Complexity of tensor network simulation for noisy quantum circuits

• URL: http://arxiv.org/abs/2606.00474v1
• Date: Sat, 30 May 2026 01:42:33 GMT
• Title: Complexity of tensor network simulation for noisy quantum circuits
• Abstract summary: Local noise affects classical simulability of quantum dynamics benchmarked by tensor-network methods.<n>We prove the following: For single-qubit depolarizing noise on arbitrary circuits, tensor networks with $mathrmpoly(n)$ bond dimension suffice for fixed absolute Hilbert-Schmidt error after $order1$ depth.<n>In higher dimensions, these bounds yield uniform-in-depth $mathrmpoly(n)$ average boundary-bond dimensions for projected entangled pair operators(PEPO) across every cut.
• Score: 2.8523943706562633
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We aim to rigorously address how local noise affects classical simulability of quantum dynamics benchmarked by tensor-network methods. Using operator entanglement entropy (OEE), we prove the following: (1) For single-qubit depolarizing noise on arbitrary circuits, tensor networks with $\mathrm{poly}(n)$ bond dimension suffice for fixed absolute Hilbert-Schmidt error after $\order{1}$ depth, while relative error demands $\order{\log n}$ depth; and this bound is optimal. (2) For single-qubit depolarizing noise on 1D local circuits, the existence of whole-trajectory error-bounded matrix product operator (MPO) of $\mathrm{poly}(n)$ bond dimension at all depths. (3) For general single-qubit noise in 1D brickwall circuits, random two-design gates with contraction coefficient $c<1/3$ yield an $\order{1}$ OEE plateau with probability $1-Te^{-Ω(n)}$, while arbitrary gates with $c<1/48$ give $\order{\log n}$ OEE in the worst case. (4) In higher dimensions, these bounds yield uniform-in-depth $\mathrm{poly}(n)$ average boundary-bond dimensions for projected entangled pair operators~(PEPO) across every cut -- under depolarizing noise at either absolute or relative accuracy, and under general noise with strong contraction at absolute accuracy. Our results establish a rigorous connection between certain noise models, circuit types, and their classical simulability.

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