{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:YQ4LCZWIDRNCLZENBTBU76JQ5E","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":"93ba620a4e3fc25c2b73fa2f7ebe816c7ed2a469d4f630beea8fd6017809781d","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2005-07-19T19:36:00Z","title_canon_sha256":"0291c1cd39785f6d0e3cc77961fd4037ff1879554bd302c3d88a9350e96cce33"},"schema_version":"1.0","source":{"id":"quant-ph/0507190","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0507190","created_at":"2026-05-18T00:09:06Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0507190v1","created_at":"2026-05-18T00:09:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0507190","created_at":"2026-05-18T00:09:06Z"},{"alias_kind":"pith_short_12","alias_value":"YQ4LCZWIDRNC","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"YQ4LCZWIDRNCLZEN","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"YQ4LCZWI","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:7899c0a953650f07e4d743cf84f63eec19774391738d67ea14ec741947e269c1","target":"graph","created_at":"2026-05-18T00:09:06Z","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":"Consider the following generalized hidden shift problem: given a function f on {0,...,M-1} x Z_N satisfying f(b,x)=f(b+1,x+s) for b=0,1,...,M-2, find the unknown shift s in Z_N. For M=N, this problem is an instance of the abelian hidden subgroup problem, which can be solved efficiently on a quantum computer, whereas for M=2, it is equivalent to the dihedral hidden subgroup problem, for which no efficient algorithm is known. For any fixed positive epsilon, we give an efficient (i.e., poly(log N)) quantum algorithm for this problem provided M > N^epsilon. The algorithm is based on the \"pretty go","authors_text":"Andrew M. Childs, Wim van Dam","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2005-07-19T19:36:00Z","title":"Quantum algorithm for a generalized hidden shift problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0507190","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:a52d4b9fa137158b221fd9431dce0bacc90ee132e6079853d85226effaa57321","target":"record","created_at":"2026-05-18T00:09:06Z","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":"93ba620a4e3fc25c2b73fa2f7ebe816c7ed2a469d4f630beea8fd6017809781d","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2005-07-19T19:36:00Z","title_canon_sha256":"0291c1cd39785f6d0e3cc77961fd4037ff1879554bd302c3d88a9350e96cce33"},"schema_version":"1.0","source":{"id":"quant-ph/0507190","kind":"arxiv","version":1}},"canonical_sha256":"c438b166c81c5a25e48d0cc34ff930e90c1cebe341e15e052974d67e28ca4174","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c438b166c81c5a25e48d0cc34ff930e90c1cebe341e15e052974d67e28ca4174","first_computed_at":"2026-05-18T00:09:06.030520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:06.030520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qr3w02JtsZyFWRxwNCVC8yigupxQkERYrGojtCBYMZd20xeyO+6vxsuCWS3LwVOss0DtRmuK/zI0NwIInpK9AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:06.031165Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0507190","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a52d4b9fa137158b221fd9431dce0bacc90ee132e6079853d85226effaa57321","sha256:7899c0a953650f07e4d743cf84f63eec19774391738d67ea14ec741947e269c1"],"state_sha256":"bfd01d6df6a01c69040f1be7fb2f1b4c40ab2aede3e1482b1a066c1c6c13a4f5"}