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We give a definition of a quantum branching program. A well-known Boolean function MOD p  is considered. We prove that any deterministic branching program and any probabilistic ordered stable branching program which (1/2 + ε)-compute the function MOD p  are of width no less than p. We construct a stable quantum branching program of width O(log p) which computes the function MOD p  with one-sided error ε &gt; 0.

On relative complexity of quantum and classical branching programs