{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:EYU6PG7EBDQW7THNA7BGLPWRMI","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":"9aeff2926608064349d4a90e91610903d4a9b1c91d819e0a3a90c69a3a259a98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2006-06-20T05:11:22Z","title_canon_sha256":"343447deecd17e49d3cdd8438c5d856d2e4679edf6db124b8c24a9301a1b8730"},"schema_version":"1.0","source":{"id":"quant-ph/0606161","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0606161","created_at":"2026-05-18T01:37:54Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0606161v2","created_at":"2026-05-18T01:37:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0606161","created_at":"2026-05-18T01:37:54Z"},{"alias_kind":"pith_short_12","alias_value":"EYU6PG7EBDQW","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"EYU6PG7EBDQW7THN","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"EYU6PG7E","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:3b1fad4f4b7f6d08965c47a338008cced204bb0c2efb4a435b36d93b993c9a67","target":"graph","created_at":"2026-05-18T01:37:54Z","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 develop the concept of a unitary t-design as a means of expressing operationally useful subsets of the stochastic properties of the uniform (Haar) measure on the unitary group U(2^n) on n qubits. In particular, sets of unitaries forming 2-designs have wide applicability to quantum information protocols. We devise an O(n)-size in-place circuit construction for an approximate unitary 2-design. We then show that this can be used to construct an efficient protocol for experimentally characterizing the fidelity of a quantum process on n qubits with quantum circuits of size O(n) without requiring","authors_text":"Christoph Dankert, Etera Livine, Joseph Emerson, Richard Cleve","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2006-06-20T05:11:22Z","title":"Exact and Approximate Unitary 2-Designs: Constructions and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0606161","kind":"arxiv","version":2},"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":"sha256:7465248fdf46b4287007122e68e92ba4c293c8203a7141344ffd8251d6178689","target":"record","created_at":"2026-05-18T01:37:54Z","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":"9aeff2926608064349d4a90e91610903d4a9b1c91d819e0a3a90c69a3a259a98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2006-06-20T05:11:22Z","title_canon_sha256":"343447deecd17e49d3cdd8438c5d856d2e4679edf6db124b8c24a9301a1b8730"},"schema_version":"1.0","source":{"id":"quant-ph/0606161","kind":"arxiv","version":2}},"canonical_sha256":"2629e79be408e16fcced07c265bed1620295be5ae6d52d8cc63c05dbc7877a6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2629e79be408e16fcced07c265bed1620295be5ae6d52d8cc63c05dbc7877a6a","first_computed_at":"2026-05-18T01:37:54.569117Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:54.569117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"byZqg3+q5VWz9uVU9ZYSb6+c8FuK6gmFrTOhjvnEVBX+npBCAM4DHVZj/XrnK840hHMpK23PEmADENt8nQOqAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:54.569788Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0606161","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7465248fdf46b4287007122e68e92ba4c293c8203a7141344ffd8251d6178689","sha256:3b1fad4f4b7f6d08965c47a338008cced204bb0c2efb4a435b36d93b993c9a67"],"state_sha256":"fc003b26c8b29a30aba698195859b7df0a795e85d550477712a9e0e9349246fa"}