{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:HVY2ERCX6OAOKVNIQS4SPUYJ4L","short_pith_number":"pith:HVY2ERCX","schema_version":"1.0","canonical_sha256":"3d71a24457f380e555a884b927d309e2f89e7c8c737031d00cd7d89f8b8033f2","source":{"kind":"arxiv","id":"2409.13809","version":2},"attestation_state":"computed","paper":{"title":"Classical Simulability of Quantum Circuits with Shallow Magic Depth","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Yifan Zhang, Yuxuan Zhang","submitted_at":"2024-09-20T18:00:00Z","abstract_excerpt":"Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to classical simulability. However, the effect of the distribution of quantum magic on the hardness of simulating a quantum circuit remains open. In this work, we investigate the classical simulability of quantum circuits with alternating Clifford and $T$ layers across three tasks: amplitude estimation, sampling, and evaluating Pauli observables. In the case wher"},"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":"2409.13809","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-09-20T18:00:00Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"4762d7eda0a339deed51bf5bde8999d685d3838d7c5dba9c1712068b6b479888","abstract_canon_sha256":"31a715725c0f52b40829234ab8b606f7c785dcbe9219e5f4bc1e87eb529ddb17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:10:28.200412Z","signature_b64":"IX4/xqi8Hji7ABc/rOIG3mzRf9qvJ+5Ql0hqvmRYNVoZSuip/tvzeMJ8THYLpNe0h5O2ze/ZDHdJHpzqS53uAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d71a24457f380e555a884b927d309e2f89e7c8c737031d00cd7d89f8b8033f2","last_reissued_at":"2026-07-05T10:10:28.200003Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:10:28.200003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classical Simulability of Quantum Circuits with Shallow Magic Depth","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Yifan Zhang, Yuxuan Zhang","submitted_at":"2024-09-20T18:00:00Z","abstract_excerpt":"Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to classical simulability. However, the effect of the distribution of quantum magic on the hardness of simulating a quantum circuit remains open. In this work, we investigate the classical simulability of quantum circuits with alternating Clifford and $T$ layers across three tasks: amplitude estimation, sampling, and evaluating Pauli observables. In the case wher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.13809","kind":"arxiv","version":2},"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/2409.13809/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":"2409.13809","created_at":"2026-07-05T10:10:28.200053+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.13809v2","created_at":"2026-07-05T10:10:28.200053+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.13809","created_at":"2026-07-05T10:10:28.200053+00:00"},{"alias_kind":"pith_short_12","alias_value":"HVY2ERCX6OAO","created_at":"2026-07-05T10:10:28.200053+00:00"},{"alias_kind":"pith_short_16","alias_value":"HVY2ERCX6OAOKVNI","created_at":"2026-07-05T10:10:28.200053+00:00"},{"alias_kind":"pith_short_8","alias_value":"HVY2ERCX","created_at":"2026-07-05T10:10:28.200053+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2412.17209","citing_title":"Classical simulability of Clifford+T circuits with Clifford-augmented matrix product states","ref_index":47,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HVY2ERCX6OAOKVNIQS4SPUYJ4L","json":"https://pith.science/pith/HVY2ERCX6OAOKVNIQS4SPUYJ4L.json","graph_json":"https://pith.science/api/pith-number/HVY2ERCX6OAOKVNIQS4SPUYJ4L/graph.json","events_json":"https://pith.science/api/pith-number/HVY2ERCX6OAOKVNIQS4SPUYJ4L/events.json","paper":"https://pith.science/paper/HVY2ERCX"},"agent_actions":{"view_html":"https://pith.science/pith/HVY2ERCX6OAOKVNIQS4SPUYJ4L","download_json":"https://pith.science/pith/HVY2ERCX6OAOKVNIQS4SPUYJ4L.json","view_paper":"https://pith.science/paper/HVY2ERCX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.13809&json=true","fetch_graph":"https://pith.science/api/pith-number/HVY2ERCX6OAOKVNIQS4SPUYJ4L/graph.json","fetch_events":"https://pith.science/api/pith-number/HVY2ERCX6OAOKVNIQS4SPUYJ4L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HVY2ERCX6OAOKVNIQS4SPUYJ4L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HVY2ERCX6OAOKVNIQS4SPUYJ4L/action/storage_attestation","attest_author":"https://pith.science/pith/HVY2ERCX6OAOKVNIQS4SPUYJ4L/action/author_attestation","sign_citation":"https://pith.science/pith/HVY2ERCX6OAOKVNIQS4SPUYJ4L/action/citation_signature","submit_replication":"https://pith.science/pith/HVY2ERCX6OAOKVNIQS4SPUYJ4L/action/replication_record"}},"created_at":"2026-07-05T10:10:28.200053+00:00","updated_at":"2026-07-05T10:10:28.200053+00:00"}