  The natural Hilbert Space of quantum particles can implement
maximum-likelihood (ML) decoding of classical information. The 'Quantum Product
Algorithm' (QPA) is computed on a Factor Graph, where function nodes are
unitary matrix operations followed by appropriate quantum measurement. QPA is
like the Sum-Product Algorithm (SPA), but without summary, giving optimal
decode with exponentially finer detail than achievable using SPA. Graph cycles
have no effect on QPA performance. QPA must be repeated a number of times
before successful and the ML codeword is obtained only after repeated quantum
'experiments'. ML amplification improves decoding accuracy, and Distributed QPA
facilitates successful evolution.
