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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 $5 \\times 5$ matrices generalize to higher dimensions such as $64 \\times 64$. 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 interferomete","title":"Program-Synthesis-Driven Autodesign of Universal Unitary Operators","url":"https://arxiv.org/abs/2607.10295","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.10295v1 Announce Type: cross \nAbstract: We 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 $5 \\times 5$ matrices generalize to higher dimensions such as $64 \\times 64$. 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. 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