{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:Y5W26XX5IOZQZ2ZJ5IN4J4QJOT","short_pith_number":"pith:Y5W26XX5","schema_version":"1.0","canonical_sha256":"c76daf5efd43b30ceb29ea1bc4f20974fb392bcbbb444f97143ac71cb82ed321","source":{"kind":"arxiv","id":"1610.05661","version":1},"attestation_state":"computed","paper":{"title":"On the class of diffusion operators for fast quantum search","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Avatar Tulsi","submitted_at":"2016-10-18T15:01:01Z","abstract_excerpt":"Grover's quantum search algorithm evolves a quantum system from a known source state $|s\\rangle$ to an unknown target state $|t\\rangle$ using the selective phase inversions, $I_{s}$ and $I_{t}$, of these two states. In one of the generalizations of Grover's algorithm, $I_{s}$ is replaced by a general diffusion operator $D_{s}$ having $|s\\rangle$ as an eigenstate and $I_{t}$ is replaced by a general selective phase rotation $I_{t}^{\\phi}$. A fast quantum search is possible as long as the operator $D_{s}$ and the angle $\\phi$ satisfies certain conditions. These conditions are very restrictive in"},"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":"1610.05661","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-10-18T15:01:01Z","cross_cats_sorted":[],"title_canon_sha256":"cef98f401d7c60ce4496e729a39c21b5798b070b8ce79dc4c019f8a8f36a6708","abstract_canon_sha256":"cf6a5af25d1e3f32393d764b48d376fcc87959435ab9f443c4ab82d81c708ade"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:58.693573Z","signature_b64":"XZrdohEi2RCCx47onzsHDRCqa8buSTpRWpPlUbgy00PD/PGjRJgrC8JztESxQLyhCp7ygmMSyZ315zCWGWguCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c76daf5efd43b30ceb29ea1bc4f20974fb392bcbbb444f97143ac71cb82ed321","last_reissued_at":"2026-05-18T01:01:58.693038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:58.693038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the class of diffusion operators for fast quantum search","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Avatar Tulsi","submitted_at":"2016-10-18T15:01:01Z","abstract_excerpt":"Grover's quantum search algorithm evolves a quantum system from a known source state $|s\\rangle$ to an unknown target state $|t\\rangle$ using the selective phase inversions, $I_{s}$ and $I_{t}$, of these two states. In one of the generalizations of Grover's algorithm, $I_{s}$ is replaced by a general diffusion operator $D_{s}$ having $|s\\rangle$ as an eigenstate and $I_{t}$ is replaced by a general selective phase rotation $I_{t}^{\\phi}$. A fast quantum search is possible as long as the operator $D_{s}$ and the angle $\\phi$ satisfies certain conditions. These conditions are very restrictive in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05661","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":"1610.05661","created_at":"2026-05-18T01:01:58.693129+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.05661v1","created_at":"2026-05-18T01:01:58.693129+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05661","created_at":"2026-05-18T01:01:58.693129+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y5W26XX5IOZQ","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y5W26XX5IOZQZ2ZJ","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y5W26XX5","created_at":"2026-05-18T12:30:53.716459+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/Y5W26XX5IOZQZ2ZJ5IN4J4QJOT","json":"https://pith.science/pith/Y5W26XX5IOZQZ2ZJ5IN4J4QJOT.json","graph_json":"https://pith.science/api/pith-number/Y5W26XX5IOZQZ2ZJ5IN4J4QJOT/graph.json","events_json":"https://pith.science/api/pith-number/Y5W26XX5IOZQZ2ZJ5IN4J4QJOT/events.json","paper":"https://pith.science/paper/Y5W26XX5"},"agent_actions":{"view_html":"https://pith.science/pith/Y5W26XX5IOZQZ2ZJ5IN4J4QJOT","download_json":"https://pith.science/pith/Y5W26XX5IOZQZ2ZJ5IN4J4QJOT.json","view_paper":"https://pith.science/paper/Y5W26XX5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.05661&json=true","fetch_graph":"https://pith.science/api/pith-number/Y5W26XX5IOZQZ2ZJ5IN4J4QJOT/graph.json","fetch_events":"https://pith.science/api/pith-number/Y5W26XX5IOZQZ2ZJ5IN4J4QJOT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y5W26XX5IOZQZ2ZJ5IN4J4QJOT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y5W26XX5IOZQZ2ZJ5IN4J4QJOT/action/storage_attestation","attest_author":"https://pith.science/pith/Y5W26XX5IOZQZ2ZJ5IN4J4QJOT/action/author_attestation","sign_citation":"https://pith.science/pith/Y5W26XX5IOZQZ2ZJ5IN4J4QJOT/action/citation_signature","submit_replication":"https://pith.science/pith/Y5W26XX5IOZQZ2ZJ5IN4J4QJOT/action/replication_record"}},"created_at":"2026-05-18T01:01:58.693129+00:00","updated_at":"2026-05-18T01:01:58.693129+00:00"}