{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:R4ZPCGZAG4A7ARCCH2DNVGHRGG","short_pith_number":"pith:R4ZPCGZA","schema_version":"1.0","canonical_sha256":"8f32f11b203701f044423e86da98f131897e6d37e2380794df762bd9202a0895","source":{"kind":"arxiv","id":"quant-ph/0609204","version":2},"attestation_state":"computed","paper":{"title":"Quantum speedup of classical mixing processes","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Peter C. Richter","submitted_at":"2006-09-26T20:52:12Z","abstract_excerpt":"Most approximation algorithms for #P-complete problems (e.g., evaluating the permanent of a matrix or the volume of a polytope) work by reduction to the problem of approximate sampling from a distribution $\\pi$ over a large set $\\S$. This problem is solved using the {\\em Markov chain Monte Carlo} method: a sparse, reversible Markov chain $P$ on $\\S$ with stationary distribution $\\pi$ is run to near equilibrium. The running time of this random walk algorithm, the so-called {\\em mixing time} of $P$, is $O(\\delta^{-1} \\log 1/\\pi_*)$ as shown by Aldous, where $\\delta$ is the spectral gap of $P$ an"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"quant-ph/0609204","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2006-09-26T20:52:12Z","cross_cats_sorted":[],"title_canon_sha256":"08a0bdc1e5d045825fa4a2053256fb5c70035253a59e81c7f12f37dc1d1c2c53","abstract_canon_sha256":"17e504d5bbefffc92fb4c012bd9a30680b76d7294104808baea490c8a8cd6008"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:45.742871Z","signature_b64":"Vn9RFTsoCXtj34mg/KqYyFFwrj/XbCYXDTvkg5UQHF9xtjBVfwhZBjlFApqjaQz1C/HgauyyL+J/kuatD2A6AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f32f11b203701f044423e86da98f131897e6d37e2380794df762bd9202a0895","last_reissued_at":"2026-05-18T04:08:45.742421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:45.742421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum speedup of classical mixing processes","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Peter C. Richter","submitted_at":"2006-09-26T20:52:12Z","abstract_excerpt":"Most approximation algorithms for #P-complete problems (e.g., evaluating the permanent of a matrix or the volume of a polytope) work by reduction to the problem of approximate sampling from a distribution $\\pi$ over a large set $\\S$. This problem is solved using the {\\em Markov chain Monte Carlo} method: a sparse, reversible Markov chain $P$ on $\\S$ with stationary distribution $\\pi$ is run to near equilibrium. The running time of this random walk algorithm, the so-called {\\em mixing time} of $P$, is $O(\\delta^{-1} \\log 1/\\pi_*)$ as shown by Aldous, where $\\delta$ is the spectral gap of $P$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0609204","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0609204","created_at":"2026-05-18T04:08:45.742482+00:00"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0609204v2","created_at":"2026-05-18T04:08:45.742482+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0609204","created_at":"2026-05-18T04:08:45.742482+00:00"},{"alias_kind":"pith_short_12","alias_value":"R4ZPCGZAG4A7","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"R4ZPCGZAG4A7ARCC","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"R4ZPCGZA","created_at":"2026-05-18T12:25:54.717736+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/R4ZPCGZAG4A7ARCCH2DNVGHRGG","json":"https://pith.science/pith/R4ZPCGZAG4A7ARCCH2DNVGHRGG.json","graph_json":"https://pith.science/api/pith-number/R4ZPCGZAG4A7ARCCH2DNVGHRGG/graph.json","events_json":"https://pith.science/api/pith-number/R4ZPCGZAG4A7ARCCH2DNVGHRGG/events.json","paper":"https://pith.science/paper/R4ZPCGZA"},"agent_actions":{"view_html":"https://pith.science/pith/R4ZPCGZAG4A7ARCCH2DNVGHRGG","download_json":"https://pith.science/pith/R4ZPCGZAG4A7ARCCH2DNVGHRGG.json","view_paper":"https://pith.science/paper/R4ZPCGZA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=quant-ph/0609204&json=true","fetch_graph":"https://pith.science/api/pith-number/R4ZPCGZAG4A7ARCCH2DNVGHRGG/graph.json","fetch_events":"https://pith.science/api/pith-number/R4ZPCGZAG4A7ARCCH2DNVGHRGG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R4ZPCGZAG4A7ARCCH2DNVGHRGG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R4ZPCGZAG4A7ARCCH2DNVGHRGG/action/storage_attestation","attest_author":"https://pith.science/pith/R4ZPCGZAG4A7ARCCH2DNVGHRGG/action/author_attestation","sign_citation":"https://pith.science/pith/R4ZPCGZAG4A7ARCCH2DNVGHRGG/action/citation_signature","submit_replication":"https://pith.science/pith/R4ZPCGZAG4A7ARCCH2DNVGHRGG/action/replication_record"}},"created_at":"2026-05-18T04:08:45.742482+00:00","updated_at":"2026-05-18T04:08:45.742482+00:00"}