Automated discovery of photonic circuits for entangled state preparation

High-fidelity heralded entangled states are essential for photonic quantum computing. We present a numerical optimization method for discovering photonic circuits that produce a target output state with maximum probability. Optimizing a circuit requires both the ability to simulate the circuit for a given set of parameters and efficiently scan through those parameters. The first requirement is complicated by the exponential growth in the computational complexity of simulating photonic circuits. To overcome this challenge, we introduce a state-of-the-art Fock-state simulation algorithm that supports automatic differentiation and GPU acceleration. The input states are Fock states, and the output states depend continuously on the circuit parameters, which are optimized using a gradient-based algorithm. Once a successful synthesis is obtained, a sparsification algorithm is used to convert the optimized unitary into a sparse photonic circuit with minimal number of non-trivial beamsplitters. We demonstrate the effectiveness of this method by reproducing analytically known Bell and GHZ state generation circuits, and numerically discovering novel circuits such as an 8-photon, 12-mode 4-GHZ circuit and a 10-photon, 16-mode 4-GHZ circuit.