{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:22CMZ4CHQRTY7D3IQSOJY6PKRT","short_pith_number":"pith:22CMZ4CH","canonical_record":{"source":{"id":"quant-ph/0208043","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2002-08-07T09:43:10Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"b72bfc00aa3ab5d8217c37fd48254528c70011357e5cf0c2e25ed293db4f2e0d","abstract_canon_sha256":"7aa2d0835ecc9e00e426f4c9d30bb69838a4ad16b7174dcdaa04d14298b3053c"},"schema_version":"1.0"},"canonical_sha256":"d684ccf04784678f8f68849c9c79ea8ccb9acc13ee35f6e0ab62aa65c8db3bd0","source":{"kind":"arxiv","id":"quant-ph/0208043","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0208043","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0208043v4","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0208043","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"pith_short_12","alias_value":"22CMZ4CHQRTY","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"22CMZ4CHQRTY7D3I","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"22CMZ4CH","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:22CMZ4CHQRTY7D3IQSOJY6PKRT","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0208043","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2002-08-07T09:43:10Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"b72bfc00aa3ab5d8217c37fd48254528c70011357e5cf0c2e25ed293db4f2e0d","abstract_canon_sha256":"7aa2d0835ecc9e00e426f4c9d30bb69838a4ad16b7174dcdaa04d14298b3053c"},"schema_version":"1.0"},"canonical_sha256":"d684ccf04784678f8f68849c9c79ea8ccb9acc13ee35f6e0ab62aa65c8db3bd0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:12.797736Z","signature_b64":"VoWQUoqETW/B2g7utQZaDaXx+0Y34bXRV+XufH8Z0RhU/wYWHl0HLoFQ5O+cRJdVB/5UHyq/Iis0DWlhzcF3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d684ccf04784678f8f68849c9c79ea8ccb9acc13ee35f6e0ab62aa65c8db3bd0","last_reissued_at":"2026-05-18T00:53:12.797366Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:12.797366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0208043","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pRkA6jfNCeZJ4FKGnnXG+UwUXcC5fE3dEk4CjAacYBZ8rl8omPNxrU+cQPg2fgSYi7jQKUOnq6sgGcQRFm6CDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T04:08:45.075061Z"},"content_sha256":"2a295ec4a7961817a3df27571d3fe3d99460176b0ac05da42428d12839cc1f46","schema_version":"1.0","event_id":"sha256:2a295ec4a7961817a3df27571d3fe3d99460176b0ac05da42428d12839cc1f46"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:22CMZ4CHQRTY7D3IQSOJY6PKRT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Circuits with Unbounded Fan-out","license":"","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Peter Hoyer (U Calgary), Robert Spalek (CWI)","submitted_at":"2002-08-07T09:43:10Z","abstract_excerpt":"We demonstrate that the unbounded fan-out gate is very powerful. Constant-depth polynomial-size quantum circuits with bounded fan-in and unbounded fan-out over a fixed basis (denoted by QNCf^0) can approximate with polynomially small error the following gates: parity, mod[q], And, Or, majority, threshold[t], exact[q], and Counting. Classically, we need logarithmic depth even if we can use unbounded fan-in gates. If we allow arbitrary one-qubit gates instead of a fixed basis, then these circuits can also be made exact in log-star depth. Sorting, arithmetical operations, phase estimation, and th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0208043","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dWNbona93SdYjk/iE6OHzr1cb5QVMj1ZpF4y+TCS+z1r8csFZ687Vurmfgi29qZR5CiSbPVpbCzNE/6iw9nLAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T04:08:45.075415Z"},"content_sha256":"8d6d2f20e0fc3ae15a2b8d1ace4d7004887e0158a3a5ab98b9df8274ad988abc","schema_version":"1.0","event_id":"sha256:8d6d2f20e0fc3ae15a2b8d1ace4d7004887e0158a3a5ab98b9df8274ad988abc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/22CMZ4CHQRTY7D3IQSOJY6PKRT/bundle.json","state_url":"https://pith.science/pith/22CMZ4CHQRTY7D3IQSOJY6PKRT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/22CMZ4CHQRTY7D3IQSOJY6PKRT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-21T04:08:45Z","links":{"resolver":"https://pith.science/pith/22CMZ4CHQRTY7D3IQSOJY6PKRT","bundle":"https://pith.science/pith/22CMZ4CHQRTY7D3IQSOJY6PKRT/bundle.json","state":"https://pith.science/pith/22CMZ4CHQRTY7D3IQSOJY6PKRT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/22CMZ4CHQRTY7D3IQSOJY6PKRT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:22CMZ4CHQRTY7D3IQSOJY6PKRT","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":"7aa2d0835ecc9e00e426f4c9d30bb69838a4ad16b7174dcdaa04d14298b3053c","cross_cats_sorted":["cs.CC"],"license":"","primary_cat":"quant-ph","submitted_at":"2002-08-07T09:43:10Z","title_canon_sha256":"b72bfc00aa3ab5d8217c37fd48254528c70011357e5cf0c2e25ed293db4f2e0d"},"schema_version":"1.0","source":{"id":"quant-ph/0208043","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0208043","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0208043v4","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0208043","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"pith_short_12","alias_value":"22CMZ4CHQRTY","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"22CMZ4CHQRTY7D3I","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"22CMZ4CH","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:8d6d2f20e0fc3ae15a2b8d1ace4d7004887e0158a3a5ab98b9df8274ad988abc","target":"graph","created_at":"2026-05-18T00:53:12Z","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":"We demonstrate that the unbounded fan-out gate is very powerful. Constant-depth polynomial-size quantum circuits with bounded fan-in and unbounded fan-out over a fixed basis (denoted by QNCf^0) can approximate with polynomially small error the following gates: parity, mod[q], And, Or, majority, threshold[t], exact[q], and Counting. Classically, we need logarithmic depth even if we can use unbounded fan-in gates. If we allow arbitrary one-qubit gates instead of a fixed basis, then these circuits can also be made exact in log-star depth. Sorting, arithmetical operations, phase estimation, and th","authors_text":"Peter Hoyer (U Calgary), Robert Spalek (CWI)","cross_cats":["cs.CC"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2002-08-07T09:43:10Z","title":"Quantum Circuits with Unbounded Fan-out"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0208043","kind":"arxiv","version":4},"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":"sha256:2a295ec4a7961817a3df27571d3fe3d99460176b0ac05da42428d12839cc1f46","target":"record","created_at":"2026-05-18T00:53:12Z","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":"7aa2d0835ecc9e00e426f4c9d30bb69838a4ad16b7174dcdaa04d14298b3053c","cross_cats_sorted":["cs.CC"],"license":"","primary_cat":"quant-ph","submitted_at":"2002-08-07T09:43:10Z","title_canon_sha256":"b72bfc00aa3ab5d8217c37fd48254528c70011357e5cf0c2e25ed293db4f2e0d"},"schema_version":"1.0","source":{"id":"quant-ph/0208043","kind":"arxiv","version":4}},"canonical_sha256":"d684ccf04784678f8f68849c9c79ea8ccb9acc13ee35f6e0ab62aa65c8db3bd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d684ccf04784678f8f68849c9c79ea8ccb9acc13ee35f6e0ab62aa65c8db3bd0","first_computed_at":"2026-05-18T00:53:12.797366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:12.797366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VoWQUoqETW/B2g7utQZaDaXx+0Y34bXRV+XufH8Z0RhU/wYWHl0HLoFQ5O+cRJdVB/5UHyq/Iis0DWlhzcF3Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:12.797736Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0208043","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a295ec4a7961817a3df27571d3fe3d99460176b0ac05da42428d12839cc1f46","sha256:8d6d2f20e0fc3ae15a2b8d1ace4d7004887e0158a3a5ab98b9df8274ad988abc"],"state_sha256":"282293569f31c559c7df3ae707b36655afc6975de6db4866fd88215fb8b5c9a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E60/aq5D8Lc/2wD4DmwHNYjdWrdzM1oiXr+wK3uaCoXaCKdnr5uxuAUqF0FMpcbT4k9rYAgfbYlTNcAle+bWCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T04:08:45.077567Z","bundle_sha256":"08075e9154d5cdc2a2e3601f75536f3a2cc2c5ca50b7761fa0ae95ace849bc7f"}}