{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:LRCWLOWY7O22YJMQ62IKLCWKYF","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":"4611393190b7e74f0c104bfe07e7aeddcea9de010639d4992e3424f6f5bf2520","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2021-06-09T18:01:57Z","title_canon_sha256":"014513415e61c3ec7d4e505a68481769b816b8968d6e5015bff6a9374ef91f75"},"schema_version":"1.0","source":{"id":"2106.05305","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.05305","created_at":"2026-07-05T04:25:10Z"},{"alias_kind":"arxiv_version","alias_value":"2106.05305v3","created_at":"2026-07-05T04:25:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.05305","created_at":"2026-07-05T04:25:10Z"},{"alias_kind":"pith_short_12","alias_value":"LRCWLOWY7O22","created_at":"2026-07-05T04:25:10Z"},{"alias_kind":"pith_short_16","alias_value":"LRCWLOWY7O22YJMQ","created_at":"2026-07-05T04:25:10Z"},{"alias_kind":"pith_short_8","alias_value":"LRCWLOWY","created_at":"2026-07-05T04:25:10Z"}],"graph_snapshots":[{"event_id":"sha256:95a670f89c631e0d43e6eadd48f3b76bb5881039d0d6323bc82fe87ac915c3fa","target":"graph","created_at":"2026-07-05T04:25:10Z","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/2106.05305/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. We prove a prominent conjecture by Brown and Susskind about how random quantum circuits' complexity increases. Consider constructing a unitary from Haar-random two-qubit quantum gates. Implementing the unitary exactly requires a circuit of some minimal number of gates - the unitary's exact circuit complexity. We prove that this complexity grows linearly with the number of random gates, with unit probability, until saturating after exponentially many random gate","authors_text":"Jens Eisert, Jonas Haferkamp, Naga B. T. Kothakonda, Nicole Yunger Halpern, Philippe Faist","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2021-06-09T18:01:57Z","title":"Linear growth of quantum circuit complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.05305","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":"sha256:253b865f4bf046816af5668c5d61e2d7f2f902041c0affa741ceb260c99804c7","target":"record","created_at":"2026-07-05T04:25:10Z","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":"4611393190b7e74f0c104bfe07e7aeddcea9de010639d4992e3424f6f5bf2520","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2021-06-09T18:01:57Z","title_canon_sha256":"014513415e61c3ec7d4e505a68481769b816b8968d6e5015bff6a9374ef91f75"},"schema_version":"1.0","source":{"id":"2106.05305","kind":"arxiv","version":3}},"canonical_sha256":"5c4565bad8fbb5ac2590f690a58acac171e4646d6d29df14bc6b201d6a63b3d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c4565bad8fbb5ac2590f690a58acac171e4646d6d29df14bc6b201d6a63b3d6","first_computed_at":"2026-07-05T04:25:10.614230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:25:10.614230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rlyUrojgSSdRLrEf63WPZIjEPdGtDIt+szBB7NL3LSiShFJ7NBzGdqkSUVxK1MiWLlib78/sfe89tWo3IkfXCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:25:10.614733Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.05305","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:253b865f4bf046816af5668c5d61e2d7f2f902041c0affa741ceb260c99804c7","sha256:95a670f89c631e0d43e6eadd48f3b76bb5881039d0d6323bc82fe87ac915c3fa"],"state_sha256":"4f712f1cb5edd4531b440bd4ae7bf720977a6e4f692dd66723aa5e4fd630db7b"}