Noise-induced contraction of MPO truncation errors in noisy random circuits and Lindbladian dynamics

• URL: http://arxiv.org/abs/2603.20400v1
• Date: Fri, 20 Mar 2026 18:19:41 GMT
• Title: Noise-induced contraction of MPO truncation errors in noisy random circuits and Lindbladian dynamics
• Abstract summary: We study how matrix-product-operator (MPO) truncation errors evolve when two simulating setups.<n>We first show that the average purity of the system density matrix relaxes to a steady value on a timescale that scales inversely with the noise rate.<n>We then show that truncation errors contract exponentially in both system size $N$ and the evolution time $t$, as the noisy dynamics maps different density matrices toward the same steady state.
• Score: 2.011411721375655
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study how matrix-product-operator (MPO) truncation errors evolve when simulating two setups: (1) 1D Haar-random circuits under either depolarizing noise or amplitude-damping noise, and (2) 1D Lindbladian dynamics of a non-integrable quantum Ising model under either depolarizing or amplitude-damping noise. We first show that the average purity of the system density matrix relaxes to a steady value on a timescale that scales inversely with the noise rate. We then show that truncation errors contract exponentially in both system size $N$ and the evolution time $t$, as the noisy dynamics maps different density matrices toward the same steady state. This yields an empirical bound on the $L_1$ truncation error that is exponentially tighter in $N$ than the existing bound. Together, these results provide empirical evidence that MPO simulation algorithms may efficiently sample from the output of 1D noisy random circuits [setup (1)] at arbitrary circuit depth, and from the steady state of 1D Lindbladian dynamics [setup (2)].

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