Classical simulation of coherent crosstalk in surface codes
Abstract
We give a polynomial-time classical algorithm which samples from the syndrome distribution of a surface code state corrupted by coherent nearest-neighbor ZZ crosstalk. Our algorithm complements the known efficient simulation algorithms for coherent single-qubit errors in the surface code. When both single-qubit coherent noise and coherent crosstalk are present, we find a complexity-theoretic obstruction to efficient simulation: unless the polynomial hierarchy collapses, there is no efficient classical algorithm for sampling from the syndrome distribution, even up to a constant multiplicative error. This is obtained by connecting the syndrome distribution under coherent noise to the output distribution of certain IQP circuits associated with a non-planar graph.
Related
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BibTeX
@misc{darmawan2026classical,
title = {{Classical simulation of coherent crosstalk in surface codes}},
author = {Andrew S. Darmawan and Yelyzaveta Kolesnyk and Robert Koenig},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40279},
eprint = {2609.40279},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40279},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classical simulation of coherent crosstalk in surface codes
AU - Andrew S. Darmawan
AU - Yelyzaveta Kolesnyk
AU - Robert Koenig
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40279
UR - https://arxiv.org/abs/2609.40279
AB - We give a polynomial-time classical algorithm which samples from the syndrome distribution of a surface code state corrupted by coherent nearest-neighbor ZZ crosstalk. Our algorithm complements the known efficient simulation algorithms for coherent single-qubit errors in the surface code. When both single-qubit coherent noise and coherent crosstalk are present, we find a complexity-theoretic obstruction to efficient simulation: unless the polynomial hierarchy collapses, there is no efficient classical algorithm for sampling from the syndrome distribution, even up to a constant multiplicative error. This is obtained by connecting the syndrome distribution under coherent noise to the output distribution of certain IQP circuits associated with a non-planar graph.
ER -