{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:KKVDB7KMV5JAHHQ6QNNID2HEDE","short_pith_number":"pith:KKVDB7KM","schema_version":"1.0","canonical_sha256":"52aa30fd4caf52039e1e835a81e8e419394d87372466f58073c00cfe13ecf0ce","source":{"kind":"arxiv","id":"1005.3676","version":1},"attestation_state":"computed","paper":{"title":"Quantum search algorithms on a regular lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Birgit Hein, Gregor Tanner","submitted_at":"2010-05-20T12:22:11Z","abstract_excerpt":"Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level-splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behaviour for the search time and th"},"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":"1005.3676","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-05-20T12:22:11Z","cross_cats_sorted":[],"title_canon_sha256":"26b8b048d0730b3327e79d4e0fe912d004618bfc32471fe3ee2aad4a2ed89d2f","abstract_canon_sha256":"08f56b3f87229bc267d772db3aa0efda40ab7964b5549714c0a430be5cd11b9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:16.381499Z","signature_b64":"fMx72wAC+evN6krYpl3ZvscGmQsuEPr0IYeO2FiI82D8LATHzkQgnlXCyB9DtyjJWMo6MKGnRWDt7/RW//61Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52aa30fd4caf52039e1e835a81e8e419394d87372466f58073c00cfe13ecf0ce","last_reissued_at":"2026-05-18T02:07:16.380761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:16.380761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum search algorithms on a regular lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Birgit Hein, Gregor Tanner","submitted_at":"2010-05-20T12:22:11Z","abstract_excerpt":"Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level-splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behaviour for the search time and th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3676","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":"1005.3676","created_at":"2026-05-18T02:07:16.380852+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.3676v1","created_at":"2026-05-18T02:07:16.380852+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.3676","created_at":"2026-05-18T02:07:16.380852+00:00"},{"alias_kind":"pith_short_12","alias_value":"KKVDB7KMV5JA","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"KKVDB7KMV5JAHHQ6","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"KKVDB7KM","created_at":"2026-05-18T12:26:09.077623+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/KKVDB7KMV5JAHHQ6QNNID2HEDE","json":"https://pith.science/pith/KKVDB7KMV5JAHHQ6QNNID2HEDE.json","graph_json":"https://pith.science/api/pith-number/KKVDB7KMV5JAHHQ6QNNID2HEDE/graph.json","events_json":"https://pith.science/api/pith-number/KKVDB7KMV5JAHHQ6QNNID2HEDE/events.json","paper":"https://pith.science/paper/KKVDB7KM"},"agent_actions":{"view_html":"https://pith.science/pith/KKVDB7KMV5JAHHQ6QNNID2HEDE","download_json":"https://pith.science/pith/KKVDB7KMV5JAHHQ6QNNID2HEDE.json","view_paper":"https://pith.science/paper/KKVDB7KM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.3676&json=true","fetch_graph":"https://pith.science/api/pith-number/KKVDB7KMV5JAHHQ6QNNID2HEDE/graph.json","fetch_events":"https://pith.science/api/pith-number/KKVDB7KMV5JAHHQ6QNNID2HEDE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KKVDB7KMV5JAHHQ6QNNID2HEDE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KKVDB7KMV5JAHHQ6QNNID2HEDE/action/storage_attestation","attest_author":"https://pith.science/pith/KKVDB7KMV5JAHHQ6QNNID2HEDE/action/author_attestation","sign_citation":"https://pith.science/pith/KKVDB7KMV5JAHHQ6QNNID2HEDE/action/citation_signature","submit_replication":"https://pith.science/pith/KKVDB7KMV5JAHHQ6QNNID2HEDE/action/replication_record"}},"created_at":"2026-05-18T02:07:16.380852+00:00","updated_at":"2026-05-18T02:07:16.380852+00:00"}