{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:I7MRHXKSUFJ7RIKKXRIQ57BW5K","short_pith_number":"pith:I7MRHXKS","schema_version":"1.0","canonical_sha256":"47d913dd52a153f8a14abc510efc36ea87adffe0ba1dcf203ae3455315a30df6","source":{"kind":"arxiv","id":"1810.10938","version":3},"attestation_state":"computed","paper":{"title":"Sample Efficient Algorithms for Learning Quantum Channels in PAC Model and the Approximate State Discrimination Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.LG"],"primary_cat":"quant-ph","authors_text":"Han-Hsuan Lin, Kai-Min Chung","submitted_at":"2018-10-25T15:50:57Z","abstract_excerpt":"We generalize the PAC (probably approximately correct) learning model to the quantum world by generalizing the concepts from classical functions to quantum processes, defining the problem of \\emph{PAC learning quantum process}, and study its sample complexity. In the problem of PAC learning quantum process, we want to learn an $\\epsilon$-approximate of an unknown quantum process $c^*$ from a known finite concept class $C$ with probability $1-\\delta$ using samples $\\{(x_1,c^*(x_1)),(x_2,c^*(x_2)),\\dots\\}$, where $\\{x_1,x_2, \\dots\\}$ are computational basis states sampled from an unknown distrib"},"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":"1810.10938","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-25T15:50:57Z","cross_cats_sorted":["cs.CC","cs.LG"],"title_canon_sha256":"b9478f90b6c95d2dd2b0b1ffaca4f51d3ee6f34a7fbf63d2618eb306cc581f23","abstract_canon_sha256":"8b618f508760518c07403a2060308deea2631a8a7087aa22aeb8b9f754d2d7dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:41:26.210589Z","signature_b64":"1T3AB+awvWzSpetXylXlSMoAPBIyeyIQOxbT7frBOHRpr5b1qbQyuUrxSSjheb1XBcCQY7UlcSUBs/Fjw/SlDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47d913dd52a153f8a14abc510efc36ea87adffe0ba1dcf203ae3455315a30df6","last_reissued_at":"2026-07-05T02:41:26.210107Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:41:26.210107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sample Efficient Algorithms for Learning Quantum Channels in PAC Model and the Approximate State Discrimination Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.LG"],"primary_cat":"quant-ph","authors_text":"Han-Hsuan Lin, Kai-Min Chung","submitted_at":"2018-10-25T15:50:57Z","abstract_excerpt":"We generalize the PAC (probably approximately correct) learning model to the quantum world by generalizing the concepts from classical functions to quantum processes, defining the problem of \\emph{PAC learning quantum process}, and study its sample complexity. In the problem of PAC learning quantum process, we want to learn an $\\epsilon$-approximate of an unknown quantum process $c^*$ from a known finite concept class $C$ with probability $1-\\delta$ using samples $\\{(x_1,c^*(x_1)),(x_2,c^*(x_2)),\\dots\\}$, where $\\{x_1,x_2, \\dots\\}$ are computational basis states sampled from an unknown distrib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10938","kind":"arxiv","version":3},"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/1810.10938/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":"1810.10938","created_at":"2026-07-05T02:41:26.210171+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.10938v3","created_at":"2026-07-05T02:41:26.210171+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10938","created_at":"2026-07-05T02:41:26.210171+00:00"},{"alias_kind":"pith_short_12","alias_value":"I7MRHXKSUFJ7","created_at":"2026-07-05T02:41:26.210171+00:00"},{"alias_kind":"pith_short_16","alias_value":"I7MRHXKSUFJ7RIKK","created_at":"2026-07-05T02:41:26.210171+00:00"},{"alias_kind":"pith_short_8","alias_value":"I7MRHXKS","created_at":"2026-07-05T02:41:26.210171+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I7MRHXKSUFJ7RIKKXRIQ57BW5K","json":"https://pith.science/pith/I7MRHXKSUFJ7RIKKXRIQ57BW5K.json","graph_json":"https://pith.science/api/pith-number/I7MRHXKSUFJ7RIKKXRIQ57BW5K/graph.json","events_json":"https://pith.science/api/pith-number/I7MRHXKSUFJ7RIKKXRIQ57BW5K/events.json","paper":"https://pith.science/paper/I7MRHXKS"},"agent_actions":{"view_html":"https://pith.science/pith/I7MRHXKSUFJ7RIKKXRIQ57BW5K","download_json":"https://pith.science/pith/I7MRHXKSUFJ7RIKKXRIQ57BW5K.json","view_paper":"https://pith.science/paper/I7MRHXKS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.10938&json=true","fetch_graph":"https://pith.science/api/pith-number/I7MRHXKSUFJ7RIKKXRIQ57BW5K/graph.json","fetch_events":"https://pith.science/api/pith-number/I7MRHXKSUFJ7RIKKXRIQ57BW5K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I7MRHXKSUFJ7RIKKXRIQ57BW5K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I7MRHXKSUFJ7RIKKXRIQ57BW5K/action/storage_attestation","attest_author":"https://pith.science/pith/I7MRHXKSUFJ7RIKKXRIQ57BW5K/action/author_attestation","sign_citation":"https://pith.science/pith/I7MRHXKSUFJ7RIKKXRIQ57BW5K/action/citation_signature","submit_replication":"https://pith.science/pith/I7MRHXKSUFJ7RIKKXRIQ57BW5K/action/replication_record"}},"created_at":"2026-07-05T02:41:26.210171+00:00","updated_at":"2026-07-05T02:41:26.210171+00:00"}