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Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes.

Ye-Hua Liu1, David Poulin1,2

  • 1Département de Physique & Institut Quantique, Université de Sherbrooke, J1K 2R1 Sherbrooke, Québec, Canada.

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|June 8, 2019
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Neural belief-propagation (BP) decoders improve quantum error correction. Training BP decoders with a specialized loss function addresses error degeneracy in quantum low-density parity-check codes, enhancing performance.

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Area of Science:

  • Quantum Information Science
  • Coding Theory
  • Machine Learning

Background:

  • Belief-propagation (BP) decoders are crucial in classical coding theory.
  • Quantum error-correcting codes face challenges due to error degeneracy.
  • BP decoders are currently unsuitable for quantum error correction.

Purpose of the Study:

  • To develop an effective decoding method for quantum low-density parity-check codes.
  • To overcome the limitations of traditional BP decoders in quantum applications.
  • To address the issue of error degeneracy in quantum error correction.

Main Methods:

  • Training neural BP decoders using deep neural network principles.
  • Implementing a novel loss function specifically designed for error degeneracy.
  • Applying the trained decoders to various quantum low-density parity-check code families.

Main Results:

  • Substantial performance improvements in BP decoders across tested quantum codes.
  • Demonstrated potential to solve the error degeneracy problem in quantum decoding.
  • Successful application of neural networks to enhance quantum error correction.

Conclusions:

  • Neural BP decoders offer a promising solution for decoding quantum error-correcting codes.
  • Tailored training methods can overcome quantum-specific decoding challenges like error degeneracy.
  • This approach significantly advances the practical implementation of quantum error correction.