{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:3QQNU5RZCFCV6J2O7BXZD4YBBR","short_pith_number":"pith:3QQNU5RZ","schema_version":"1.0","canonical_sha256":"dc20da763911455f274ef86f91f3010c4a00893762102763f5c09e1454c64860","source":{"kind":"arxiv","id":"quant-ph/0108062","version":1},"attestation_state":"computed","paper":{"title":"Universal quantum gates","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jean-Luc Brylinski, Ranee Brylinski","submitted_at":"2001-08-13T16:10:52Z","abstract_excerpt":"In this paper we study universality for quantum gates acting on qudits.Qudits are states in a Hilbert space of dimension d where d is at least two. We determine which 2-qudit gates V have the properties (i) the collection of all 1-qudit gates together with V produces all n-qudit gates up to arbitrary precision, or (ii) the collection of all 1-qudit gates together with V produces all n-qudit gates exactly. We show that (i) and (ii) are equivalent conditions on V, and they hold if and only if V is not a primitive gate. Here we say V is primitive if it transforms any decomposable tensor into a de"},"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":"quant-ph/0108062","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2001-08-13T16:10:52Z","cross_cats_sorted":[],"title_canon_sha256":"7c65eed7665ea39da20af99824118b87ec87f91bdf15779aaa8aa22e11f44664","abstract_canon_sha256":"a3ca0d11417cc1f2ec77a68791631ad26f4a0345089fb8247e7ebfdf73da7e18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:45:41.118303Z","signature_b64":"/rVIzHvjbWzxNoGPBvnc2W2zBXulHaId+4WnU/c3c3bAyL4eZl6dO0LTVXBGTK3IC0GT/2S735JUUy35NrLgBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc20da763911455f274ef86f91f3010c4a00893762102763f5c09e1454c64860","last_reissued_at":"2026-07-04T14:45:41.117944Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:45:41.117944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universal quantum gates","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jean-Luc Brylinski, Ranee Brylinski","submitted_at":"2001-08-13T16:10:52Z","abstract_excerpt":"In this paper we study universality for quantum gates acting on qudits.Qudits are states in a Hilbert space of dimension d where d is at least two. We determine which 2-qudit gates V have the properties (i) the collection of all 1-qudit gates together with V produces all n-qudit gates up to arbitrary precision, or (ii) the collection of all 1-qudit gates together with V produces all n-qudit gates exactly. We show that (i) and (ii) are equivalent conditions on V, and they hold if and only if V is not a primitive gate. Here we say V is primitive if it transforms any decomposable tensor into a de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0108062","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/0108062/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"quant-ph/0108062","created_at":"2026-07-04T14:45:41.118003+00:00"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0108062v1","created_at":"2026-07-04T14:45:41.118003+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0108062","created_at":"2026-07-04T14:45:41.118003+00:00"},{"alias_kind":"pith_short_12","alias_value":"3QQNU5RZCFCV","created_at":"2026-07-04T14:45:41.118003+00:00"},{"alias_kind":"pith_short_16","alias_value":"3QQNU5RZCFCV6J2O","created_at":"2026-07-04T14:45:41.118003+00:00"},{"alias_kind":"pith_short_8","alias_value":"3QQNU5RZ","created_at":"2026-07-04T14:45:41.118003+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":5,"internal_anchor_count":4,"sample":[{"citing_arxiv_id":"2607.08200","citing_title":"Efficient High-Dimensional Quantum Circuit Synthesis: From Multi-Controlled Gates to Isometries and Quantum Channels","ref_index":7,"is_internal_anchor":true},{"citing_arxiv_id":"2607.07586","citing_title":"Fidelity Analysis of Adiabatically Driven Donor Spins as Two-Qubit and Ququart Systems","ref_index":34,"is_internal_anchor":true},{"citing_arxiv_id":"2606.03722","citing_title":"Characterizing quantum channels from local-unitary invariants","ref_index":35,"is_internal_anchor":true},{"citing_arxiv_id":"2606.28169","citing_title":"Time Evolution on Hybrid Tensor Networks -- A Novel and Parallelizable Algorithm","ref_index":10,"is_internal_anchor":true},{"citing_arxiv_id":"2604.11534","citing_title":"Quantum circuit optimization for arbitrary high-dimensional bipartite quantum computation","ref_index":44,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3QQNU5RZCFCV6J2O7BXZD4YBBR","json":"https://pith.science/pith/3QQNU5RZCFCV6J2O7BXZD4YBBR.json","graph_json":"https://pith.science/api/pith-number/3QQNU5RZCFCV6J2O7BXZD4YBBR/graph.json","events_json":"https://pith.science/api/pith-number/3QQNU5RZCFCV6J2O7BXZD4YBBR/events.json","paper":"https://pith.science/paper/3QQNU5RZ"},"agent_actions":{"view_html":"https://pith.science/pith/3QQNU5RZCFCV6J2O7BXZD4YBBR","download_json":"https://pith.science/pith/3QQNU5RZCFCV6J2O7BXZD4YBBR.json","view_paper":"https://pith.science/paper/3QQNU5RZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=quant-ph/0108062&json=true","fetch_graph":"https://pith.science/api/pith-number/3QQNU5RZCFCV6J2O7BXZD4YBBR/graph.json","fetch_events":"https://pith.science/api/pith-number/3QQNU5RZCFCV6J2O7BXZD4YBBR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3QQNU5RZCFCV6J2O7BXZD4YBBR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3QQNU5RZCFCV6J2O7BXZD4YBBR/action/storage_attestation","attest_author":"https://pith.science/pith/3QQNU5RZCFCV6J2O7BXZD4YBBR/action/author_attestation","sign_citation":"https://pith.science/pith/3QQNU5RZCFCV6J2O7BXZD4YBBR/action/citation_signature","submit_replication":"https://pith.science/pith/3QQNU5RZCFCV6J2O7BXZD4YBBR/action/replication_record"}},"created_at":"2026-07-04T14:45:41.118003+00:00","updated_at":"2026-07-04T14:45:41.118003+00:00"}