Mitigating the barren plateau problem in linear optics

Abstract

We prove that variational quantum algorithms using discrete variable boson samplers suffer from barren plateaus and that by changing to fermionic statistics, which is classically efficient to simulate, the barren plateau scaling is less severe. Moreover, when using fermionic statistics the cost landscape boils down to one unit frequency Fourier mode per variational parameter, irrespective of circuit design, ansatz or variational problem, allowing for more efficient parameter shift rules. This simplified cost landscape allows for the gradient-free Rotosolve algorithm to be used to gain a considerable speed-up over the original bosonic algorithm. Motivated by this, we propose a non-linear parametrised phase shifter, the dual-valued phase shifter, that generates these single-harmonic cost landscapes for bosonic statistics. 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. Despite this, the classical simulability of free fermions and the fact the fermionic algorithm can defeat the bosonic algorithm casts doubt on whether the quantum advantage of boson sampling results in any practical advantage in this setting.

arXiv comment49 pages, 18 figures, 2 tables