{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:B2KVI4BK4MPUVRJ4NAYZGYPWNV","short_pith_number":"pith:B2KVI4BK","schema_version":"1.0","canonical_sha256":"0e9554702ae31f4ac53c68319361f66d5a0c1332cb83f9b9df9e553b0fd0aea2","source":{"kind":"arxiv","id":"2210.06796","version":1},"attestation_state":"computed","paper":{"title":"Circuit depth versus energy in topologically ordered systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el"],"primary_cat":"quant-ph","authors_text":"Arkin Tikku, Isaac H. Kim","submitted_at":"2022-10-13T07:21:30Z","abstract_excerpt":"We prove a nontrivial circuit-depth lower bound for preparing a low-energy state of a locally interacting quantum many-body system in two dimensions, assuming the circuit is geometrically local. For preparing any state which has an energy density of at most $\\epsilon$ with respect to Kitaev's toric code Hamiltonian on a two dimensional lattice $\\Lambda$, we prove a lower bound of $\\Omega\\left(\\min\\left(1/\\epsilon^{\\frac{1-\\alpha}{2}}, \\sqrt{|\\Lambda|}\\right)\\right)$ for any $\\alpha >0$. We discuss two implications. First, our bound implies that the lowest energy density obtainable from a large"},"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":"2210.06796","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2022-10-13T07:21:30Z","cross_cats_sorted":["cond-mat.str-el"],"title_canon_sha256":"2085d041f5b57a797dc67dd14884fe2056aefd6d4d0d4e03409723fc4573b581","abstract_canon_sha256":"792c1c6b42bdf1d5de3e8c65d6bce8b038a6362c164aa16129f1fe27f7f70be9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:06:20.600697Z","signature_b64":"gUrVNhenWReA7lfKzNWDmP+6C+o9dKmRUrbD2WnJgpPGsmAyYBoymeZ+LSaF3YHJHyodn+rQ8VAQvFcgvv0IBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e9554702ae31f4ac53c68319361f66d5a0c1332cb83f9b9df9e553b0fd0aea2","last_reissued_at":"2026-07-05T05:06:20.600169Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:06:20.600169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Circuit depth versus energy in topologically ordered systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el"],"primary_cat":"quant-ph","authors_text":"Arkin Tikku, Isaac H. Kim","submitted_at":"2022-10-13T07:21:30Z","abstract_excerpt":"We prove a nontrivial circuit-depth lower bound for preparing a low-energy state of a locally interacting quantum many-body system in two dimensions, assuming the circuit is geometrically local. For preparing any state which has an energy density of at most $\\epsilon$ with respect to Kitaev's toric code Hamiltonian on a two dimensional lattice $\\Lambda$, we prove a lower bound of $\\Omega\\left(\\min\\left(1/\\epsilon^{\\frac{1-\\alpha}{2}}, \\sqrt{|\\Lambda|}\\right)\\right)$ for any $\\alpha >0$. We discuss two implications. First, our bound implies that the lowest energy density obtainable from a large"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.06796","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.06796/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2210.06796","created_at":"2026-07-05T05:06:20.600220+00:00"},{"alias_kind":"arxiv_version","alias_value":"2210.06796v1","created_at":"2026-07-05T05:06:20.600220+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.06796","created_at":"2026-07-05T05:06:20.600220+00:00"},{"alias_kind":"pith_short_12","alias_value":"B2KVI4BK4MPU","created_at":"2026-07-05T05:06:20.600220+00:00"},{"alias_kind":"pith_short_16","alias_value":"B2KVI4BK4MPUVRJ4","created_at":"2026-07-05T05:06:20.600220+00:00"},{"alias_kind":"pith_short_8","alias_value":"B2KVI4BK","created_at":"2026-07-05T05:06:20.600220+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.26090","citing_title":"Fast mixing of all-to-all quantum systems at high temperatures","ref_index":161,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B2KVI4BK4MPUVRJ4NAYZGYPWNV","json":"https://pith.science/pith/B2KVI4BK4MPUVRJ4NAYZGYPWNV.json","graph_json":"https://pith.science/api/pith-number/B2KVI4BK4MPUVRJ4NAYZGYPWNV/graph.json","events_json":"https://pith.science/api/pith-number/B2KVI4BK4MPUVRJ4NAYZGYPWNV/events.json","paper":"https://pith.science/paper/B2KVI4BK"},"agent_actions":{"view_html":"https://pith.science/pith/B2KVI4BK4MPUVRJ4NAYZGYPWNV","download_json":"https://pith.science/pith/B2KVI4BK4MPUVRJ4NAYZGYPWNV.json","view_paper":"https://pith.science/paper/B2KVI4BK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2210.06796&json=true","fetch_graph":"https://pith.science/api/pith-number/B2KVI4BK4MPUVRJ4NAYZGYPWNV/graph.json","fetch_events":"https://pith.science/api/pith-number/B2KVI4BK4MPUVRJ4NAYZGYPWNV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B2KVI4BK4MPUVRJ4NAYZGYPWNV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B2KVI4BK4MPUVRJ4NAYZGYPWNV/action/storage_attestation","attest_author":"https://pith.science/pith/B2KVI4BK4MPUVRJ4NAYZGYPWNV/action/author_attestation","sign_citation":"https://pith.science/pith/B2KVI4BK4MPUVRJ4NAYZGYPWNV/action/citation_signature","submit_replication":"https://pith.science/pith/B2KVI4BK4MPUVRJ4NAYZGYPWNV/action/replication_record"}},"created_at":"2026-07-05T05:06:20.600220+00:00","updated_at":"2026-07-05T05:06:20.600220+00:00"}