{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:I26JR5OATT4GHB3TGXG6EMOFWY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9a22945064a9620d865c7b37bb72f8728e5e36d292619f97be4cbe636ac49de1","cross_cats_sorted":["cs.DS"],"license":"","primary_cat":"quant-ph","submitted_at":"2004-02-16T23:32:23Z","title_canon_sha256":"f2923e8fabf9f3ca8095ffac4ef9f479094b210c30ff1eb88f56d91092e36c71"},"schema_version":"1.0","source":{"id":"quant-ph/0402107","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0402107","created_at":"2026-07-04T14:48:38Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0402107v1","created_at":"2026-07-04T14:48:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0402107","created_at":"2026-07-04T14:48:38Z"},{"alias_kind":"pith_short_12","alias_value":"I26JR5OATT4G","created_at":"2026-07-04T14:48:38Z"},{"alias_kind":"pith_short_16","alias_value":"I26JR5OATT4GHB3T","created_at":"2026-07-04T14:48:38Z"},{"alias_kind":"pith_short_8","alias_value":"I26JR5OA","created_at":"2026-07-04T14:48:38Z"}],"graph_snapshots":[{"event_id":"sha256:faedaff2f281bb7f5ab89111e20b87c2cbb82cd1870d595be48759d4537fe350","target":"graph","created_at":"2026-07-04T14:48:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/quant-ph/0402107/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show how to search N items arranged on a $\\sqrt{N}\\times\\sqrt{N}$ grid in time $O(\\sqrt N \\log N)$, using a discrete time quantum walk. This result for the first time exhibits a significant difference between discrete time and continuous time walks without coin degrees of freedom, since it has been shown recently that such a continuous time walk needs time $\\Omega(N)$ to perform the same task. Our result furthermore improves on a previous bound for quantum local search by Aaronson and Ambainis. We generalize our result to 3 and more dimensions where the walk yields the optimal performance o","authors_text":"Alexander Rivosh, Andris Ambainis, Julia Kempe","cross_cats":["cs.DS"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2004-02-16T23:32:23Z","title":"Coins Make Quantum Walks Faster"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0402107","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d0d1e2d15698df71dd3f98b2bbd27be401abd6da311d8801dd3ca4ec60b8f2da","target":"record","created_at":"2026-07-04T14:48:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9a22945064a9620d865c7b37bb72f8728e5e36d292619f97be4cbe636ac49de1","cross_cats_sorted":["cs.DS"],"license":"","primary_cat":"quant-ph","submitted_at":"2004-02-16T23:32:23Z","title_canon_sha256":"f2923e8fabf9f3ca8095ffac4ef9f479094b210c30ff1eb88f56d91092e36c71"},"schema_version":"1.0","source":{"id":"quant-ph/0402107","kind":"arxiv","version":1}},"canonical_sha256":"46bc98f5c09cf863877335cde231c5b639192f81ea0abb00a673bda2c729f7be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46bc98f5c09cf863877335cde231c5b639192f81ea0abb00a673bda2c729f7be","first_computed_at":"2026-07-04T14:48:38.739734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:48:38.739734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wgdred4ZNM4kRoojfvYxJjdtMmGxydPKFmVQV/1K9yR4x+wVJfSupeQ9qbxqWUPAWrgyKYoHtp244lPxCcCrAA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:48:38.740067Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0402107","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0d1e2d15698df71dd3f98b2bbd27be401abd6da311d8801dd3ca4ec60b8f2da","sha256:faedaff2f281bb7f5ab89111e20b87c2cbb82cd1870d595be48759d4537fe350"],"state_sha256":"655358b74a200112760512210a51fc553f747bd1e3736e32a5df0a14e43dfb1d"}