Doctor of Philosophy in Combinatorics and Optimization - Quantum Computing

University of Waterloo

Combinatorics is the study of discrete structures and their properties. Many modern scientific advances have employed combinatorial structures to model the physical world, and recent advances in computational technology have made such investigations feasible. In particular, since computers process discrete data, combinatorics has become indispensable to computer science. Optimization, or mathematical programming, is the study of maximizing and minimizing functions subject to specified boundary conditions or constraints. With the emergence of computers, optimization experienced a dramatic growth as a mathematical theory, enhancing both combinatorics and classical analysis. The functions to be optimized arise in engineering, the physical and management sciences, and in various branches of mathematics. The PhD involves about two years of grad courses followed by research and a dissertation, and typically lasts four years.Today's computers and other information processing devices manipulate information using what is known as the classical approximation to the laws of physics. However, we have known for some time that there is a more accurate description of the laws - the one provided by quantum mechanics. The study of how the laws of quantum mechanics affect computing, cryptography, and similar information processing tasksis known as quantum information processing. In the 1990s, a sequence of results culminated in an efficient quantum algorithm for decomposing integers into their prime factors.