[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85875-en":3,"doc-seo-85875-105":29,"detail-sidebar-cat-0-en-105":83},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85875,687197207639,"Asher","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Program Synthesis Driven Autodesign of Universal Unitary Operators","AI-driven program synthesis autonomously discovers fundamental strategies for decomposing unitary matrices in photonic networks by extending DreamCoder to complex-valued linear algebra. The generated decomposition programs achieve the minimal N(N−1)/2 Mach–Zehnder interferometer count and go beyond Reck and Clements architectures while encoding dimension-agnostic invariants that generalize from 5×5 to 64×64 without retraining. The same engine also exploits matrix-specific structure to reduce interferometer counts below universal bounds, including Householder matrices (2N−3 MZIs) and sparse-matrix SVD cases with up to 38% fewer MZIs at 95% sparsity.","arXiv :2607 . 10295v1 [physics .optics] 11 Jul 2026  \nProgram-Synthesis-Driven Autodesign of Universal Unitary Operators  \nYifei Zhang, 1, 2, ∗ Dong Chen,3, ∗ Fan Wang,4, 2 Wenrui Zhang,3 Yan Chen,5 Dingding Han,6, 7 Jianmin Yuan,8 Xiangjin Kong, 1, 2,† and Yu-Gang Ma 1, 2, 9,‡ 1 Key Laboratory of Nuclear Physics and Ion-beam Application (MOE),  \nInstitute of Modern Physics, Fudan University, Shanghai 200433, China  \n2 Research Center for Theoretical Nuclear Physics, NSFC and Fudan University, Shanghai 200438, China  \n3 Huawei Technologies Co., Ltd, Beijing 100095, China  \n4 Department of Industrial Engineering and Decision Analytics,  \nHong Kong University of Science and Technology, HongKong, China  \n5 Hunan Key Laboratory of Mechanism and Technology of Quantum Information, Changsha 410073, China 6 School of Information Science and Technology, Fudan University, Shanghai 200433, China 7 Research Institute of Intelligent Complex Systems, Fudan University, Shanghai 200433, China 8 Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China 9 School of Physics, East China Normal University, Shanghai 200062, China  \nWe demonstrate that AI-driven program synthesis can autonomously discover fundamental strategies for decomposing unitary matrices in photonic networks. By extending DreamCoder to complex-valued linear algebra, the system generates decomposition programs achieving the minimal N (N −1)/2 Mach–Zehnder interferometers, distinct from both Reck and Clements architectures. Learned programs encode dimension-agnostic invariants: strategies discovered for 5 × 5 matrices generalize to higher dimensions such as 64 × 64. The discovered programs encode interpretable, dimension-agnostic construction rules. These rules generalize across matrix sizes without retraining, demonstrating that autonomous program synthesis can serve as a scalable paradigm for algorithm discovery and the automated design of universal unitary operators. Beyond universal decompositions, the system automatically exploits matrix structure to reduce the interferometer count below the universal theoretical bound. For instance, for Householder matrices, it discovers a dimension-independent rule that requires only 2N − 3 MZIs. This achieves linear, rather than quadratic, scaling and generalizes to arbitrary N without retraining. For matrices obtained from the singular value decomposition of sparse matrices, reductions generally increase with sparsity, reaching up to 38% fewer MZIs than the universal theoretical bound N(N − 1)/2 at 95% sparsity. These MZI reductions translate directly into practical hardware benefits for scalable photonic implementations. Taken together, the system functions as a single unified engine that discovers both universal decomposition rules and matrix-specific optimizations, without being provided with the structural or analytical properties of the input matrices.  \nUnitary transformations lie at the foundation of quantum mechanics, governing the evolution of quantum states inclosed systems [1], and are central to modern photonic computing and quantum information processing [2–4] . In linear optical systems, unitary matrices determine how multimode fields interfere and propagate through reconfigurable interferometric networks, allowing direct hardware implementations of matrix operations with ultrahigh speed, low energy consumption, and intrinsic parallelism [4, 5] . These capabilities make photonic platforms attractive for optical neural networks [6–11], where unitaries implement trainable linear layers, and for quantum computation [2, 12–15], where they realize universal linear-optical circuits. Rapid advancesin integrated photonics have produced large-scale, low-loss, and programmable interferometer meshes [16–18], motivating scalable and systematic methods to realize arbitrary highdimensional unitaries in hardware.  \nIn practice, arbitrary N × N unitary transformations are implemented by decomposing them into seq","cbCaimnwR1loVlca","https://ap.wps.com/l/cbCaimnwR1loVlca","pdf",1483742,1,13,"English","en",105,"# Motivation and Background\n## Unitary transformations in quantum and photonics\n## Universal decomposition via Mach–Zehnder meshes\n# Automated Program Synthesis Framework\n## DreamCoder extension to complex-valued linear algebra\n# Universal Decomposition Results\n## Minimal MZI count and new elimination orderings\n## Dimension-agnostic construction rules\n# Matrix-Specific Optimization\n## Householder matrices: linear scaling\n## SVD of sparse matrices: sparsity-driven MZI reduction\n# Unified Autodesign Engine","[{\"question\":\"How does the method reduce interferometer counts for structured matrices beyond the universal bound?\",\"answer\":\"It automatically exploits matrix structure to lower the MZI number, including a dimension-independent rule for Householder matrices using only 2N−3 MZIs and reductions for matrices from SVD of sparse inputs, reaching up to 38% fewer MZIs at high sparsity.\"}]",1784206869,33,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":78,"head_meta":80,"extra_data":82,"updated_unix":27},"program-synthesis-driven-autodesign-of-universal-unitary-operators","",{"@graph":35,"@context":77},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/program-synthesis-driven-autodesign-of-universal-unitary-operators/85875/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"How does the method reduce interferometer counts for structured matrices beyond the universal bound?","Question",{"text":75,"@type":76},"It automatically exploits matrix structure to lower the MZI number, including a dimension-independent rule for Householder matrices using only 2N−3 MZIs and reductions for matrices from SVD of sparse inputs, reaching up to 38% fewer MZIs at high sparsity.","Answer","https://schema.org",{"og:url":51,"og:type":79,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":81,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":84},[85,89,93,97,102,107,112,115,120,123,127],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":45,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":45,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":45,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":45,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":98,"slug":130},19,"General","general"]