{"paper":{"title":"Uniform Mixing in Chiral Quantum Walks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Unitary signings allow complete graphs to achieve probabilistic uniform mixing in continuous-time quantum walks.","cross_cats":["quant-ph"],"primary_cat":"math.CO","authors_text":"Benjamin Mustico, Christino Tamon, Gabriel Tucker, Hanmeng Zhan, Jessy Jacob Mesapam, Luke Levine","submitted_at":"2026-05-06T02:12:09Z","abstract_excerpt":"This paper studies uniform mixing in continuous-time quantum walks. We show that for some unitary signing $\\sigma$, the complete graph $K^\\sigma_n$ has probabilistic uniform mixing. In contrast, Ahmadi \\etal (2003) proved that no complete graph has uniform mixing except for $K_2$, $K_3$, and $K_4$. Our technique is based on a stopping rule for quantum walks which reduces global to local uniform mixing. As a corollary, we found an orientation of $H(n,4)$ that mixes to uniform faster than any other Hamming graphs, which improves a result of Godsil and Zhan (2019). We also show that there are inf"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For some unitary signing σ the complete graph K^σ_n has probabilistic uniform mixing. There are infinite families of oriented circulants with average uniform mixing, a chiral violation of Godsil's No-Go theorem.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The existence of a suitable unitary signing σ or orientation that satisfies the local uniform mixing condition via the stopping rule technique; the paper assumes the quantum walk model on these signed graphs behaves as described without additional decoherence or implementation constraints.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Signed complete graphs and oriented circulants exhibit uniform mixing in quantum walks, providing a chiral violation of Godsil's no-go theorem for average mixing.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Unitary signings allow complete graphs to achieve probabilistic uniform mixing in continuous-time quantum walks.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ea7ffd5c248a966cf1ddf61eca0ba1edfc04656201113960cbd057dbee7d8f8c"},"source":{"id":"2605.04414","kind":"arxiv","version":2},"verdict":{"id":"6b0466a2-ee24-48b9-8df5-0f49bd435840","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T16:03:59.252476Z","strongest_claim":"For some unitary signing σ the complete graph K^σ_n has probabilistic uniform mixing. There are infinite families of oriented circulants with average uniform mixing, a chiral violation of Godsil's No-Go theorem.","one_line_summary":"Signed complete graphs and oriented circulants exhibit uniform mixing in quantum walks, providing a chiral violation of Godsil's no-go theorem for average mixing.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The existence of a suitable unitary signing σ or orientation that satisfies the local uniform mixing condition via the stopping rule technique; the paper assumes the quantum walk model on these signed graphs behaves as described without additional decoherence or implementation constraints.","pith_extraction_headline":"Unitary signings allow complete graphs to achieve probabilistic uniform mixing in continuous-time quantum walks."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.04414/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:19.981542Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T14:29:07.660970Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"7c49514849906d1808c890e0814840512b07d3ffe67f1f294438dbffa9408812"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"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"}