Mitigating the barren plateau problem in linear optics

Abstract: We demonstrate a significant speedup of variational quantum algorithms that use discrete variable boson sampling when the parametrised phase shifters are constrained to have two distinct eigenvalues. This results in a cost landscape with less local minima and barren plateaus regardless of the problem, ansatz or circuit layout. This works without reliance on any classical pre-processing and allows for the fast gradient-free Rotosolve algorithm to be used. 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 boson sampling variational algorithm for all tests we conducted.