Quantum analogues of classical optimization algorithms.

Abstract

This thesis explores the quantum analogues of algorithms used in mathematical optimization. The thesis focuses primarily on the iterative gradient search algorithm (algorithm for finding the minimum or maximum of a function) and the Newton-Raphson algorithm. The thesis introduces a new quantum gradient algorithm suggested by Professor Thomas Konrad and colleagues and a quantum analogue of the Newton-Raphson Method, a method for finding approximations to the roots or zeroes of a real-valued function. The quantum gradient algorithm and the quantum Newton-Raphson are shown to give a polynomial speed up over their classical analogues.