{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:6YDYNK4OV7TE2JLUCUMJMUO4PB","short_pith_number":"pith:6YDYNK4O","schema_version":"1.0","canonical_sha256":"f60786ab8eafe64d257415189651dc7869dcf14ec7acde20ec48bd0b4445ff1d","source":{"kind":"arxiv","id":"0708.2096","version":1},"attestation_state":"computed","paper":{"title":"Non-uniform mixing of quantum walk on cycles","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Christino Tamon, Dillon Ethier, Jennifer Lin, Kevin Andrew, Leon Bergen, Peter Hernberg, William Adamczak","submitted_at":"2007-08-15T20:12:04Z","abstract_excerpt":"A classical lazy random walk on cycles is known to mix to the uniform distribution. In contrast, we show that a continuous-time quantum walk on cycles exhibit strong non-uniform mixing properties. Our results include the following:\n  - The instantaneous distribution of a quantum walk on most even-length cycles is never uniform. - The average distribution of a quantum walk on any Abelian circulant graph is never uniform. As a corollary, the average distribution of a quantum walk on any standard circulant graph, such as the cycles, complete graphs, and even hypercubes, is never uniform."},"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":"0708.2096","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2007-08-15T20:12:04Z","cross_cats_sorted":[],"title_canon_sha256":"8b1da121c56657f8deb7f1bc90409757bd7817e9996dacd747299674a93cfa0b","abstract_canon_sha256":"97ea15566c99ed090318d056c5f8605b25cb07c48301bbec15e2f1b8e457f0dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:32.551744Z","signature_b64":"z1LSuidDomUwomaULWRDwf9A7Mz6AZCQNXy8DcJ3TjwgpbJwgEDO4+VJTjGYKsZWHHCyKXoYDssNLPOCZL67Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f60786ab8eafe64d257415189651dc7869dcf14ec7acde20ec48bd0b4445ff1d","last_reissued_at":"2026-05-18T04:16:32.551251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:32.551251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-uniform mixing of quantum walk on cycles","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Christino Tamon, Dillon Ethier, Jennifer Lin, Kevin Andrew, Leon Bergen, Peter Hernberg, William Adamczak","submitted_at":"2007-08-15T20:12:04Z","abstract_excerpt":"A classical lazy random walk on cycles is known to mix to the uniform distribution. In contrast, we show that a continuous-time quantum walk on cycles exhibit strong non-uniform mixing properties. Our results include the following:\n  - The instantaneous distribution of a quantum walk on most even-length cycles is never uniform. - The average distribution of a quantum walk on any Abelian circulant graph is never uniform. As a corollary, the average distribution of a quantum walk on any standard circulant graph, such as the cycles, complete graphs, and even hypercubes, is never uniform."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.2096","kind":"arxiv","version":1},"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":"0708.2096","created_at":"2026-05-18T04:16:32.551328+00:00"},{"alias_kind":"arxiv_version","alias_value":"0708.2096v1","created_at":"2026-05-18T04:16:32.551328+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.2096","created_at":"2026-05-18T04:16:32.551328+00:00"},{"alias_kind":"pith_short_12","alias_value":"6YDYNK4OV7TE","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6YDYNK4OV7TE2JLU","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6YDYNK4O","created_at":"2026-05-18T12:25:55.427421+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/6YDYNK4OV7TE2JLUCUMJMUO4PB","json":"https://pith.science/pith/6YDYNK4OV7TE2JLUCUMJMUO4PB.json","graph_json":"https://pith.science/api/pith-number/6YDYNK4OV7TE2JLUCUMJMUO4PB/graph.json","events_json":"https://pith.science/api/pith-number/6YDYNK4OV7TE2JLUCUMJMUO4PB/events.json","paper":"https://pith.science/paper/6YDYNK4O"},"agent_actions":{"view_html":"https://pith.science/pith/6YDYNK4OV7TE2JLUCUMJMUO4PB","download_json":"https://pith.science/pith/6YDYNK4OV7TE2JLUCUMJMUO4PB.json","view_paper":"https://pith.science/paper/6YDYNK4O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0708.2096&json=true","fetch_graph":"https://pith.science/api/pith-number/6YDYNK4OV7TE2JLUCUMJMUO4PB/graph.json","fetch_events":"https://pith.science/api/pith-number/6YDYNK4OV7TE2JLUCUMJMUO4PB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6YDYNK4OV7TE2JLUCUMJMUO4PB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6YDYNK4OV7TE2JLUCUMJMUO4PB/action/storage_attestation","attest_author":"https://pith.science/pith/6YDYNK4OV7TE2JLUCUMJMUO4PB/action/author_attestation","sign_citation":"https://pith.science/pith/6YDYNK4OV7TE2JLUCUMJMUO4PB/action/citation_signature","submit_replication":"https://pith.science/pith/6YDYNK4OV7TE2JLUCUMJMUO4PB/action/replication_record"}},"created_at":"2026-05-18T04:16:32.551328+00:00","updated_at":"2026-05-18T04:16:32.551328+00:00"}