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 order1-layer and Θ(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 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 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.
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BibTeX
@misc{shao2026complexity,
title = {{Complexity of tensor network simulation for noisy quantum circuits}},
author = {Yuguo Shao and Zishuo Zhao and Song Cheng and Zhengwei Liu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.00474},
eprint = {2606.00474},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.00474},
}
RIS
TY - UNPB
TI - Complexity of tensor network simulation for noisy quantum circuits
AU - Yuguo Shao
AU - Zishuo Zhao
AU - Song Cheng
AU - Zhengwei Liu
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2606.00474
UR - https://arxiv.org/abs/2606.00474
AB - 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 order1-layer and Θ(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 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 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.
ER -