Comparing thresholds of XZZX and rotated surface codes under spatio-temporal correlated noise
Abstract
While independent and identically distributed noise is typically assumed in quantum computing research, complex error models such as correlated and spatio-temporal errors remain underexplored. In this paper, the performance of XZZX and rotated surface codes is evaluated under these complex noise models. Standard graph-based decoders struggle with the hyperedges generated by correlated errors on bias-tailored codes. To address this, we employ the Minimum Weight Parity Factor (MWPF) decoder, which natively processes syndrome hypergraphs without artificial edge decomposition. Our simulations show that under strong Z-biased circuit-level correlated noise (η=100), the threshold of the rotated code degrades to ≈ 0.36%, while the XZZX code drops to ≈ 0.70%. Furthermore, a distinct non-monotonic threshold dependence is observed for the XZZX code across different bias ratios. While the XZZX code effectively absorbs high-density Z-type hyperedges at extreme biases, it exhibits a threshold minimum at moderate biases (η≈ 10) because transverse X and Y errors actively bridge the diagonal strings, breaking the code's one-dimensional decoupling symmetry. These findings demonstrate that utilizing hypergraph-aware decoders is critical, as the performance of bias-tailored codes is highly sensitive to the geometric structure of spatio-temporal correlated noise.
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BibTeX
@misc{koul2026comparing,
title = {{Comparing thresholds of XZZX and rotated surface codes under spatio-temporal correlated noise}},
author = {Dhruv Koul},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06059},
eprint = {2610.06059},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06059},
}
RIS
TY - UNPB
TI - Comparing thresholds of XZZX and rotated surface codes under spatio-temporal correlated noise
AU - Dhruv Koul
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06059
UR - https://arxiv.org/abs/2610.06059
AB - While independent and identically distributed noise is typically assumed in quantum computing research, complex error models such as correlated and spatio-temporal errors remain underexplored. In this paper, the performance of XZZX and rotated surface codes is evaluated under these complex noise models. Standard graph-based decoders struggle with the hyperedges generated by correlated errors on bias-tailored codes. To address this, we employ the Minimum Weight Parity Factor (MWPF) decoder, which natively processes syndrome hypergraphs without artificial edge decomposition. Our simulations show that under strong Z-biased circuit-level correlated noise (η=100), the threshold of the rotated code degrades to ≈ 0.36%, while the XZZX code drops to ≈ 0.70%. Furthermore, a distinct non-monotonic threshold dependence is observed for the XZZX code across different bias ratios. While the XZZX code effectively absorbs high-density Z-type hyperedges at extreme biases, it exhibits a threshold minimum at moderate biases (η≈ 10) because transverse X and Y errors actively bridge the diagonal strings, breaking the code's one-dimensional decoupling symmetry. These findings demonstrate that utilizing hypergraph-aware decoders is critical, as the performance of bias-tailored codes is highly sensitive to the geometric structure of spatio-temporal correlated noise.
ER -