Classical Simulation Complexity of Quantum Branching Programs (Draft)

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 δ we present a classical deterministic branching program of the same length and width at most (1 + 2/(1 − 2δ))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.