{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RW2PPP4VV34UVNIXFX5ELJHOZ5","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":"7df3a3e3c2d5efd5b51288371953fdda03c0942ff83fb53fb6ca66792fde7090","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-01-19T19:10:42Z","title_canon_sha256":"49c5143f42a9f69b7dd035f5b8a89d5f7184a567111fdfb1bf2d09d060da9abe"},"schema_version":"1.0","source":{"id":"1501.04592","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04592","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04592v3","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04592","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"RW2PPP4VV34U","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RW2PPP4VV34UVNIX","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RW2PPP4V","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:5587b2a241a6385756d9f97b888f1d7f21eebd4341c284118500e35ddeeda7da","target":"graph","created_at":"2026-05-18T00:53:40Z","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":"A unitary 2-design can be viewed as a quantum analogue of a 2-universal hash function: it is indistinguishable from a truly random unitary by any procedure that queries it twice. We show that exact unitary 2-designs on n qubits can be implemented by quantum circuits consisting of ~O(n) elementary gates in logarithmic depth. This is essentially a quadratic improvement in size (and in width times depth) over all previous implementations that are exact or approximate (for sufficiently strong approximations).","authors_text":"Chunhao Wang, Debbie Leung, Li Liu, Richard Cleve","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-01-19T19:10:42Z","title":"Near-linear constructions of exact unitary 2-designs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04592","kind":"arxiv","version":3},"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:c0808026d44e1aaac8248e31e38d967706cdba6afac07600b2cf97534289cf24","target":"record","created_at":"2026-05-18T00:53:40Z","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":"7df3a3e3c2d5efd5b51288371953fdda03c0942ff83fb53fb6ca66792fde7090","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-01-19T19:10:42Z","title_canon_sha256":"49c5143f42a9f69b7dd035f5b8a89d5f7184a567111fdfb1bf2d09d060da9abe"},"schema_version":"1.0","source":{"id":"1501.04592","kind":"arxiv","version":3}},"canonical_sha256":"8db4f7bf95aef94ab5172dfa45a4eecf4f546c4fd79be5a6d807a426491f627a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8db4f7bf95aef94ab5172dfa45a4eecf4f546c4fd79be5a6d807a426491f627a","first_computed_at":"2026-05-18T00:53:40.647331Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:40.647331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s3OtpTlckxvDtQGIzrEIJkMvBtfpigMxYVQcokagUO/XuzRLT5fmBZW4NRoMI/7KJUllSmP+CBVXptV7ZefLCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:40.647917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04592","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0808026d44e1aaac8248e31e38d967706cdba6afac07600b2cf97534289cf24","sha256:5587b2a241a6385756d9f97b888f1d7f21eebd4341c284118500e35ddeeda7da"],"state_sha256":"caa65bc45182b39b6d491d4a186dfb0e0d5950403263a94109757adbecc0628a"}