{"paper":{"title":"Fermion lattices can be simulated by same-size qubit lattices with $\\mathcal{O}(1)$ interaction overhead","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Two-dimensional fermion lattices can be simulated on equal-sized qubit lattices with no asymptotic interaction or space overhead.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Berend Klaver, Gregor Aigner, Martin Lanthaler, Wolfgang Lechner","submitted_at":"2026-05-12T18:00:04Z","abstract_excerpt":"Local interactions among electrons underlie many complex properties of correlated materials. While the Jordan-Wigner transformation can preserve this locality along one spatial dimension, interactions along the remaining dimensions typically incur substantial overhead. We show how to simulate all geometrically local interactions on an $N$-site two-dimensional fermion lattice with no asymptotic overhead in the number of interactions and no space overhead. The primary overhead of our method is circuit depth, which on a qubit lattice matches that of fermionic swap networks, scaling as $\\mathcal{O"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show how to simulate all geometrically local interactions on an N-site two-dimensional fermion lattice with no asymptotic overhead in the number of interactions and no space overhead.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The dynamic reorientation of the Jordan-Wigner string can be realized in hardware without introducing hidden asymptotic costs in gate count or connectivity beyond what is already assumed for qubit lattices and swap networks.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Fermion lattices can be simulated on same-size qubit lattices with O(1) interaction overhead by dynamically reorienting the Jordan-Wigner transformation.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Two-dimensional fermion lattices can be simulated on equal-sized qubit lattices with no asymptotic interaction or space overhead.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d34cd083b77d254699ce123e86bec86cbaa2d9ba920ce5da893eb0ac6438abf4"},"source":{"id":"2605.12600","kind":"arxiv","version":1},"verdict":{"id":"987a31f7-6148-4575-9d04-c3424e87a1f5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:37:11.894447Z","strongest_claim":"We show how to simulate all geometrically local interactions on an N-site two-dimensional fermion lattice with no asymptotic overhead in the number of interactions and no space overhead.","one_line_summary":"Fermion lattices can be simulated on same-size qubit lattices with O(1) interaction overhead by dynamically reorienting the Jordan-Wigner transformation.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The dynamic reorientation of the Jordan-Wigner string can be realized in hardware without introducing hidden asymptotic costs in gate count or connectivity beyond what is already assumed for qubit lattices and swap networks.","pith_extraction_headline":"Two-dimensional fermion lattices can be simulated on equal-sized qubit lattices with no asymptotic interaction or space overhead."},"references":{"count":67,"sample":[{"doi":"","year":2022,"title":"D. P. Arovas, E. Berg, S. A. Kivelson, and S. Raghu, The Hubbard Model, Annual Review of Condensed Matter Physics13, 239 (2022)","work_id":"1bfeed19-b5b0-4ad4-bab7-492dd25bbc48","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"M. Qin, T. Sch¨ afer, S. Andergassen, P. Corboz, and E. Gull, The Hubbard Model: A Computational Per- spective, Annual Review of Condensed Matter Physics 13, 275 (2022)","work_id":"bba6f4b9-1010-4bdd-bed9-b46eb88c9c0e","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1982,"title":"R. P. Feynman, Simulating physics with computers, International Journal of Theoretical Physics21, 467 (1982)","work_id":"61bc3f01-355c-4399-9e96-f1b27be6b09f","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2002,"title":"S. B. Bravyi and A. Y. Kitaev, Fermionic Quantum Com- putation, Annals of Physics298, 210 (2002)","work_id":"598f444b-4b3a-48bb-a290-7a7981bb6863","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2005,"title":"F. Verstraete and J. I. Cirac, Mapping local Hamiltoni- ans of fermions to local Hamiltonians of spins, Journal of Statistical Mechanics: Theory and Experiment2005, P09012 (2005)","work_id":"f535ee1f-6a22-4e66-bf18-66c5a448b513","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":67,"snapshot_sha256":"9eb393cf4d8dcb5a92ad60cb5c06d56e8b2ccbb836554c187f1ff192fea5989a","internal_anchors":2},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}