Belief Propagation for Classical and Quantum Systems: Overview and Recent Results

This article reviews belief propagation (BP) for classical inference problems and describes its extension to quantum systems, which is known as BP with quantum messages (BPQM). Since BP plays a key role in many low-complexity decoders for error-correcting codes, BPQM enables the practical extension of these decoders to classical quantum channels, such as the pure state channel.