{"paper":{"title":"Code Swendsen-Wang Dynamics","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"Code Swendsen-Wang dynamics mixes rapidly for the 4D toric code and other code Hamiltonians with efficient Gibbs samplers.","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"quant-ph","authors_text":"Dominik Hangleiter, Nathan Ju, Umesh Vazirani","submitted_at":"2025-10-09T16:54:39Z","abstract_excerpt":"Recent advances in quantum Gibbs sampling leave open the central question of rapid mixing near and below phase transitions. This challenge is especially relevant for code Hamiltonians whose Gibbs states capture phenomena such as the thermal stability of quantum topological order. In this work, we formulate a new Markov chain, Code Swendsen-Wang dynamics, which uses global updates to prepare the Gibbs states of arbitrary code Hamiltonians. We establish Code Swendsen-Wang dynamics as the right generalization of Swendsen-Wang dynamics for the Ising model to quantum and classical code Hamiltonians"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish Code Swendsen-Wang dynamics as the right generalization of Swendsen-Wang dynamics for the Ising model to quantum and classical code Hamiltonians: it mixes rapidly for all previously known code Hamiltonians with efficient Gibbs samplers, resolves the central open case of the 4D toric code, and meets fundamental barriers exactly at first-order phase transitions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The newly defined global updates in Code Swendsen-Wang dynamics are correctly formulated so that the resulting Markov chain is ergodic and its mixing-time analysis applies to arbitrary code Hamiltonians, including the 4D toric code.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Code Swendsen-Wang dynamics generalizes classical Swendsen-Wang to quantum and classical code Hamiltonians, achieving rapid mixing for known cases including the open 4D toric code case while hitting barriers at first-order transitions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Code Swendsen-Wang dynamics mixes rapidly for the 4D toric code and other code Hamiltonians with efficient Gibbs samplers.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3c9f7f0f5516ae3c54e3f488a775cee3ed4c9a1668e1365c709c55966e56c58a"},"source":{"id":"2510.08446","kind":"arxiv","version":3},"verdict":{"id":"fc60c323-5a81-4039-a6a3-84d4d099ef3d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T08:59:02.249903Z","strongest_claim":"We establish Code Swendsen-Wang dynamics as the right generalization of Swendsen-Wang dynamics for the Ising model to quantum and classical code Hamiltonians: it mixes rapidly for all previously known code Hamiltonians with efficient Gibbs samplers, resolves the central open case of the 4D toric code, and meets fundamental barriers exactly at first-order phase transitions.","one_line_summary":"Code Swendsen-Wang dynamics generalizes classical Swendsen-Wang to quantum and classical code Hamiltonians, achieving rapid mixing for known cases including the open 4D toric code case while hitting barriers at first-order transitions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The newly defined global updates in Code Swendsen-Wang dynamics are correctly formulated so that the resulting Markov chain is ergodic and its mixing-time analysis applies to arbitrary code Hamiltonians, including the 4D toric code.","pith_extraction_headline":"Code Swendsen-Wang dynamics mixes rapidly for the 4D toric code and other code Hamiltonians with efficient Gibbs samplers."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.08446/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"29364945e3a67b6e97ca7c4487383dd663c4f68f059626d0ce9837c9d50b94ea"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}