Designing photonic circuits that prepare graph states with high fidelity and success probability is a central challenge in linear optical quantum computing. Existing approaches rely on hand-crafted designs or fusion-based assemblies. In the absence of multiplexing and boosting, both postselected ballistic circuits and sequential fusion exhibit exponentially decreasing single-shot yields—a fundamental limitation that makes optimizing individual resource state generators particularly important, as these serve as building blocks in larger FBQC architectures. We present a general-purpose optimization framework for automated photonic circuit discovery using a polynomial-based simulation approach, enabling efficient strong simulation and gradient-based optimization. Our framework employs a two-pass optimization procedure: The first pass identifies a unitary transformation that prepares the desired state with perfect fidelity and maximal success probability, and the second pass implements a sparsification algorithm that reduces this solution to a compact photonic circuit with minimal beam-splitter count while preserving performance. This sparsification procedure often reveals underlying mathematical structure, producing highly simplified circuits with rational reflection coefficients. We demonstrate our approach by discovering optimized circuits for three-, four-, and five-qubit graph states across multiple equivalence classes. For four-qubit states, our circuits achieve success probabilities of $2.053\times {10}^{-3}$ to $7.813\times {10}^{-3}$, outperforming the fusion baseline by up to $4.7\times$. For five-qubit states, we achieve $5.926\times {10}^{-5}$ to $1.157\times {10}^{-3}$, demonstrating up to $7.5\times$ improvement. These results include the first known state preparation circuits for certain five-qubit graph states.

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• Photonics
• Quantum circuits
• Quantum computation
• Quantum control