发表机构
Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Institute of Modern Physics, Fudan University, Shanghai 200433, China; Research Center for Theoretical Nuclear Physics, NSFC and Fudan University, Shanghai 200438, China; Huawei Technologies Co., Ltd, Beijing 100095, China; Department of Industrial Engineering and Decision Analytics, Hong Kong University of Science and Technology, HongKong, China; Hunan Key Laboratory of Mechanism and Technology of Quantum Information, Changsha 410073, China; School of Information Science and Technology, Fudan University, Shanghai 200433, China; Research Institute of Intelligent Complex Systems, Fudan University, Shanghai 200433, China; Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China; School of Physics, East China Normal University, Shanghai 200062, China（核物理与离子束应用重点实验室（教育部），现代物理研究所，复旦大学，上海200433，中国; 理论核物理研究中心，国家自然科学基金委员会和复旦大学，上海200438，中国; 华为技术有限公司，北京100095，中国; 工业工程与决策分析系，香港科技大学，香港，中国; 湖南量子信息机制与技术重点实验室，长沙410073，中国; 信息科学与技术学院，复旦大学，上海200433，中国; 智能复杂系统研究所，复旦大学，上海200433，中国; 原子与分子物理研究所，吉林大学，长春130012，中国; 物理学院，华东师范大学，上海200062，中国）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究利用人工智能驱动的程序合成，通过扩展DreamCoder到复值线性代数，发现光子网络中酉矩阵分解策略，其生成的程序编码与维度无关的不变量及构造规则，还能利用矩阵结构减少干涉仪数量，为酉算子自动设计提供可扩展范式。
AI 中文摘要
我们证明了人工智能驱动的程序合成可以自主发现光子网络中酉矩阵分解的基本策略。通过将DreamCoder扩展到复值线性代数，该系统生成的分解程序使用最少的$N(N - 1)/2$个马赫曾德尔干涉仪，不同于雷克和克莱门茨架构。学习到的程序编码与维度无关的不变量，为$5×5$矩阵发现的策略可推广到更高维度如$64×64$。发现的程序编码可解释的、与维度无关的构造规则，无需重新训练即可跨矩阵大小推广。该系统还能利用矩阵结构将干涉仪数量减少到通用理论界限以下，如对Householder矩阵发现仅需$2N - 3$个MZIs的规则，对稀疏矩阵奇异值分解得到的矩阵，在95%稀疏度时比通用理论界限少38%的MZIs。这些减少直接转化为可扩展光子实现的实际硬件优势。总之，该系统作为一个统一引擎，能发现通用分解规则和特定矩阵优化，无需输入矩阵的结构或分析属性。
英文摘要
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. 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.
