Mitigating the barren plateau problem in linear optics

We prove the existence of barren plateaus in variational quantum algorithms using linear optics with either bosonic or fermionic particles and demonstrate that fermionic linear optics is less susceptible to the barren plateau problem. We use this to motivate a new photonic device, the dual-valued phase shifter, that is a non-linear phase shifter with two distinct eigenvalues. This component results in variational cost landscapes with fewer local minima regardless of the problem, ansatz or circuit layout. We propose three ways to achieve this by using either non-linear optics, measurement-induced non-linearities, or entangled resource states simulating fermionic statistics. The latter two require linear optics only, allowing for implementation with widely-available technology today. We show this outperforms the best-known linear optical variational algorithm for all tests we conducted.