Belief Propagation with Quantum Messages for Symmetric Classical-Quantum Channels

• URL: http://arxiv.org/abs/2207.04984v1
• Date: Mon, 11 Jul 2022 16:14:49 GMT
• Title: Belief Propagation with Quantum Messages for Symmetric Classical-Quantum Channels
• Authors: S. Brandsen, Avijit Mandal, and Henry D. Pfister
• Abstract summary: In 2016, Renes introduced a belief propagation with quantum messages (BPQM) We propose an extension of BPQM to general binary-input symmetric classical-quantum (BSCQ) channels based on the implementation of a symmetric "paired measurement"
• Score: 6.831109886531548
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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