Quantum mechanics

Algorithm

Quantum computer

Biology

Quantum error correction

Statistics

Theoretical computer science

Degeneracy (biology)

Coding (social sciences)

Computer science

Statistical physics

Decoding methods

Physics

Low-density parity-check code

Bioinformatics

Coding theory

Mathematics

Belief propagation

Quantum

Error detection and correction

Physical Review Letters

Belief-propagation (BP) decoders play a vital role in modern coding theory, but they are not suitable to decode quantum error-correcting codes because of a unique quantum feature called error degeneracy. Inspired by an exact mapping between BP and deep neural networks, we train neural BP decoders for quantum low-density parity-check (LDPC) codes with a loss function tailored to error degeneracy. Training substantially improves the performance of BP decoders for all families of codes we tested and may solve the degeneracy problem which plagues the decoding of quantum LDPC codes.

Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes