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.

arXiv:2609.40279 [quant-ph]

(or arXiv:2609.40279v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.40279 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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