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  3. Localized Statistics Decoding For Quantum Low-density Parity-check Codes.
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Localized statistics decoding for quantum low-density parity-check codes.

Timo Hillmann1, Lucas Berent2, Armanda O Quintavalle3

  • 1Chalmers University of Technology, Gothenburg, Sweden. timo.hillmann@rwth-aachen.de.

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Summary
This summary is machine-generated.

We developed localized statistics decoding, a new algorithm for quantum error correction. This method enhances quantum computing efficiency and is suitable for real-time experimental data processing.

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Area of Science:

  • Quantum Information Science
  • Quantum Error Correction
  • Fault-Tolerant Quantum Computing

Background:

  • Quantum low-density parity-check (QLDPC) codes offer reduced overhead for fault-tolerant quantum computing compared to surface codes.
  • A practical decoding algorithm is crucial for implementing QLDPC codes.

Purpose of the Study:

  • To introduce a novel, practical decoding algorithm for arbitrary QLDPC codes.
  • To address the barrier of implementing QLDPC codes by developing an efficient decoding strategy.

Main Methods:

  • Localized statistics decoding: a reliability-guided inversion decoder.
  • On-the-fly elimination: a parallel matrix factorization strategy for decoding graph analysis.
  • Identification, validation, and solution of local decoding regions.

Main Results:

  • Localized statistics decoding matches the performance of state-of-the-art decoders.
  • Reduced runtime complexity in the sub-threshold regime.
  • High parallelizability suitable for specialized hardware.

Conclusions:

  • Localized statistics decoding is a viable and efficient method for QLDPC codes.
  • The algorithm's parallel nature and hardware amenability make it promising for real-time syndrome decoding in experiments.
  • This work advances the practical implementation of QLDPC codes for quantum computing.