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.
Cite
@article{arxiv.quant-ph/0010043,
title = {Quantum Factor Graphs},
author = {Matthew G. Parker},
journal= {arXiv preprint arXiv:quant-ph/0010043},
year = {2007}
}
Comments
Minor modifications. 24 pages, Latex, 14 figures, Presented in part at 2nd Int. Symp. on Turbo Codes and Related Topics, Brest, France, Sept 4-7, 2000 Accepted for publication in "Annals of Telecom." 2001