{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OETEZG6TN5GHC7GWUPQEUFNVK7","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":"f6b308f21789b38b2d738ee5835404558577606b9ea6721462fa3aafad290103","cross_cats_sorted":["cs.CC","cs.IT","math-ph","math.IT","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-07-08T17:48:33Z","title_canon_sha256":"07abc888d98f1fc76ac431eef67b4549a03969f0accf2132d16defa416e809b9"},"schema_version":"1.0","source":{"id":"2507.06216","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.06216","created_at":"2026-07-05T11:39:56Z"},{"alias_kind":"arxiv_version","alias_value":"2507.06216v2","created_at":"2026-07-05T11:39:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.06216","created_at":"2026-07-05T11:39:56Z"},{"alias_kind":"pith_short_12","alias_value":"OETEZG6TN5GH","created_at":"2026-07-05T11:39:56Z"},{"alias_kind":"pith_short_16","alias_value":"OETEZG6TN5GHC7GW","created_at":"2026-07-05T11:39:56Z"},{"alias_kind":"pith_short_8","alias_value":"OETEZG6T","created_at":"2026-07-05T11:39:56Z"}],"graph_snapshots":[{"event_id":"sha256:d6d954e08ce74759d4d0ad616f73bfedc025b1a1389872988b09ff0d9710c670","target":"graph","created_at":"2026-07-05T11:39:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.06216/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct $\\varepsilon$-approximate unitary $k$-designs on $n$ qubits in circuit depth $O(\\log k \\log \\log n k / \\varepsilon)$. The depth is exponentially improved over all known results in all three parameters $n$, $k$, $\\varepsilon$. We further show that each dependence is optimal up to exponentially smaller factors. Our construction uses $\\tilde{{O}}(nk)$ ancilla qubits and ${O}(nk)$ bits of randomness, which are also optimal up to $\\log(n k)$ factors. An alternative construction achieves a smaller ancilla count $\\tilde{{O}}(n)$ with circuit depth ${O}(k \\log \\log nk/\\varepsilon)$. To ac","authors_text":"Fernando Brandao, Hsin-Yuan Huang, Laura Cui, Thomas Schuster","cross_cats":["cs.CC","cs.IT","math-ph","math.IT","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-07-08T17:48:33Z","title":"Unitary designs in nearly optimal depth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06216","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:f69abf415189cccc5f4cc3b4cb42ae63f754f98e33c54248ab54e8e643f95b22","target":"record","created_at":"2026-07-05T11:39:56Z","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":"f6b308f21789b38b2d738ee5835404558577606b9ea6721462fa3aafad290103","cross_cats_sorted":["cs.CC","cs.IT","math-ph","math.IT","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-07-08T17:48:33Z","title_canon_sha256":"07abc888d98f1fc76ac431eef67b4549a03969f0accf2132d16defa416e809b9"},"schema_version":"1.0","source":{"id":"2507.06216","kind":"arxiv","version":2}},"canonical_sha256":"71264c9bd36f4c717cd6a3e04a15b557ec98e4fde444b90dbe526fe349b88020","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71264c9bd36f4c717cd6a3e04a15b557ec98e4fde444b90dbe526fe349b88020","first_computed_at":"2026-07-05T11:39:56.172870Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:39:56.172870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Qoeb0YfLxFqQNOsbyTfFzkd8EwgWrn/KXlFYz8EteRy0b7rytXez9IRuhbmYYK2mRsdJSfOEejDk0M6zlE5Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:39:56.173349Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.06216","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f69abf415189cccc5f4cc3b4cb42ae63f754f98e33c54248ab54e8e643f95b22","sha256:d6d954e08ce74759d4d0ad616f73bfedc025b1a1389872988b09ff0d9710c670"],"state_sha256":"49b422f8f6ab6524785e0a0aa2b4188e819eff42ef5a3df98609b62e33f4f22c"}