{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FNXMRN665JW4OB7XHRHVTJTXP7","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":"0a720f1b8760224e6e834b4834bbed638c2555fc080a13a1ff96d2115c0397ab","cross_cats_sorted":["cond-mat.str-el","cs.CC","cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-07-10T15:27:48Z","title_canon_sha256":"983d6d95a951127a2443f6e1f873b458c02fdd73d8ae23e032eb9ef896cb0499"},"schema_version":"1.0","source":{"id":"2407.07754","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.07754","created_at":"2026-07-05T09:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"2407.07754v2","created_at":"2026-07-05T09:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.07754","created_at":"2026-07-05T09:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"FNXMRN665JW4","created_at":"2026-07-05T09:56:52Z"},{"alias_kind":"pith_short_16","alias_value":"FNXMRN665JW4OB7X","created_at":"2026-07-05T09:56:52Z"},{"alias_kind":"pith_short_8","alias_value":"FNXMRN66","created_at":"2026-07-05T09:56:52Z"}],"graph_snapshots":[{"event_id":"sha256:f3c663a635a9c2fb1b81c0c3300258aeddf1f04d1a5b7f45d70c0d6bf06a2066","target":"graph","created_at":"2026-07-05T09:56:52Z","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/2407.07754/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that random quantum circuits on any geometry, including a 1D line, can form approximate unitary designs over $n$ qubits in $\\log n$ depth. In a similar manner, we construct pseudorandom unitaries (PRUs) in 1D circuits in $\\text{poly}(\\log n)$ depth, and in all-to-all-connected circuits in $\\text{poly}(\\log \\log n)$ depth. In all three cases, the $n$ dependence is optimal and improves exponentially over known results. These shallow quantum circuits have low complexity and create only short-range entanglement, yet are indistinguishable from unitaries with exponential complexity. Our con","authors_text":"Hsin-Yuan Huang, Jonas Haferkamp, Thomas Schuster","cross_cats":["cond-mat.str-el","cs.CC","cs.IT","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-07-10T15:27:48Z","title":"Random unitaries in extremely low depth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.07754","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":"sha256:24cb9cf28ad1aa6dc111f8436eac0bd552dea9899e5ebe816b03c799baf3dd7f","target":"record","created_at":"2026-07-05T09:56:52Z","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":"0a720f1b8760224e6e834b4834bbed638c2555fc080a13a1ff96d2115c0397ab","cross_cats_sorted":["cond-mat.str-el","cs.CC","cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-07-10T15:27:48Z","title_canon_sha256":"983d6d95a951127a2443f6e1f873b458c02fdd73d8ae23e032eb9ef896cb0499"},"schema_version":"1.0","source":{"id":"2407.07754","kind":"arxiv","version":2}},"canonical_sha256":"2b6ec8b7deea6dc707f73c4f59a6777fe53c9a90353dafe7b0050a391d639648","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b6ec8b7deea6dc707f73c4f59a6777fe53c9a90353dafe7b0050a391d639648","first_computed_at":"2026-07-05T09:56:52.979474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:56:52.979474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d7ysTrIm3KHn/xDFHmQd2j9XGPFIE38X+pTDV7YFQpMqwQIsKplIdHkE6f6dv9lHueh4pP48pmPRkvyqJe+tDw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:56:52.979910Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.07754","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24cb9cf28ad1aa6dc111f8436eac0bd552dea9899e5ebe816b03c799baf3dd7f","sha256:f3c663a635a9c2fb1b81c0c3300258aeddf1f04d1a5b7f45d70c0d6bf06a2066"],"state_sha256":"30ab9c49d0e53e14d45f1aec9adb8f8eca768cd3654ad33c54da59121fc381cc"}