{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:7RTJV6DC33PVTYZNBWHQ5U7NOL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3b5f0f82d9398b0d682ec14b6192dd4cc8c348a0fef5a0c742493fbc8bbf7332","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2022-06-23T07:12:10Z","title_canon_sha256":"280fdd381acc8f9cb1ed15ac45d6e6a1b3df907752ca67b7c8584cf5b06b33a4"},"schema_version":"1.0","source":{"id":"2206.11506","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.11506","created_at":"2026-07-05T05:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"2206.11506v1","created_at":"2026-07-05T05:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.11506","created_at":"2026-07-05T05:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"7RTJV6DC33PV","created_at":"2026-07-05T05:18:33Z"},{"alias_kind":"pith_short_16","alias_value":"7RTJV6DC33PVTYZN","created_at":"2026-07-05T05:18:33Z"},{"alias_kind":"pith_short_8","alias_value":"7RTJV6DC","created_at":"2026-07-05T05:18:33Z"}],"graph_snapshots":[{"event_id":"sha256:0a030d8c31aa9e25b8080457d5556c514d46b039b2d603a2b34cf1b7a5e0874a","target":"graph","created_at":"2026-07-05T05:18:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2206.11506/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Efficient measures to determine similarity of quantum states, such as the fidelity metric, have been widely studied. In this paper, we address the problem of defining a similarity measure for quantum operations that can be \\textit{efficiently estimated}. Given two quantum operations, $U_1$ and $U_2$, represented in their circuit forms, we first develop a quantum sampling circuit to estimate the normalized Schatten 2-norm of their difference ($\\| U_1-U_2 \\|_{S_2}$) with precision $\\epsilon$, using only one clean qubit and one classical random variable. We prove a Poly$(\\frac{1}{\\epsilon})$ uppe","authors_text":"Hideyuki Miyahara, Louis-S. Bouchard, Vwani Roychowdhury, Yiyou Chen","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2022-06-23T07:12:10Z","title":"Quantum Approximation of Normalized Schatten Norms and Applications to Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.11506","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5cb061b7859a95e92234f0f160748a1ceed4d379aa95c2f454c6d95e3f10cbbf","target":"record","created_at":"2026-07-05T05:18:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3b5f0f82d9398b0d682ec14b6192dd4cc8c348a0fef5a0c742493fbc8bbf7332","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2022-06-23T07:12:10Z","title_canon_sha256":"280fdd381acc8f9cb1ed15ac45d6e6a1b3df907752ca67b7c8584cf5b06b33a4"},"schema_version":"1.0","source":{"id":"2206.11506","kind":"arxiv","version":1}},"canonical_sha256":"fc669af862dedf59e32d0d8f0ed3ed72f57c6a9415530a4550d1a2cd0e2fb9ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc669af862dedf59e32d0d8f0ed3ed72f57c6a9415530a4550d1a2cd0e2fb9ab","first_computed_at":"2026-07-05T05:18:33.375644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:18:33.375644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8hNYnkhEAifyHnzrp9+3dx1Yy96po9HAe6ca4Yp2VL09gPHrphSaL+s7kejMQ6o+7xz7PWfDov2zusrd4GlwCw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:18:33.376139Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.11506","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cb061b7859a95e92234f0f160748a1ceed4d379aa95c2f454c6d95e3f10cbbf","sha256:0a030d8c31aa9e25b8080457d5556c514d46b039b2d603a2b34cf1b7a5e0874a"],"state_sha256":"de632cdecee1c059bafe8128c58f17fbece2e07ea87954854eb10709e4b34988"}