{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:UGP6IDKXFVHSDTJYWCZFW4J26K","short_pith_number":"pith:UGP6IDKX","schema_version":"1.0","canonical_sha256":"a19fe40d572d4f21cd38b0b25b713af2beb92539a152c89bb573e84d5fa619d1","source":{"kind":"arxiv","id":"0911.1102","version":1},"attestation_state":"computed","paper":{"title":"Searching via walking: How to find a marked subgraph of a graph using quantum walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Daniel Reitzner, Mark Hillery, Vladimir Buzek","submitted_at":"2009-11-05T19:01:14Z","abstract_excerpt":"We show how a quantum walk can be used to find a marked edge or a marked complete subgraph of a complete graph. We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation. The edges are marked by adding elements to them that impart a specific phase shift to the particle as it enters or leaves the edge. If the complete graph has N vertices and the subgraph has K vertices, the particle becomes localized on the subgraph in O(N/K) steps. This leads to a quantum search that is quadratically faster than a corresponding classical search. We show how "},"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":"0911.1102","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-11-05T19:01:14Z","cross_cats_sorted":[],"title_canon_sha256":"8c5461d025d1639ddd39833a5a3018f63a39cecbd30f1da93f41a148b15f8f21","abstract_canon_sha256":"987e835b877d77c30c0c54e61d7b2dd770b53a9b7b884366ae62da273d095c2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:59.150925Z","signature_b64":"4UubiyGe86132wPIb05fuYFG7RonlDnD4UVUzFynSLfQQnbFlTqOTHQkCBp/U/XZUOjOVaU5B/KlFipe9A08AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a19fe40d572d4f21cd38b0b25b713af2beb92539a152c89bb573e84d5fa619d1","last_reissued_at":"2026-05-18T02:10:59.150058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:59.150058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Searching via walking: How to find a marked subgraph of a graph using quantum walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Daniel Reitzner, Mark Hillery, Vladimir Buzek","submitted_at":"2009-11-05T19:01:14Z","abstract_excerpt":"We show how a quantum walk can be used to find a marked edge or a marked complete subgraph of a complete graph. We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation. The edges are marked by adding elements to them that impart a specific phase shift to the particle as it enters or leaves the edge. If the complete graph has N vertices and the subgraph has K vertices, the particle becomes localized on the subgraph in O(N/K) steps. This leads to a quantum search that is quadratically faster than a corresponding classical search. We show how "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1102","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":"0911.1102","created_at":"2026-05-18T02:10:59.150205+00:00"},{"alias_kind":"arxiv_version","alias_value":"0911.1102v1","created_at":"2026-05-18T02:10:59.150205+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1102","created_at":"2026-05-18T02:10:59.150205+00:00"},{"alias_kind":"pith_short_12","alias_value":"UGP6IDKXFVHS","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"UGP6IDKXFVHSDTJY","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"UGP6IDKX","created_at":"2026-05-18T12:26:02.257875+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/UGP6IDKXFVHSDTJYWCZFW4J26K","json":"https://pith.science/pith/UGP6IDKXFVHSDTJYWCZFW4J26K.json","graph_json":"https://pith.science/api/pith-number/UGP6IDKXFVHSDTJYWCZFW4J26K/graph.json","events_json":"https://pith.science/api/pith-number/UGP6IDKXFVHSDTJYWCZFW4J26K/events.json","paper":"https://pith.science/paper/UGP6IDKX"},"agent_actions":{"view_html":"https://pith.science/pith/UGP6IDKXFVHSDTJYWCZFW4J26K","download_json":"https://pith.science/pith/UGP6IDKXFVHSDTJYWCZFW4J26K.json","view_paper":"https://pith.science/paper/UGP6IDKX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0911.1102&json=true","fetch_graph":"https://pith.science/api/pith-number/UGP6IDKXFVHSDTJYWCZFW4J26K/graph.json","fetch_events":"https://pith.science/api/pith-number/UGP6IDKXFVHSDTJYWCZFW4J26K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UGP6IDKXFVHSDTJYWCZFW4J26K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UGP6IDKXFVHSDTJYWCZFW4J26K/action/storage_attestation","attest_author":"https://pith.science/pith/UGP6IDKXFVHSDTJYWCZFW4J26K/action/author_attestation","sign_citation":"https://pith.science/pith/UGP6IDKXFVHSDTJYWCZFW4J26K/action/citation_signature","submit_replication":"https://pith.science/pith/UGP6IDKXFVHSDTJYWCZFW4J26K/action/replication_record"}},"created_at":"2026-05-18T02:10:59.150205+00:00","updated_at":"2026-05-18T02:10:59.150205+00:00"}