{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:763FGQEJSEJCYCZOT7SHOGYWZ3","short_pith_number":"pith:763FGQEJ","schema_version":"1.0","canonical_sha256":"ffb653408991122c0b2e9fe4771b16cee8ef250ec31ca2293b4fb0bacd9cd5ae","source":{"kind":"arxiv","id":"2305.15398","version":6},"attestation_state":"computed","paper":{"title":"Learning t-doped stabilizer states","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alioscia Hamma, Lorenzo Leone, Salvatore F. E. Oliviero","submitted_at":"2023-05-24T17:57:10Z","abstract_excerpt":"In this paper, we present a learning algorithm aimed at learning states obtained from computational basis states by Clifford circuits doped with a finite number $t$ of $T$-gates. The algorithm learns an exact tomographic description of $t$-doped stabilizer states in terms of Pauli observables. This is possible because such states are countable and form a discrete set. To tackle the problem, we introduce a novel algebraic framework for $t$-doped stabilizer states, which extends beyond $T$-gates and includes doping with any kind of local non-Clifford gate. The algorithm requires resources of com"},"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":"2305.15398","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-05-24T17:57:10Z","cross_cats_sorted":[],"title_canon_sha256":"14a7b818bb5df009bf70111cc2bad93cb5919f12b77eaf4c666a1bcdc662e835","abstract_canon_sha256":"478afac1a69e3b208a67d4a944bb38e81816a168fe7f3c508a1be0546fa3391c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:23:53.641727Z","signature_b64":"6M53R3KwcdczrzIKxbt0HXOStHhyXrhM0lnNl7XfXFP6p0muEdMCCSHzdgcAOTUqKp3RVLl0hRaZqXRp+A+vAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffb653408991122c0b2e9fe4771b16cee8ef250ec31ca2293b4fb0bacd9cd5ae","last_reissued_at":"2026-07-05T08:23:53.641133Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:23:53.641133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Learning t-doped stabilizer states","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alioscia Hamma, Lorenzo Leone, Salvatore F. E. Oliviero","submitted_at":"2023-05-24T17:57:10Z","abstract_excerpt":"In this paper, we present a learning algorithm aimed at learning states obtained from computational basis states by Clifford circuits doped with a finite number $t$ of $T$-gates. The algorithm learns an exact tomographic description of $t$-doped stabilizer states in terms of Pauli observables. This is possible because such states are countable and form a discrete set. To tackle the problem, we introduce a novel algebraic framework for $t$-doped stabilizer states, which extends beyond $T$-gates and includes doping with any kind of local non-Clifford gate. The algorithm requires resources of com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.15398","kind":"arxiv","version":6},"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/2305.15398/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":"2305.15398","created_at":"2026-07-05T08:23:53.641207+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.15398v6","created_at":"2026-07-05T08:23:53.641207+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.15398","created_at":"2026-07-05T08:23:53.641207+00:00"},{"alias_kind":"pith_short_12","alias_value":"763FGQEJSEJC","created_at":"2026-07-05T08:23:53.641207+00:00"},{"alias_kind":"pith_short_16","alias_value":"763FGQEJSEJCYCZO","created_at":"2026-07-05T08:23:53.641207+00:00"},{"alias_kind":"pith_short_8","alias_value":"763FGQEJ","created_at":"2026-07-05T08:23:53.641207+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.14967","citing_title":"Spin versus Magic: Lessons from Gluon and Graviton Scattering","ref_index":82,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/763FGQEJSEJCYCZOT7SHOGYWZ3","json":"https://pith.science/pith/763FGQEJSEJCYCZOT7SHOGYWZ3.json","graph_json":"https://pith.science/api/pith-number/763FGQEJSEJCYCZOT7SHOGYWZ3/graph.json","events_json":"https://pith.science/api/pith-number/763FGQEJSEJCYCZOT7SHOGYWZ3/events.json","paper":"https://pith.science/paper/763FGQEJ"},"agent_actions":{"view_html":"https://pith.science/pith/763FGQEJSEJCYCZOT7SHOGYWZ3","download_json":"https://pith.science/pith/763FGQEJSEJCYCZOT7SHOGYWZ3.json","view_paper":"https://pith.science/paper/763FGQEJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.15398&json=true","fetch_graph":"https://pith.science/api/pith-number/763FGQEJSEJCYCZOT7SHOGYWZ3/graph.json","fetch_events":"https://pith.science/api/pith-number/763FGQEJSEJCYCZOT7SHOGYWZ3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/763FGQEJSEJCYCZOT7SHOGYWZ3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/763FGQEJSEJCYCZOT7SHOGYWZ3/action/storage_attestation","attest_author":"https://pith.science/pith/763FGQEJSEJCYCZOT7SHOGYWZ3/action/author_attestation","sign_citation":"https://pith.science/pith/763FGQEJSEJCYCZOT7SHOGYWZ3/action/citation_signature","submit_replication":"https://pith.science/pith/763FGQEJSEJCYCZOT7SHOGYWZ3/action/replication_record"}},"created_at":"2026-07-05T08:23:53.641207+00:00","updated_at":"2026-07-05T08:23:53.641207+00:00"}