Complexity of tensor network simulation for noisy quantum circuits

Abstract:We aim to rigorously address how local noise affects the classical simulability of quantum dynamics benchmarked by tensor-network methods. Using operator entanglement entropy (OEE) as a unifying criterion, we prove the following: (1) For single-qubit depolarizing noise, geometry-independent $\order{1}$-layer and $\Theta(\log n)$-layer thresholds for fixed absolute and relative Hilbert--Schmidt error are established, beyond which polynomial bond dimension suffices; on 1D local circuits with a product initial input, whole-trajectory MPO approximations are constructed at fixed purified distance with $\mathrm{poly}(n)$ bond dimension. (2) For general single-qubit noise, we identify sufficient contractivity conditions for MPO approximations with constant bond dimension, in both the average and worst cases. (3) We further extend the above results to higher dimensions, yielding $\mathrm{poly}(n)$ average boundary-bond dimensions for projected entangled pair operators (PEPO) across every cut. Our results establish a rigorous connection between certain noise models, circuit types, and their classical simulability.

Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)

arXiv:2606.00474 [cond-mat.str-el]

(or arXiv:2606.00474v2 [cond-mat.str-el] for this version)

https://doi.org/10.48550/arXiv.2606.00474 Focus to learn more arXiv-issued DOI via DataCite

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