Decoding with alternating weighted graph sparsification for quantum low-density parity-check codes
Abstract
Real-time decoding is a fundamental necessity for building fault-tolerant quantum computers. In this work, we introduce decoding with alternating weighted graph sparsification (DAWG), an ensemble based approach that combines Tanner graph sparsification with ensembling belief-propagation (BP) decoders. The DAWG decoder runs BP decoders over the full detector error model Tanner graph for certain iterations to then transfer the posteriors to a sparsified graph in which additional rounds of BP are run. Each of the decoders in the ensemble uses a different transfer matrix to map the posterior information to the sparsified graph. We use the serial schedule for the minimum-sum BP decoders and, thus, employ Vibe decoding ideas by randomizing the schedules of each of them. The performance of the DAWG decoder is then numerically studied for bivariate bicycle codes and superdense color code circuits to be compared with other state-of-the-art decoding approaches. Importantly, the DAWG decoder shows a similar performance to Relay belief-propagation and Vibe decoding when combined with an order-$0$ Localized Statistics Decoding (LSD-$0$) post-processor. Crucially, the post-processor is called an order of magnitude less times than for Vibe with the same ensemble size, indicating that the introduced latency tail will be minimal. Furthermore, LSD-$0$ operates on a sparsified decoding graph of a fraction of the size of the full detector error model, which simplifies the resources required by specialized hardware to support it. Overall, the DAWG+LSD-$0$ decoder represents a viable low-cost BP-based decoding algorithm for quantum error correction codes.
Related
- Accelerating A*-Based Algorithms for Decoding Quantum Low-Density Parity-Check Codes
- Optimally Weighted Constrained Shadow Tomography for Reduced Density Matrices
- Scaling Alternating-Bias-Assisted Annealing for Precision Transmon Frequency Targeting on Superconducting Quantum Processors
- Fault-tolerant and fully addressable unitary logical gates via round-robin sparsification
- Dithered Belief Propagation for Real-Time Quantum Memory Decoding
BibTeX
@misc{martinez2026decoding,
title = {{Decoding with alternating weighted graph sparsification for quantum low-density parity-check codes}},
author = {Josu Etxezarreta Martinez and Francisco Garcia-Herrero and Ruben M. Otxoa and Reza Dastbasteh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35735},
eprint = {2610.35735},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35735},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Decoding with alternating weighted graph sparsification for quantum low-density parity-check codes
AU - Josu Etxezarreta Martinez
AU - Francisco Garcia-Herrero
AU - Ruben M. Otxoa
AU - Reza Dastbasteh
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35735
UR - https://arxiv.org/abs/2610.35735
AB - Real-time decoding is a fundamental necessity for building fault-tolerant quantum computers. In this work, we introduce decoding with alternating weighted graph sparsification (DAWG), an ensemble based approach that combines Tanner graph sparsification with ensembling belief-propagation (BP) decoders. The DAWG decoder runs BP decoders over the full detector error model Tanner graph for certain iterations to then transfer the posteriors to a sparsified graph in which additional rounds of BP are run. Each of the decoders in the ensemble uses a different transfer matrix to map the posterior information to the sparsified graph. We use the serial schedule for the minimum-sum BP decoders and, thus, employ Vibe decoding ideas by randomizing the schedules of each of them. The performance of the DAWG decoder is then numerically studied for bivariate bicycle codes and superdense color code circuits to be compared with other state-of-the-art decoding approaches. Importantly, the DAWG decoder shows a similar performance to Relay belief-propagation and Vibe decoding when combined with an order-$0$ Localized Statistics Decoding (LSD-$0$) post-processor. Crucially, the post-processor is called an order of magnitude less times than for Vibe with the same ensemble size, indicating that the introduced latency tail will be minimal. Furthermore, LSD-$0$ operates on a sparsified decoding graph of a fraction of the size of the full detector error model, which simplifies the resources required by specialized hardware to support it. Overall, the DAWG+LSD-$0$ decoder represents a viable low-cost BP-based decoding algorithm for quantum error correction codes.
ER -