Entanglement-Dependent Error Bounds for Hamiltonian Simulation
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Quantum Physics arXiv:2602.00555 (quant-ph) [Submitted on 31 Jan 2026] Title:Entanglement-Dependent Error Bounds for Hamiltonian Simulation Authors:Prateek P. Kulkarni View a PDF of the paper titled Entanglement-Dependent Error Bounds for Hamiltonian Simulation, by Prateek P. Kulkarni View PDF HTML (experimental) Abstract:We establish tight connections between entanglement entropy and the approximation error in Trotter-Suzuki product formulas for Hamiltonian simulation. Product formulas remain the workhorse of quantum simulation on near-term devices, yet standard error analyses yield worst-case bounds that can vastly overestimate the resources required for structured problems. For systems governed by geometrically local Hamiltonians with maximum entanglement entropy $S_\text{max}$ across all bipartitions, we prove that the first-order Trotter error scales as $\mathcal{O}(t^2 S_\text{max} \operatorname{polylog}(n)/r)$ rather than the worst-case $\mathcal{O}(t^2 n/r)$, where $n$ is the system size and $r$ is the number of Trotter steps. This yields improvements of $\tilde{\Omega}(n^2)$ for one-dimensional area-law systems and $\tilde{\Omega}(n^{3/2})$ for two-dimensional systems. We extend these bounds to higher-order Suzuki formulas, where the improvement factor involves $2^{pS^*/2}$ for the $p$-th order formula. We further establish a separation result demonstrating that volume-law entangled systems fundamentally require $\tilde{\Omega}(n)$ more Trotter steps than area-law systems to achieve the same precision. This separation is tight up to logarithmic factors. Our analysis combines Lieb-Robinson bounds for locality, tensor network representations for entanglement structure, and novel commutator-entropy inequalities that bound the expectation value of nested commutators by the Schmidt rank of the state. These results have immediate applications to quantum chemistry, condensed matter simulation, and resource estimation for fault-tolerant quantum computing. Comments: Subjects: Quantum Physics (quant-ph); Computational Complexity (cs.CC) Cite as: arXiv:2602.00555 [quant-ph] (or arXiv:2602.00555v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.00555 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Prateek P. Kulkarni [view email] [v1] Sat, 31 Jan 2026 06:34:37 UTC (57 KB) Full-text links: Access Paper: View a PDF of the paper titled Entanglement-Dependent Error Bounds for Hamiltonian Simulation, by Prateek P. KulkarniView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: cs cs.CC 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)