Optimized Matrix-Product State Simulations of Quantum Error Correction Circuits

Quantum Physics arXiv:2609.03073 (quant-ph) [Submitted on 2 Sep 2026] Title:Optimized Matrix-Product State Simulations of Quantum Error Correction Circuits Authors:Asier Piñeiro Orioli, Chen Zhao, Guido Masella, Tommaso Macrì, Hengyun Zhou, Shannon Whitlock View a PDF of the paper titled Optimized Matrix-Product State Simulations of Quantum Error Correction Circuits, by Asier Pi\~neiro Orioli and 5 other authors View PDF HTML (experimental) Abstract:Simulating quantum error correction (QEC) circuits including non-Clifford gates at scale is important to accelerate progress toward fault-tolerant quantum computing. Here we demonstrate that matrix product state (MPS) techniques can handle many QEC circuits exactly and without restriction on gate types. Crucially, we find that MPS efficiency depends sensitively on implementation choices, and we introduce a series of targeted optimizations that reduce bond dimensions and simulation time by several orders of magnitude compared to naive approaches. We illustrate this with examples including: (a) a rotated surface code quantum memory up to distance 11, (b) logical Bell-state preparation up to distance 9, (c) a 15-to-1 magic-state distillation circuit including hundreds of QEC rounds that we optimize to be simulated with only 11 logical qubits (187 physical qubits) and a maximal bond dimension of 64 in under 40 seconds, and (d) a narrow, deep random circuit that scales linearly with the number of T gates. These results demonstrate the importance of circuit-level optimizations and position MPS as a valuable complement to near-Clifford simulators for QEC circuits. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.03073 [quant-ph] (or arXiv:2609.03073v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.03073 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Asier Piñeiro Orioli [view email] [v1] Wed, 2 Sep 2026 18:42:47 UTC (414 KB) Full-text links: Access Paper: View a PDF of the paper titled Optimized Matrix-Product State Simulations of Quantum Error Correction Circuits, by Asier Pi\~neiro Orioli and 5 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?)