The basic unit of information in a computer is a bit (a binary digit, either 0 or 1). The basic unit of information in a quantum computer is a qubit. A qubit is a two- dimensional complex vector of magnitude one. While the construction of quantum computers is still in the research and development stages, there are many theoretical problems to tackle. One problem that is of interest to mathematicians is that of error-correcting codes. One way to deal with errors in codes is to find a projection matrix P of rank k so that for matrices A1, A2,..., AN, PAiP equals some scalar multiple of P.

My main objective was to find a way to construct the projection matrices so that PAiP equals some scalar multiple of P. The scalar multiple has to belong to the k rank numerical range of Ai.

The project is important because if developed, quantum computers will be faster and more powerful than classical computers.

This project was of interest to me because I enjoy linear algebra.

The most important part of my project was to find these error-correcting matrices and study their properties in order to find a general solution to error correction in quantum computers.

The most enjoyable thing I have done this summer was to write a program that helps with my research.