{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:ABS242S2HRZSLEB7A3IFZEPN72","short_pith_number":"pith:ABS242S2","schema_version":"1.0","canonical_sha256":"0065ae6a5a3c7325903f06d05c91edfe9c304d5c6a02bd553ec31c3b2ecf749e","source":{"kind":"arxiv","id":"2105.02885","version":2},"attestation_state":"computed","paper":{"title":"Pauli error estimation via Population Recovery","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Ryan O'Donnell, Steven T. Flammia","submitted_at":"2021-05-06T18:00:02Z","abstract_excerpt":"Motivated by estimation of quantum noise models, we study the problem of learning a Pauli channel, or more generally the Pauli error rates of an arbitrary channel. By employing a novel reduction to the \"Population Recovery\" problem, we give an extremely simple algorithm that learns the Pauli error rates of an $n$-qubit channel to precision $\\epsilon$ in $\\ell_\\infty$ using just $O(1/\\epsilon^2) \\log(n/\\epsilon)$ applications of the channel. This is optimal up to the logarithmic factors. Our algorithm uses only unentangled state preparation and measurements, and the post-measurement classical r"},"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":"2105.02885","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"quant-ph","submitted_at":"2021-05-06T18:00:02Z","cross_cats_sorted":[],"title_canon_sha256":"f98792f089a06a308b7dbcf002c4c4c18aa3a9ec4eee5a20e3bc74d2e549c7f9","abstract_canon_sha256":"03e781344b3aba18f87da2f47f0d209545030851e51ef3e57467d78d41c9db79"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:18:16.968254Z","signature_b64":"DKnBrkdVjJylmgHb9QrUs08wU7TXSxkCQ7NMYMSkSzOIHnLngzvi0yN6zlmWuafGRMqn9m106cU4ODrtG4eZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0065ae6a5a3c7325903f06d05c91edfe9c304d5c6a02bd553ec31c3b2ecf749e","last_reissued_at":"2026-07-05T03:18:16.967843Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:18:16.967843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pauli error estimation via Population Recovery","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Ryan O'Donnell, Steven T. Flammia","submitted_at":"2021-05-06T18:00:02Z","abstract_excerpt":"Motivated by estimation of quantum noise models, we study the problem of learning a Pauli channel, or more generally the Pauli error rates of an arbitrary channel. By employing a novel reduction to the \"Population Recovery\" problem, we give an extremely simple algorithm that learns the Pauli error rates of an $n$-qubit channel to precision $\\epsilon$ in $\\ell_\\infty$ using just $O(1/\\epsilon^2) \\log(n/\\epsilon)$ applications of the channel. This is optimal up to the logarithmic factors. Our algorithm uses only unentangled state preparation and measurements, and the post-measurement classical r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.02885","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/2105.02885/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":"2105.02885","created_at":"2026-07-05T03:18:16.967898+00:00"},{"alias_kind":"arxiv_version","alias_value":"2105.02885v2","created_at":"2026-07-05T03:18:16.967898+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.02885","created_at":"2026-07-05T03:18:16.967898+00:00"},{"alias_kind":"pith_short_12","alias_value":"ABS242S2HRZS","created_at":"2026-07-05T03:18:16.967898+00:00"},{"alias_kind":"pith_short_16","alias_value":"ABS242S2HRZSLEB7","created_at":"2026-07-05T03:18:16.967898+00:00"},{"alias_kind":"pith_short_8","alias_value":"ABS242S2","created_at":"2026-07-05T03:18:16.967898+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.07702","citing_title":"Weakly-Driven Quantum Walks for Memory-Constrained Pauli Channel Learning","ref_index":41,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ABS242S2HRZSLEB7A3IFZEPN72","json":"https://pith.science/pith/ABS242S2HRZSLEB7A3IFZEPN72.json","graph_json":"https://pith.science/api/pith-number/ABS242S2HRZSLEB7A3IFZEPN72/graph.json","events_json":"https://pith.science/api/pith-number/ABS242S2HRZSLEB7A3IFZEPN72/events.json","paper":"https://pith.science/paper/ABS242S2"},"agent_actions":{"view_html":"https://pith.science/pith/ABS242S2HRZSLEB7A3IFZEPN72","download_json":"https://pith.science/pith/ABS242S2HRZSLEB7A3IFZEPN72.json","view_paper":"https://pith.science/paper/ABS242S2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2105.02885&json=true","fetch_graph":"https://pith.science/api/pith-number/ABS242S2HRZSLEB7A3IFZEPN72/graph.json","fetch_events":"https://pith.science/api/pith-number/ABS242S2HRZSLEB7A3IFZEPN72/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ABS242S2HRZSLEB7A3IFZEPN72/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ABS242S2HRZSLEB7A3IFZEPN72/action/storage_attestation","attest_author":"https://pith.science/pith/ABS242S2HRZSLEB7A3IFZEPN72/action/author_attestation","sign_citation":"https://pith.science/pith/ABS242S2HRZSLEB7A3IFZEPN72/action/citation_signature","submit_replication":"https://pith.science/pith/ABS242S2HRZSLEB7A3IFZEPN72/action/replication_record"}},"created_at":"2026-07-05T03:18:16.967898+00:00","updated_at":"2026-07-05T03:18:16.967898+00:00"}