{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FXURT27O5EK76ITIC6EPBZDR2L","short_pith_number":"pith:FXURT27O","schema_version":"1.0","canonical_sha256":"2de919ebeee915ff22681788f0e471d2f1efa5bd9d343f709a77d1a9b11f14b1","source":{"kind":"arxiv","id":"1605.00619","version":1},"attestation_state":"computed","paper":{"title":"A Note on Oracle Separations for BQP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Lijie Chen","submitted_at":"2016-05-02T19:04:14Z","abstract_excerpt":"In 2009, using the $\\textsf{Fourier Checking}$ problem, Aaronson claimed to construct the relativized worlds such that $\\textsf{BQP} \\not\\subset \\mathsf{BPP_{path}}$ and $\\textsf{BQP} \\not\\subset \\textsf{SZK}$. However, there are subtle errors in the original proof. In this paper, we point out the issues, and rescue these two separations by using more sophisticated constructions.\n  Meanwhile, we take the opportunity to study the complexity classes $\\mathsf{BPP_{path}}$ and $\\textsf{SZK}$. We give general ways to construct functions which are hard for $\\textsf{SZK}$ and $\\mathsf{BPP_{path}}$ (i"},"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":"1605.00619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-05-02T19:04:14Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"e90f697640ef3754900422094817564e5e5ddd71e6fdb1fe8a76c0e1074b8121","abstract_canon_sha256":"eae9c1fd6137a0a75079cf9fc4fcf71cd100b09162f4838d273e579b84619373"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:48.423740Z","signature_b64":"sYDMPQnR6ExFbQ9pinp0rj+/rF/U2Yw7dFmJNZhtkNGe64xOHqqXFzA3m/AGerlsArp1KC4aILquTjW+4bliBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2de919ebeee915ff22681788f0e471d2f1efa5bd9d343f709a77d1a9b11f14b1","last_reissued_at":"2026-05-18T01:15:48.423229Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:48.423229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on Oracle Separations for BQP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Lijie Chen","submitted_at":"2016-05-02T19:04:14Z","abstract_excerpt":"In 2009, using the $\\textsf{Fourier Checking}$ problem, Aaronson claimed to construct the relativized worlds such that $\\textsf{BQP} \\not\\subset \\mathsf{BPP_{path}}$ and $\\textsf{BQP} \\not\\subset \\textsf{SZK}$. However, there are subtle errors in the original proof. In this paper, we point out the issues, and rescue these two separations by using more sophisticated constructions.\n  Meanwhile, we take the opportunity to study the complexity classes $\\mathsf{BPP_{path}}$ and $\\textsf{SZK}$. We give general ways to construct functions which are hard for $\\textsf{SZK}$ and $\\mathsf{BPP_{path}}$ (i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00619","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":"1605.00619","created_at":"2026-05-18T01:15:48.423322+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.00619v1","created_at":"2026-05-18T01:15:48.423322+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00619","created_at":"2026-05-18T01:15:48.423322+00:00"},{"alias_kind":"pith_short_12","alias_value":"FXURT27O5EK7","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FXURT27O5EK76ITI","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FXURT27O","created_at":"2026-05-18T12:30:15.759754+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.03435","citing_title":"Computational Complexity and Simulability of Non-Hermitian Quantum Dynamics","ref_index":55,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FXURT27O5EK76ITIC6EPBZDR2L","json":"https://pith.science/pith/FXURT27O5EK76ITIC6EPBZDR2L.json","graph_json":"https://pith.science/api/pith-number/FXURT27O5EK76ITIC6EPBZDR2L/graph.json","events_json":"https://pith.science/api/pith-number/FXURT27O5EK76ITIC6EPBZDR2L/events.json","paper":"https://pith.science/paper/FXURT27O"},"agent_actions":{"view_html":"https://pith.science/pith/FXURT27O5EK76ITIC6EPBZDR2L","download_json":"https://pith.science/pith/FXURT27O5EK76ITIC6EPBZDR2L.json","view_paper":"https://pith.science/paper/FXURT27O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.00619&json=true","fetch_graph":"https://pith.science/api/pith-number/FXURT27O5EK76ITIC6EPBZDR2L/graph.json","fetch_events":"https://pith.science/api/pith-number/FXURT27O5EK76ITIC6EPBZDR2L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FXURT27O5EK76ITIC6EPBZDR2L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FXURT27O5EK76ITIC6EPBZDR2L/action/storage_attestation","attest_author":"https://pith.science/pith/FXURT27O5EK76ITIC6EPBZDR2L/action/author_attestation","sign_citation":"https://pith.science/pith/FXURT27O5EK76ITIC6EPBZDR2L/action/citation_signature","submit_replication":"https://pith.science/pith/FXURT27O5EK76ITIC6EPBZDR2L/action/replication_record"}},"created_at":"2026-05-18T01:15:48.423322+00:00","updated_at":"2026-05-18T01:15:48.423322+00:00"}