Toward Low-latency Iterative Decoding of QLDPC Codes Under Circuit-Level Noise

Toward Low-latency Iterative Decoding of QLDPC Codes Under Circuit-Level Noise

27 Mar 2024 | Anqi Gong*, Sebastian Cammerer†, and Joseph M. Renes*
The paper introduces a sliding window decoder based on belief propagation (BP) with guided decimation (GDG) for decoding quantum low-density parity-check (QLDPC) codes under circuit-level noise. The sliding window approach keeps the decoding complexity reasonable by processing syndrome outputs from a small number of subsequent rounds (the window) to determine fault locations. Within each window, multiple rounds of BP are employed, with the variable node (VN) expected to flip being selected based on its posterior log-likelihood ratio (LLR) history. The VN with the smallest LLR is chosen for decimation, and guessing is allowed at early steps to improve convergence. The GDG decoder is applied to bivariate bicycle (BB) codes, achieving similar logical error rates to BP with additional ordered-statistics decoding (OSD) post-processing. For a window size of three syndrome cycles, a multi-threaded CPU implementation of GDG achieves a worst-case decoding latency of 3ms per window for the [[144,12,12]] code. The paper also discusses the performance of GDG in data qubit noise and single-shot syndrome noise decoding, showing its effectiveness in handling circuit-level noise.The paper introduces a sliding window decoder based on belief propagation (BP) with guided decimation (GDG) for decoding quantum low-density parity-check (QLDPC) codes under circuit-level noise. The sliding window approach keeps the decoding complexity reasonable by processing syndrome outputs from a small number of subsequent rounds (the window) to determine fault locations. Within each window, multiple rounds of BP are employed, with the variable node (VN) expected to flip being selected based on its posterior log-likelihood ratio (LLR) history. The VN with the smallest LLR is chosen for decimation, and guessing is allowed at early steps to improve convergence. The GDG decoder is applied to bivariate bicycle (BB) codes, achieving similar logical error rates to BP with additional ordered-statistics decoding (OSD) post-processing. For a window size of three syndrome cycles, a multi-threaded CPU implementation of GDG achieves a worst-case decoding latency of 3ms per window for the [[144,12,12]] code. The paper also discusses the performance of GDG in data qubit noise and single-shot syndrome noise decoding, showing its effectiveness in handling circuit-level noise.
Reach us at info@study.space
[slides and audio] Toward Low-latency Iterative Decoding of QLDPC Codes Under Circuit-Level Noise