{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OR2MQFIWD7V3D37TEBOGQOIHJS","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":"3b2300785c94e535c079b7188263e3daa50be08841527f8d03c1e5a0b3586fbd","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-01T03:35:48Z","title_canon_sha256":"bb516e6aaad96f1b308d14245ee9229ce18afa980c2f666d768893b3d4c2c8e7"},"schema_version":"1.0","source":{"id":"1907.00529","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.00529","created_at":"2026-05-17T23:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"1907.00529v1","created_at":"2026-05-17T23:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00529","created_at":"2026-05-17T23:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"OR2MQFIWD7V3","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OR2MQFIWD7V3D37T","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OR2MQFIW","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:09df84c0bd71b50caf9aa0da8d8b4246898704e7452cb1f9be0cecf04eb78382","target":"graph","created_at":"2026-05-17T23:41:51Z","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"},"paper":{"abstract_excerpt":"The fastest known classical algorithm deciding the $k$-colorability of $n$-vertex graph requires running time $\\Omega(2^n)$ for $k\\ge 5$. In this work, we present an exponential-space quantum algorithm computing the chromatic number with running time $O(1.9140^n)$ using quantum random access memory (QRAM). Our approach is based on Ambainis et al's quantum dynamic programming with applications of Grover's search to branching algorithms. We also present a polynomial-space quantum algorithm not using QRAM for the graph $20$-coloring problem with running time $O(1.9575^n)$. In the polynomial-space","authors_text":"Kazuya Shimizu, Ryuhei Mori","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-01T03:35:48Z","title":"Exponential-time quantum algorithms for graph coloring problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00529","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:cb3929c89d4d3c8f6c977da7be32e9d8c819622f0e566452011ba1c5a469a2a4","target":"record","created_at":"2026-05-17T23:41:51Z","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":"3b2300785c94e535c079b7188263e3daa50be08841527f8d03c1e5a0b3586fbd","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-01T03:35:48Z","title_canon_sha256":"bb516e6aaad96f1b308d14245ee9229ce18afa980c2f666d768893b3d4c2c8e7"},"schema_version":"1.0","source":{"id":"1907.00529","kind":"arxiv","version":1}},"canonical_sha256":"7474c815161febb1eff3205c6839074cb28e27c85d82e5cfae58ea6382387b2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7474c815161febb1eff3205c6839074cb28e27c85d82e5cfae58ea6382387b2b","first_computed_at":"2026-05-17T23:41:51.320234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:51.320234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B3cM3UEH3rKNkxdimBX9NOyGJ5spC0Ce97O8pbmCx4XoEDUTX+0kQvE1fnfb3QhOGHF0r1y4dB+JwOsoW2inDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:51.320947Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.00529","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb3929c89d4d3c8f6c977da7be32e9d8c819622f0e566452011ba1c5a469a2a4","sha256:09df84c0bd71b50caf9aa0da8d8b4246898704e7452cb1f9be0cecf04eb78382"],"state_sha256":"a57ea0475d84aec06549dc0a19491dc2ad12f67280bd2bf6cc4ad011aa1d1f9e"}