Complexity Bounds on Some Fundamental Computational Problems for Quantum Branching Programs

Abstract

We study quantum computational complexity of several problems connected to the Hidden Subgroup Problem. This problem drew substantial attention when a polynomial time quantum algorithm for it was found. The algorithm generalized the quantum algorithms for factoring integers and finding discrete logarithms.<br /> We consider the the problems in the context of quantum ordered read-once decision diagrams. Our presentation starts with some fundamental functions related to the Hidden Subgroup Problem. These functions include Equality, Periodicity and simplified "Simon". We show linear upper and lower bounds on the width of quantum OBDD representations of these functions.<br /> In the second part of the research we show upper and lower bounds for the Hidden Subgroup Test.