Ordered Quantum Branching Programs Are More Powerful than Ordered Probabilistic Branching Programs under a Bounded-Width Restriction

Abstract

One of important questions on quantum computing is whether there is a computational gap between the model that may use quantum effects and the model that may not. Researchers have shown that some quantum automaton models are more powerful than classical ones. As one of classical computational models, branching programs have been studied intensively as well as automaton models, and several types of branching programs are introduced including read-once branching programs and bounded-width branching programs. In this paper, we introduce a new quantum computational model, a quantum branching program, as an extension of a classical probabilistic branching program, and make comparison of the power of these two models. We show that, under a bounded-width restriction, ordered quantum branching programs can compute some function that ordered probabilistic branching programs cannot compute.