Circuit-level benchmarks of GKP-concatenated qLDPC Codes
Abstract
Scalable fault-tolerant quantum error correction based on Gottesman-Kitaev-Preskill (GKP) codes requires finite-rate outer codes that can exploit analog GKP information under realistic circuit noise. However, quantum low-density parity-check (qLDPC) outer codes have not been systematically compared as candidates for circuit-level GKP concatenation. Here, we benchmark BB and tricycle codes using a unified simulation framework that progresses from code-capacity noise to repeated noisy syndrome extraction and schedule-resolved displacement propagation. Across all three noise models, analog-informed belief-propagation with ordered-statistics decoding (BP-OSD) yields higher finite-size crossing estimates than hard-decision decoding. In the full circuit model, the analog-informed crossings are σth≃0.212 for the selected BB sequence and 0.142 for the tricycle sequence, corresponding to squeezing requirements of approximately 10.46 dB and 13.94 dB, respectively. These results show that analog GKP information continues to improve decoding under circuit-level noise. Under the common simulation assumptions used here, the selected BB sequence also yields a higher finite-size crossing estimate than the selected tricycle sequence.
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BibTeX
@misc{yao2026circuitlevel,
title = {{Circuit-level benchmarks of GKP-concatenated qLDPC Codes}},
author = {Yuan Yao and Ruipeng Xing and Jianshuo Gao and Xiao Yuan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35282},
eprint = {2609.35282},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35282},
}
RIS
TY - UNPB
TI - Circuit-level benchmarks of GKP-concatenated qLDPC Codes
AU - Yuan Yao
AU - Ruipeng Xing
AU - Jianshuo Gao
AU - Xiao Yuan
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35282
UR - https://arxiv.org/abs/2609.35282
AB - Scalable fault-tolerant quantum error correction based on Gottesman-Kitaev-Preskill (GKP) codes requires finite-rate outer codes that can exploit analog GKP information under realistic circuit noise. However, quantum low-density parity-check (qLDPC) outer codes have not been systematically compared as candidates for circuit-level GKP concatenation. Here, we benchmark BB and tricycle codes using a unified simulation framework that progresses from code-capacity noise to repeated noisy syndrome extraction and schedule-resolved displacement propagation. Across all three noise models, analog-informed belief-propagation with ordered-statistics decoding (BP-OSD) yields higher finite-size crossing estimates than hard-decision decoding. In the full circuit model, the analog-informed crossings are σ_th≃0.212 for the selected BB sequence and 0.142 for the tricycle sequence, corresponding to squeezing requirements of approximately 10.46 dB and 13.94 dB, respectively. These results show that analog GKP information continues to improve decoding under circuit-level noise. Under the common simulation assumptions used here, the selected BB sequence also yields a higher finite-size crossing estimate than the selected tricycle sequence.
ER -