{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:GJHSA6IJ5RCGPQ7H7AEMA2EFGG","short_pith_number":"pith:GJHSA6IJ","schema_version":"1.0","canonical_sha256":"324f207909ec4467c3e7f808c06885318709fbc50c7afd64e1c0974f421d02a8","source":{"kind":"arxiv","id":"1905.12053","version":1},"attestation_state":"computed","paper":{"title":"Unitary designs from statistical mechanics in random quantum circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cond-mat.str-el","hep-th"],"primary_cat":"quant-ph","authors_text":"Nicholas Hunter-Jones","submitted_at":"2019-05-28T19:58:19Z","abstract_excerpt":"Random quantum circuits are proficient information scramblers and efficient generators of randomness, rapidly approximating moments of the unitary group. We study the convergence of local random quantum circuits to unitary $k$-designs. Employing a statistical mechanical mapping, we give an exact expression of the distance to forming an approximate design as a lattice partition function. In the statistical mechanics model, the approach to randomness has a simple interpretation in terms of domain walls extending through the circuit. We analytically compute the second moment, showing that random "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1905.12053","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-05-28T19:58:19Z","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","hep-th"],"title_canon_sha256":"dccf1d155837a44521324c5cefde4d26d78fa3a4ca52f083d123323bb38b5cee","abstract_canon_sha256":"773e194ad28c4affbad2139b285b37adb8f0ae4bd9b1c1f9e82884f09cb6332d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:41.953193Z","signature_b64":"o5xY4ziOLkmzf3c7PLENAF61eZnwat1c9w0Lg5FpRcBL/kcL+bDRgyqrECYNEMDClwBlws24NyTjWIYf21NDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"324f207909ec4467c3e7f808c06885318709fbc50c7afd64e1c0974f421d02a8","last_reissued_at":"2026-05-17T23:44:41.952756Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:41.952756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unitary designs from statistical mechanics in random quantum circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cond-mat.str-el","hep-th"],"primary_cat":"quant-ph","authors_text":"Nicholas Hunter-Jones","submitted_at":"2019-05-28T19:58:19Z","abstract_excerpt":"Random quantum circuits are proficient information scramblers and efficient generators of randomness, rapidly approximating moments of the unitary group. We study the convergence of local random quantum circuits to unitary $k$-designs. Employing a statistical mechanical mapping, we give an exact expression of the distance to forming an approximate design as a lattice partition function. In the statistical mechanics model, the approach to randomness has a simple interpretation in terms of domain walls extending through the circuit. We analytically compute the second moment, showing that random "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12053","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.12053","created_at":"2026-05-17T23:44:41.952823+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.12053v1","created_at":"2026-05-17T23:44:41.952823+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.12053","created_at":"2026-05-17T23:44:41.952823+00:00"},{"alias_kind":"pith_short_12","alias_value":"GJHSA6IJ5RCG","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"GJHSA6IJ5RCGPQ7H","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"GJHSA6IJ","created_at":"2026-05-18T12:33:18.533446+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":10,"internal_anchor_count":5,"sample":[{"citing_arxiv_id":"2408.12739","citing_title":"Quantum Convolutional Neural Networks are Effectively Classically Simulable","ref_index":106,"is_internal_anchor":true},{"citing_arxiv_id":"2408.01545","citing_title":"Operator space fragmentation in perturbed Floquet-Clifford circuits","ref_index":78,"is_internal_anchor":true},{"citing_arxiv_id":"2409.02187","citing_title":"Late-time ensembles of quantum states in quantum chaotic systems","ref_index":56,"is_internal_anchor":true},{"citing_arxiv_id":"2505.18396","citing_title":"The Lie Algebra of XY-mixer Topologies and Warm Starting QAOA for Constrained Optimization","ref_index":38,"is_internal_anchor":true},{"citing_arxiv_id":"2506.22755","citing_title":"Scaling Laws of Quantum Information Lifetime in Monitored Quantum Dynamics","ref_index":37,"is_internal_anchor":true},{"citing_arxiv_id":"2604.23192","citing_title":"Coherence dynamics in quantum many-body systems with conservation laws","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2604.20828","citing_title":"Arrow of Time as an indicator of Measurement-Induced Phase Transitions","ref_index":60,"is_internal_anchor":false},{"citing_arxiv_id":"2604.05043","citing_title":"Quantum state randomization constrained by non-Abelian symmetries","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2604.05031","citing_title":"Geometry of Free Fermion Commutants","ref_index":59,"is_internal_anchor":false},{"citing_arxiv_id":"2605.03023","citing_title":"Arts & crafts: Strong random unitaries and geometric locality","ref_index":8,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GJHSA6IJ5RCGPQ7H7AEMA2EFGG","json":"https://pith.science/pith/GJHSA6IJ5RCGPQ7H7AEMA2EFGG.json","graph_json":"https://pith.science/api/pith-number/GJHSA6IJ5RCGPQ7H7AEMA2EFGG/graph.json","events_json":"https://pith.science/api/pith-number/GJHSA6IJ5RCGPQ7H7AEMA2EFGG/events.json","paper":"https://pith.science/paper/GJHSA6IJ"},"agent_actions":{"view_html":"https://pith.science/pith/GJHSA6IJ5RCGPQ7H7AEMA2EFGG","download_json":"https://pith.science/pith/GJHSA6IJ5RCGPQ7H7AEMA2EFGG.json","view_paper":"https://pith.science/paper/GJHSA6IJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.12053&json=true","fetch_graph":"https://pith.science/api/pith-number/GJHSA6IJ5RCGPQ7H7AEMA2EFGG/graph.json","fetch_events":"https://pith.science/api/pith-number/GJHSA6IJ5RCGPQ7H7AEMA2EFGG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GJHSA6IJ5RCGPQ7H7AEMA2EFGG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GJHSA6IJ5RCGPQ7H7AEMA2EFGG/action/storage_attestation","attest_author":"https://pith.science/pith/GJHSA6IJ5RCGPQ7H7AEMA2EFGG/action/author_attestation","sign_citation":"https://pith.science/pith/GJHSA6IJ5RCGPQ7H7AEMA2EFGG/action/citation_signature","submit_replication":"https://pith.science/pith/GJHSA6IJ5RCGPQ7H7AEMA2EFGG/action/replication_record"}},"created_at":"2026-05-17T23:44:41.952823+00:00","updated_at":"2026-05-17T23:44:41.952823+00:00"}