Noise-induced contraction of MPO truncation errors in noisy random circuits and Lindbladian dynamics
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917355394695168 |
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| author | Wei, Zhi-Yuan Rajakumar, Joel Nelson, Jon Malz, Daniel Gullans, Michael J. Gorshkov, Alexey V. |
| author_facet | Wei, Zhi-Yuan Rajakumar, Joel Nelson, Jon Malz, Daniel Gullans, Michael J. Gorshkov, Alexey V. |
| contents | 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)]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20400 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Noise-induced contraction of MPO truncation errors in noisy random circuits and Lindbladian dynamics Wei, Zhi-Yuan Rajakumar, Joel Nelson, Jon Malz, Daniel Gullans, Michael J. Gorshkov, Alexey V. Quantum Physics Statistical Mechanics 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)]. |
| title | Noise-induced contraction of MPO truncation errors in noisy random circuits and Lindbladian dynamics |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2603.20400 |