Decoding correlated errors in quantum LDPC codes

Area of Science:

• Quantum Information Science
• Quantum Computing
• Error Correction Codes

Background:

• Correlated errors in quantum codes pose a significant challenge for fault-tolerant quantum computing.
• Existing decoding methods struggle with circuit-level noise and correlated errors.

Purpose of the Study:

• To introduce an efficient decoding framework for quantum Low-Density Parity-Check (LDPC) codes under circuit-level noise.
• To address correlated errors by modifying the error model while preserving decoding equivalence.

Main Methods:

• Graph augmentation and rewiring for inference (GARI) method to modify the correlated detector error model.
• Elimination of 4-cycles involving Y-type errors in the graph representation.
• Application of a normalized min-sum decoder with a hybrid serial-layered schedule.
• Ensemble decoding using 24 parallel decoders for enhanced performance.

Main Results:

• Achieved a logical error rate of (6.70 ± 1.93) × 10^-9 for the distance 12 Bivariate Bicycle code at a physical error rate of 10^-3.
• Demonstrated performance on par with XYZ-Relay-BP through ensemble decoding.
• Preliminary FPGA results show real-time capability with an average decoding latency of 273 ns.

Conclusions:

• The GARI framework effectively decodes quantum LDPC codes with correlated errors.
• The proposed method achieves high accuracy and low latency, suitable for real-time applications.
• This work advances the practical implementation of fault-tolerant quantum computers.