Large Width Nondeterministic Quantum OBDDs

In this paper we investigate ordered binary decision diagrams (OBDD) – a model for computing Boolean functions. The aim of this work is a comparative complexity analysis of quantum and classical nondeterministic OBDDs of large width. We study the complexity of computing the Boolean function "Equality" in nondeterministic quantum OBDDs for different order of reading variables in comparison with the classical complexity. We show that when using the order of reading for which the width of the classical nondeterministic OBDD is constant, the width of the quantum model is linear and the proved lower bound is tight. We define a Boolean function for which the width of nondeterministic quantum OBDD is exponential for any order of reading variables. We construct a quantum algorithm for computing this function with zero error. We present a result on the relationship between complexity classes for quantum and classical nondeterministic OBDDs of large width.