{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:3ISFZCQQ2NAKVO3LEEJFEUH6TN","short_pith_number":"pith:3ISFZCQQ","schema_version":"1.0","canonical_sha256":"da245c8a10d340aabb6b21125250fe9b78bdd9554a914fedf8f1f82e4370657a","source":{"kind":"arxiv","id":"2107.12390","version":3},"attestation_state":"computed","paper":{"title":"General parameter-shift rules for quantum gradients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Cedric Yen-Yu Lin, Cody Wang, David Wierichs, Josh Izaac","submitted_at":"2021-07-26T18:00:02Z","abstract_excerpt":"Variational quantum algorithms are ubiquitous in applications of noisy intermediate-scale quantum computers. Due to the structure of conventional parametrized quantum gates, the evaluated functions typically are finite Fourier series of the input parameters. In this work, we use this fact to derive new, general parameter-shift rules for single-parameter gates, and provide closed-form expressions to apply them. These rules are then extended to multi-parameter quantum gates by combining them with the stochastic parameter-shift rule. We perform a systematic analysis of quantum resource requiremen"},"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":"2107.12390","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2021-07-26T18:00:02Z","cross_cats_sorted":[],"title_canon_sha256":"e1350f6fb17ac7b774d395f18139fe5d8b5214d3141ee37169cf47ce78752344","abstract_canon_sha256":"894a68ac4ec505502e7e00c62e64fb6099f90e85988e6a81252ef296378fe70e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:15:44.313712Z","signature_b64":"zNMSq4pDvHzFiExRRU85yCEOp/aeBPDubFArlKRKzxE4wIuH0Bdh498gv8/8qEwgOlBcYzxkvxTwS2TKcE4HDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da245c8a10d340aabb6b21125250fe9b78bdd9554a914fedf8f1f82e4370657a","last_reissued_at":"2026-07-05T04:15:44.313238Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:15:44.313238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"General parameter-shift rules for quantum gradients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Cedric Yen-Yu Lin, Cody Wang, David Wierichs, Josh Izaac","submitted_at":"2021-07-26T18:00:02Z","abstract_excerpt":"Variational quantum algorithms are ubiquitous in applications of noisy intermediate-scale quantum computers. Due to the structure of conventional parametrized quantum gates, the evaluated functions typically are finite Fourier series of the input parameters. In this work, we use this fact to derive new, general parameter-shift rules for single-parameter gates, and provide closed-form expressions to apply them. These rules are then extended to multi-parameter quantum gates by combining them with the stochastic parameter-shift rule. We perform a systematic analysis of quantum resource requiremen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.12390","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/2107.12390/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":"2107.12390","created_at":"2026-07-05T04:15:44.313293+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.12390v3","created_at":"2026-07-05T04:15:44.313293+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.12390","created_at":"2026-07-05T04:15:44.313293+00:00"},{"alias_kind":"pith_short_12","alias_value":"3ISFZCQQ2NAK","created_at":"2026-07-05T04:15:44.313293+00:00"},{"alias_kind":"pith_short_16","alias_value":"3ISFZCQQ2NAKVO3L","created_at":"2026-07-05T04:15:44.313293+00:00"},{"alias_kind":"pith_short_8","alias_value":"3ISFZCQQ","created_at":"2026-07-05T04:15:44.313293+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.05297","citing_title":"Continuous-variable ADAPT-VQE for bosonic lattice models","ref_index":108,"is_internal_anchor":false},{"citing_arxiv_id":"2403.02988","citing_title":"An Operational Framework for Nonclassicality in Quantum Communication Networks","ref_index":57,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3ISFZCQQ2NAKVO3LEEJFEUH6TN","json":"https://pith.science/pith/3ISFZCQQ2NAKVO3LEEJFEUH6TN.json","graph_json":"https://pith.science/api/pith-number/3ISFZCQQ2NAKVO3LEEJFEUH6TN/graph.json","events_json":"https://pith.science/api/pith-number/3ISFZCQQ2NAKVO3LEEJFEUH6TN/events.json","paper":"https://pith.science/paper/3ISFZCQQ"},"agent_actions":{"view_html":"https://pith.science/pith/3ISFZCQQ2NAKVO3LEEJFEUH6TN","download_json":"https://pith.science/pith/3ISFZCQQ2NAKVO3LEEJFEUH6TN.json","view_paper":"https://pith.science/paper/3ISFZCQQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.12390&json=true","fetch_graph":"https://pith.science/api/pith-number/3ISFZCQQ2NAKVO3LEEJFEUH6TN/graph.json","fetch_events":"https://pith.science/api/pith-number/3ISFZCQQ2NAKVO3LEEJFEUH6TN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3ISFZCQQ2NAKVO3LEEJFEUH6TN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3ISFZCQQ2NAKVO3LEEJFEUH6TN/action/storage_attestation","attest_author":"https://pith.science/pith/3ISFZCQQ2NAKVO3LEEJFEUH6TN/action/author_attestation","sign_citation":"https://pith.science/pith/3ISFZCQQ2NAKVO3LEEJFEUH6TN/action/citation_signature","submit_replication":"https://pith.science/pith/3ISFZCQQ2NAKVO3LEEJFEUH6TN/action/replication_record"}},"created_at":"2026-07-05T04:15:44.313293+00:00","updated_at":"2026-07-05T04:15:44.313293+00:00"}