Efficient Trainability of Linear Optical Modules in Quantum Optical Neural Networks

The existence of “barren plateau landscapes” for generic discrete-variable quantum neural networks, which obstructs efficient gradient-based optimization cost functions defined by global measurements, would be surprising in the case linear optical modules networks due to tunability intensity continuous variable states and relevant unitary group having exponentially smaller dimension. We demonstrate that coherent light m modes can generically compiled efficiently if total scales sublinearly with m, extend this result based on homodyne, heterodyne, or photon detection measurement statistics, noisy presence attenuation. further trainability mode circuits variational mean field energy estimation positive quadratic Hamiltonians input do not have vanishing m.