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.