Performance of Planar XYZ and XZZX Codes under Homogeneous and Spatially Nonuniform Noise
Abstract
The minimum-weight perfect matching (MWPM) decoder is a standard decoding strategy for surface codes, but its performance can degrade considerably under biased noise. In this work, a modified family of surface codes, termed the XYZ planar code, is introduced, and MWPM is extended to posterior MWPM (pMWPM), which exploits the information provided by mixed stabilizers with almost no increase in decoding complexity. The XYZ--pMWPM and XZZX code--decoder combinations are compared under homogeneous independent and identically distributed (IID) Pauli noise and processor-derived independent nonidentically distributed (INID) noise. Under homogeneous biased Pauli noise, pMWPM substantially increases the threshold of the XYZ planar code relative to conventional MWPM. At finite code distances, particularly for small codes under strong bias, XYZ--pMWPM achieves logical error rates comparable to or lower than those of XZZX. Under INID noise, the pseudothreshold ordering observed under the corresponding homogeneous IID references is not always preserved; in some hardware--distance settings, XYZ--pMWPM achieves pseudothresholds comparable to or higher than those of XZZX. Within XZZX, qubit-specific weighting consistently yields higher INID pseudothresholds than average-rate weighting for the hardware instances considered. It is further found that the IID--INID pseudothreshold shift depends strongly on the physical-error scalarization and the construction of the homogeneous IID reference. These results show that pMWPM efficiently exploits the mixed-stabilizer structure of the XYZ planar code and provides competitive finite-distance decoding under biased and spatially nonuniform noise.
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BibTeX
@misc{wang2026performance,
title = {{Performance of Planar XYZ and XZZX Codes under Homogeneous and Spatially Nonuniform Noise}},
author = {Zhiwei Wang and Liqi Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.23236},
eprint = {2605.23236},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.23236},
}
RIS
TY - UNPB
TI - Performance of Planar XYZ and XZZX Codes under Homogeneous and Spatially Nonuniform Noise
AU - Zhiwei Wang
AU - Liqi Wang
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2605.23236
UR - https://arxiv.org/abs/2605.23236
AB - The minimum-weight perfect matching (MWPM) decoder is a standard decoding strategy for surface codes, but its performance can degrade considerably under biased noise. In this work, a modified family of surface codes, termed the XYZ planar code, is introduced, and MWPM is extended to posterior MWPM (pMWPM), which exploits the information provided by mixed stabilizers with almost no increase in decoding complexity. The XYZ--pMWPM and XZZX code--decoder combinations are compared under homogeneous independent and identically distributed (IID) Pauli noise and processor-derived independent nonidentically distributed (INID) noise. Under homogeneous biased Pauli noise, pMWPM substantially increases the threshold of the XYZ planar code relative to conventional MWPM. At finite code distances, particularly for small codes under strong bias, XYZ--pMWPM achieves logical error rates comparable to or lower than those of XZZX. Under INID noise, the pseudothreshold ordering observed under the corresponding homogeneous IID references is not always preserved; in some hardware--distance settings, XYZ--pMWPM achieves pseudothresholds comparable to or higher than those of XZZX. Within XZZX, qubit-specific weighting consistently yields higher INID pseudothresholds than average-rate weighting for the hardware instances considered. It is further found that the IID--INID pseudothreshold shift depends strongly on the physical-error scalarization and the construction of the homogeneous IID reference. These results show that pMWPM efficiently exploits the mixed-stabilizer structure of the XYZ planar code and provides competitive finite-distance decoding under biased and spatially nonuniform noise.
ER -