Low-rank propagation for tridiagonalizable open quantum systems: near-linear scaling with system size

Quantum Physics arXiv:2609.25368 (quant-ph) [Submitted on 21 Sep 2026] Title:Low-rank propagation for tridiagonalizable open quantum systems: near-linear scaling with system size Authors:Roman Ovsiannikov, Kurt Jacobs, Andrii G. Sotnikov, Denys I. Bondar View a PDF of the paper titled Low-rank propagation for tridiagonalizable open quantum systems: near-linear scaling with system size, by Roman Ovsiannikov and 3 other authors View PDF HTML (experimental) Abstract:The quadratic growth of the density matrix with Hilbert-space dimension D is the central obstacle to simulating large open quantum systems. We introduce a deterministic algorithm that eliminates it for Lindblad dynamics whose Hamiltonian consists of a time-dependent diagonal part plus terms that are tridiagonal after reordering the basis. The state is a low-rank ensemble of vectors, propagated by tridiagonal split-operator steps and ensemble rank truncation of short-time Kraus branches, so that memory and cost per step are linear in D at fixed rank. For a driven nitrogen-vacancy-cavity model, rank 16 reproduces full density-matrix observables to relative error below $10^{-5}$, the method is up to two orders of magnitude faster than QuTiP already at $D \approx 500$, and its runtime scales nearly linearly. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.25368 [quant-ph] (or arXiv:2609.25368v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.25368 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Roman Ovsiannikov [view email] [v1] Mon, 21 Sep 2026 20:07:43 UTC (242 KB) Full-text links: Access Paper: View a PDF of the paper titled Low-rank propagation for tridiagonalizable open quantum systems: near-linear scaling with system size, by Roman Ovsiannikov and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)