Belief Propagation with Quantum Messages for Symmetric Classical-Quantum Channels

TL;DR

This paper extends belief propagation with quantum messages to general symmetric classical-quantum channels using a symmetric paired measurement, enabling a practical quantum decoding method with local operations.

Contribution

It introduces a new paired-measurement BPQM (PMBPQM) method for symmetric classical-quantum channels, broadening the applicability of quantum belief propagation decoding.

Findings

Proposes a symmetric paired measurement for BPQM.

Provides a concrete, implementable quantum decoder.

Achieves suboptimal but practical decoding for BSCQ 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.