Classical Simulation Complexity of Quantum Branching Programs

Abstract

We present classical simulation techniques for measure once quantum branching programs. For bounded error syntactic quantum branching program of width $w$ that computes a function with error $delta$ we present a classical deterministic branching program of the same length and width at most $(1+2/(1-2delta))^{2w}$ that computes the same function. Second technique is a classical stochastic simulation technique for bounded error and unbounded error quantum branching programs. Our result is that it is possible stochastically-classically simulate quantum branching programs with the same length and almost the same width, but we lost bounded error acceptance property