{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/variational-quantum-eigensolver-for-the","title":"Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice","arxiv_id":"2108.02175","date":"2021-08-04","proceeding":null,"authors":["Joris Kattemölle","Jasper van Wezel"],"abstract":"Establishing the nature of the ground state of the Heisenberg antiferromagnet (HAFM) on the kagome lattice is well known to be a prohibitively difficult problem for classical computers. Here, we give a detailed proposal for a Variational Quantum Eigensolver (VQE) intending to solve this physical problem on a quantum computer. At the same time, this VQE constitutes an explicit experimental proposal for showing a useful quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) devices because of its natural hardware compatibility. We classically emulate noiseless and noisy quantum computers with either 2D-grid or all-to-all connectivity and simulate patches of the kagome HAFM of up to 20 sites. In the noiseless case, the ground-state energy, as found by the VQE, approaches the true ground-state energy exponentially as a function of the circuit depth. Furthermore, VQEs for the HAFM on any graph can inherently perform their quantum computations in a decoherence-free subspace that protects against collective longitudinal and collective transversal noise, adding to the noise-resilience of these algorithms. Nevertheless, the extent of the effects of other noise types suggests the need for error mitigation and performance targets alternative to high-fidelity ground-state preparation, even for essentially hardware-native VQEs.","url_abs":"https://arxiv.org/abs/2108.02175v3","url_pdf":"https://arxiv.org/pdf/2108.02175v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"variational-quantum-eigensolver-for-the","repo_url":"https://github.com/barbireau/HVQE","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"variational-quantum-eigensolver-for-the","repo_url":"https://github.com/kattemolle/HVQE","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2108.02175","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2108.02175"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/barbireau/HVQE","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/kattemolle/HVQE","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":7},"by_repo_kind":{"official":{"samples":7,"ran":0,"repositories":2}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"2f3f952b4f2593f3","entry":"fun","repo":"kattemolle/HVQE","repo_kind":"official","path":"analysis/scaling.py","file_url":"https://github.com/kattemolle/HVQE/blob/HEAD/analysis/scaling.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"2f3f952b4f2593f3"}},{"code_sha256_prefix":"cdae483e263e4b20","entry":"get_E_lst","repo":"kattemolle/HVQE","repo_kind":"official","path":"_HVQE.py","file_url":"https://github.com/kattemolle/HVQE/blob/HEAD/_HVQE.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"cdae483e263e4b20"}},{"code_sha256_prefix":"850b77023d147fdb","entry":"load_data","repo":"kattemolle/HVQE","repo_kind":"official","path":"_HVQE.py","file_url":"https://github.com/kattemolle/HVQE/blob/HEAD/_HVQE.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"850b77023d147fdb"}},{"code_sha256_prefix":"69093490eb9512f7","entry":"load_data_line","repo":"kattemolle/HVQE","repo_kind":"official","path":"noise.py","file_url":"https://github.com/kattemolle/HVQE/blob/HEAD/noise.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"69093490eb9512f7"}},{"code_sha256_prefix":"cc468d14e33d9b52","entry":"optimal_line","repo":"kattemolle/HVQE","repo_kind":"official","path":"_HVQE.py","file_url":"https://github.com/kattemolle/HVQE/blob/HEAD/_HVQE.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"cc468d14e33d9b52"}},{"code_sha256_prefix":"b28a1a15f4eb783d","entry":"round_assert","repo":"barbireau/HVQE","repo_kind":"official","path":"qem.py","file_url":"https://github.com/barbireau/HVQE/blob/HEAD/qem.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"b28a1a15f4eb783d"}},{"code_sha256_prefix":"32c2ac11b1d0d582","entry":"total_calls","repo":"kattemolle/HVQE","repo_kind":"official","path":"analysis/scaling.py","file_url":"https://github.com/kattemolle/HVQE/blob/HEAD/analysis/scaling.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"32c2ac11b1d0d582"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}