unitary matrices. It is important to understand the set of numbers
W(C,A) = {trace(CUA*U*): U unitary},
which is known as the C-numerical range of A*, especially, with restriction on the choice of unitary matrices.
For more background, see
Research opportunities: How to construct the C-numerical ranges and determine the maximum modulus of the complex numbers in the set are important research problems.
Prerequisities: Math 211 Linear Algebra.
Suggested prerequisities: Programming skills in Matlab and Maple will be very helpful. One can write computer programs to generate the set W(C,A) and solve the optimization problems.
Students with more advanced mathematics courses such as Math 307, 311 may be able to study some theoretical aspects of the problems.
Contact: Chi-Kwong Li
Last updated at Wednesday, 09-Apr-2008 16:27:27 EDT.