Estimating Fock-state linear optics evolution using coherent states

This paper presents two methods for simulating the interference of bosonic Fock states through linear interferometers using coherent states. The first method repeats the interferometer, injects coherent states in particular modes, and uses symmetric combinations of the outputs to reconstruct the state amplitudes of the Fock-state interference. The second method constructs a new interferometer that can be probed with coherent states on individual inputs to extract the required state amplitudes. The two approaches here show explicitly where the classical computational difficultly arises. In the first approach, the computational hardness is in the measurement post-processing, and in the second approach, it is within the construction of the required state evolution