Quantum embedding learning on variational photonic quantum circuits

Quantum embedding is a key technique in quantum machine learning, mapping classical data into a high-dimensional Hilbert space through parameterized quantum circuits to enhance data separability. While effective on general quantum devices, its implementation on photonic platforms faces severe challenges, as entangling gates rely on post-selection and lead to exponentially decreasing success probabilities when cascaded. To address this, we propose a quantum embedding learning approach tailored for photonic quantum circuits, which incorporates multi-photon post-selection into a variational ansatz, enabling the efficient generation of entanglement while maintaining circuit scalability on NISQ devices. By training the transfer matrices, our method achieves the desired photon distribution probabilities and input-output correspondence. We demonstrate its versatility through three tasks: Bell-state projection, quantum support vector machines (qSVM), and quantum clustering of K-means. The experimental results indicate enhanced performance in state discrimination, classification, and clustering, showing that the method provides a practical route to implement quantum embedding in integrated photonic circuits.