{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:NTNFM44BTQRBRO3CWWADWLCEN6","short_pith_number":"pith:NTNFM44B","schema_version":"1.0","canonical_sha256":"6cda5673819c2218bb62b5803b2c446fa5dcef39a6dfa4dfab44fc237ceae6c3","source":{"kind":"arxiv","id":"2312.04858","version":1},"attestation_state":"computed","paper":{"title":"A short tutorial on Wirtinger Calculus with applications in quantum information","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Kelvin Koor, Leong Chuan Kwek, Patrick Rebentrost, Yixian Qiu","submitted_at":"2023-12-08T06:26:04Z","abstract_excerpt":"The optimization of system parameters is a ubiquitous problem in science and engineering. The traditional approach involves setting to zero the partial derivatives of the objective function with respect to each parameter, in order to extract the optimal solution. However, the system parameters often take the form of complex matrices. In such situations, conventional methods become unwieldy. The `Wirtinger Calculus' provides a relatively simple methodology for such optimization problems. In this tutorial, we provide a pedagogical introduction to Wirtinger Calculus. To illustrate the utility of "},"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":"2312.04858","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-12-08T06:26:04Z","cross_cats_sorted":[],"title_canon_sha256":"c3d59e1cb223b4fbf6b9705e64846ac4ca77f072554df2e9c9a09aeb7cf1176b","abstract_canon_sha256":"ffeebd554ce59ded56e663da0c52089551f12e8ad4b7c940322eab88eef58dac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:21:53.486783Z","signature_b64":"C9FNvohHuTFeOWP1Be5DDiTRdoX2Ws6559NuMobeTF78gQ5XPGWBMHEA6FCO2OZ57rVAKxUP22Fo0lBkEwyhCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cda5673819c2218bb62b5803b2c446fa5dcef39a6dfa4dfab44fc237ceae6c3","last_reissued_at":"2026-07-05T07:21:53.486339Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:21:53.486339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A short tutorial on Wirtinger Calculus with applications in quantum information","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Kelvin Koor, Leong Chuan Kwek, Patrick Rebentrost, Yixian Qiu","submitted_at":"2023-12-08T06:26:04Z","abstract_excerpt":"The optimization of system parameters is a ubiquitous problem in science and engineering. The traditional approach involves setting to zero the partial derivatives of the objective function with respect to each parameter, in order to extract the optimal solution. However, the system parameters often take the form of complex matrices. In such situations, conventional methods become unwieldy. The `Wirtinger Calculus' provides a relatively simple methodology for such optimization problems. In this tutorial, we provide a pedagogical introduction to Wirtinger Calculus. To illustrate the utility of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.04858","kind":"arxiv","version":1},"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/2312.04858/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":"2312.04858","created_at":"2026-07-05T07:21:53.486390+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.04858v1","created_at":"2026-07-05T07:21:53.486390+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.04858","created_at":"2026-07-05T07:21:53.486390+00:00"},{"alias_kind":"pith_short_12","alias_value":"NTNFM44BTQRB","created_at":"2026-07-05T07:21:53.486390+00:00"},{"alias_kind":"pith_short_16","alias_value":"NTNFM44BTQRBRO3C","created_at":"2026-07-05T07:21:53.486390+00:00"},{"alias_kind":"pith_short_8","alias_value":"NTNFM44B","created_at":"2026-07-05T07:21:53.486390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":5,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.23017","citing_title":"Complex Stochastic Gradient Descent and Directional Bias in Reproducing Kernel Hilbert Spaces","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2512.24405","citing_title":"Sufficient and Necessary Conditions for Eckart-Young like Result for Tubal Tensors","ref_index":23,"is_internal_anchor":false},{"citing_arxiv_id":"2605.12557","citing_title":"Localization in OFDM Passive Distributed Antenna Systems with Pilots and Unknown Data Payloads: A Marginal Maximum Likelihood Approach","ref_index":33,"is_internal_anchor":false},{"citing_arxiv_id":"2604.23017","citing_title":"Complex Stochastic Gradient Descent and Directional Bias in Reproducing Kernel Hilbert Spaces","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2604.20384","citing_title":"Hessian-vector products for tensor networks via recursive tangent-state propagation","ref_index":34,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NTNFM44BTQRBRO3CWWADWLCEN6","json":"https://pith.science/pith/NTNFM44BTQRBRO3CWWADWLCEN6.json","graph_json":"https://pith.science/api/pith-number/NTNFM44BTQRBRO3CWWADWLCEN6/graph.json","events_json":"https://pith.science/api/pith-number/NTNFM44BTQRBRO3CWWADWLCEN6/events.json","paper":"https://pith.science/paper/NTNFM44B"},"agent_actions":{"view_html":"https://pith.science/pith/NTNFM44BTQRBRO3CWWADWLCEN6","download_json":"https://pith.science/pith/NTNFM44BTQRBRO3CWWADWLCEN6.json","view_paper":"https://pith.science/paper/NTNFM44B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.04858&json=true","fetch_graph":"https://pith.science/api/pith-number/NTNFM44BTQRBRO3CWWADWLCEN6/graph.json","fetch_events":"https://pith.science/api/pith-number/NTNFM44BTQRBRO3CWWADWLCEN6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NTNFM44BTQRBRO3CWWADWLCEN6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NTNFM44BTQRBRO3CWWADWLCEN6/action/storage_attestation","attest_author":"https://pith.science/pith/NTNFM44BTQRBRO3CWWADWLCEN6/action/author_attestation","sign_citation":"https://pith.science/pith/NTNFM44BTQRBRO3CWWADWLCEN6/action/citation_signature","submit_replication":"https://pith.science/pith/NTNFM44BTQRBRO3CWWADWLCEN6/action/replication_record"}},"created_at":"2026-07-05T07:21:53.486390+00:00","updated_at":"2026-07-05T07:21:53.486390+00:00"}