Program-Synthesis-Driven Autodesign of Universal Unitary Operators
Authors: Yifei Zhang, Dong Chen, Fan Wang, Wenrui Zhang, Yan Chen, Dingding Han, Jianmin Yuan, Xiangjin Kong, +1 more
Organizations: Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Institute of Modern Physics, Fudan University, Shanghai 200433, 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 · Research Center for Theoretical Nuclear Physics, NSFC and Fudan University, Shanghai 200438, China · School of Physics, East China Normal University, Shanghai 200062, China
Abstract
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 5×5 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.
Can Large Language Models (LLMs) understand and reason about quantum operators? Despite their remarkable capabilities in mathematics and symbolic reasoning, LLMs remain inherently blind to quantum representations such as unitary matrices. In this work, we take a step toward bridging this gap by introducing an approach that maps unitary operators into the latent space of an LLM, enabling unified modeling over quantum and linguistic inputs. We instantiate this idea on Clifford+T circuit synthesis over a Pauli rotation gate set, where our model achieves results competitive with state-of-the-art methods and scales consistently with training data, with no signs of saturation. Our approach further enables language-conditioned synthesis, allowing gate constraints unseen during training to be specified directly in natural language. This work suggests a path toward quantum--aware foundation models that can natively interpret and reason about quantum operations, which could have broader implications reaching across quantum compilation and algorithm discovery.
Bosonic Gaussian unitaries are fundamental building blocks of central continuous-variable quantum technologies such as quantum-optic interferometry and bosonic error-correction schemes. In this work, we present the first time-efficient algorithm for learning bosonic Gaussian unitaries with a rigorous analysis. Our algorithm produces an estimate of the unknown unitary that is accurate to small worst-case error, measured by the physically motivated energy-constrained diamond distance. Its runtime and query complexity scale polynomially with the number of modes, the inverse target accuracy, and natural energy parameters quantifying the allowed input energy and the unitary's output-energy growth. The protocol uses only experimentally friendly photonic resources: coherent and squeezed probes, passive linear optics, and heterodyne/homodyne detection. We then employ an efficient classical post-processing routine that leverages a symplectic regularization step to project matrix estimates onto the symplectic group. In the limit of unbounded input energy, our procedure attains arbitrarily high precision using only 2m+2 queries, where m is the number of modes. To our knowledge, this is the first provably efficient learning algorithm for a multiparameter family of continuous-variable unitaries.
Photonic quantum computing is a promising platform for scalable quantum machine learning, but designing effective hybrid architectures remains challenging under hardware and optimization constraints. Existing approaches rely on manually tuned architectures that fail to account for the collaboration between classical preprocessing, phase encoding, and photonic circuit structure, limiting both accuracy and hardware compatibility. In this paper, we propose a neural architecture search framework for hybrid photonic quantum-classical models that combines genetic algorithm-based search with learnable quantum phase encoding to systematically explore the joint design space of classical and quantum components. Our framework encodes 19 hyperparameters across six gene groups and evolves a population of hybrid architectures using group-based crossover, per-gene mutation, and elitism, evaluating each candidate on a short training budget before full retraining of the best found design. We evaluate our framework on two image classification benchmarks, Digits and MNIST, achieving final validation accuracies of 99.44% and 98.78%, respectively, with first-principles execution time estimates on the Quandela Ascella photonic QPU projecting single-image inference at 67 ms (Digits) and 149 ms (MNIST). Our quantum contribution analysis further shows that the photonic layer extracts non-redundant features orthogonal to the classical pathway, providing a measurable accuracy advantage over classical-only baselines. Our results demonstrate that automated architecture search is both practical and impactful for hybrid photonic systems, opening the way for systematic design space exploration of quantum AI on photonic devices.
Farah Elnakhal, Alberto Marchisio, Nouhaila Innan +2