Universal Hamiltonian simulators in one and two dimensions

[2102.02991] Universal Hamiltonian simulators in one and two dimensions Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2102.02991 (quant-ph) [Submitted on 5 Feb 2021 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Universal Hamiltonian simulators in one and two dimensions Authors: Leo Zhou , Dorit Aharonov View PDF HTML (experimental) Abstract: A major quantum computing application is analog Hamiltonian simulations, in which the low-lying spectrum of a simulator Hamiltonian $H'$ encodes the physics of a target Hamiltonian $H$. Some families of 2D spin-lattice Hamiltonians---such as the Heisenberg or XY model on the square lattice---are known to be ``universal'' simulators, in the sense that they can simulate any target Hamiltonian. Unfortunately, while the known simulations of 1D or 2D target Hamiltonians are efficient, they require resources growing exponentially with system sizes for target Hamiltonians with general connectivity. This leaves many important cases such as 3D or all-to-all-connected target Hamiltonians out of reach in practice. Here we remedy this situation and show how the known 2D universal families of Hamiltonians and a new 1D family can simulate all target local Hamiltonians, with only polynomial-scaling overhead. This exponential improvement is achieved by a nonperturbative method combining the quantum phase-estimation algorithm and the circuit-to-Hamiltonian construction. Furthermore, all Hamiltonians efficiently simulable by quantum circuits, including nonlocal ones, also have efficient analog simulators in our 2D and 1D universal families. Our work establishes that analog simulations of general Hamiltonians can be made efficient, significantly expanding the application potential of analog Hamiltonian simulations in near-term quantum technologies. Comments: 10+16 pages, 3 figures, 1 table. Journal version. Revised to include discussion about dynamics simulators Subjects: Quantum Physics (quant-ph) ; Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2102.02991 [quant-ph] (or arXiv:2102.02991v2 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2102.02991 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Nature Communications 17, 6888 (2026) Related DOI : https://doi.org/10.1038/s41467-026-71686-4 Focus to learn more DOI(s) linking to related resources Submission history From: Leo Zhou [ view email ] [v1] Fri, 5 Feb 2021 04:18:38 UTC (602 KB) [v2] Fri, 28 Aug 2026 07:53:20 UTC (920 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2021-02 Change to browse by: cond-mat cond-mat.str-el 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 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? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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