 Since each transition is (essentially) independent of the previous (if we disregard the distinction between accepted and rejected languages), the PFA essentially becomes a kind of Markov chain.By contrast, in a QFA, the manifold is complex projective space formula_17, and the transition matrices are unitary matrices.Each point in formula_17 corresponds to a quantum-mechanical probability amplitude or pure state; the unitary matrices can be thought of as governing the time evolution of the system (viz in the Schrödinger picture).