Evidence for the conjecture that sampling generalized cat states with linear optics is hard

Boson-sampling has been presented as a simplified model for linear optical quantum computing. In the boson-sampling model, Fock states are passed through a linear optics network and sampled via number-resolved photodetection. It has been shown that this sampling problem likely cannot be efficiently classically simulated. This raises the question as to whether there are other quantum states of light for which the equivalent sampling problem is also computationally hard. We present evidence, without using a full complexity proof, that a very broad class of quantum states of light --- arbitrary superpositions of two or more coherent states --- when evolved via passive linear optics and sampled with number-resolved photodetection, likely implements a classically hard sampling problem.