Optimization of Quantum Algorithms for Applications

Abstract

I aim to design and evaluate quantum algorithms that perform optimally with respect to metrics that make or break the applicability of these algorithms. Specifically, I analyze two applications: Bitcoin mining and estimating expectation values from a system of linear equations. For the former I develop a quantum algorithm for Bitcoin mining which optimizes the probability of successfully mining Bitcoin. For the later I give a quantum algorithm with query complexity that is optimally dependent on accuracy. I ensure that my quantum algorithms are relevant to applications by designing algorithms that are end-to-end for their applications, as opposed to algorithms that only address a subroutine. My work yields quantum algorithms that are directly comparable to their classical counterparts. By making this comparison, I develop necessary conditions for quantum algorithms to outperform classical algorithms at solving systems of linear equations and Bitcoin mining.