Belief Propagation with Quantum Messages for Symmetric Classical-Quantum Channels
Abstract
Belief propagation (BP) is a classical algorithm that approximates the marginal distribution associated with a factor graph by passing messages between adjacent nodes in the graph. It gained popularity in the 1990's as a powerful decoding algorithm for LDPC codes. In 2016, Renes introduced a belief propagation with quantum messages (BPQM) and described how it could be used to decode classical codes defined by tree factor graphs that are sent over the classical-quantum pure-state channel. In this work, we propose an extension of BPQM to general binary-input symmetric classical-quantum (BSCQ) channels based on the implementation of a symmetric "paired measurement". While this new paired-measurement BPQM (PMBPQM) approach is suboptimal in general, it provides a concrete BPQM decoder that can be implemented with local operations.
Keywords
Cite
@article{arxiv.2207.04984,
title = {Belief Propagation with Quantum Messages for Symmetric Classical-Quantum Channels},
author = {S. Brandsen and Avijit Mandal and Henry D. Pfister},
journal= {arXiv preprint arXiv:2207.04984},
year = {2022}
}
Comments
Extended version of submission to the 2022 Information Theory Workshop in Mumbai, India