Quantum Factor Graphs

Abstract

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.