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

Quantum Physics [Submitted on 20 Mar 2026] Noise-induced contraction of MPO truncation errors in noisy random circuits and Lindbladian dynamics Zhi-Yuan Wei, Joel Rajakumar, Jon Nelson, Daniel Malz, Michael J. Gullans, Alexey V. Gorshkov 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)]. Comments: 20 pages, 12 figures. Comments are welcome Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2603.20400 [quant-ph]   (or arXiv:2603.20400v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.20400 Focus to learn more Submission history From: Zhi-Yuan Wei [view email] [v1] Fri, 20 Mar 2026 18:19:41 UTC (633 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.stat-mech References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)