Sampling arbitrary photon-added or photon-subtracted squeezed states is in the same complexity class as boson sampling

Boson sampling is a simple model for nonuniversal linear optics quantum computing using far fewer physical resources than universal schemes. An input state comprising vacuum and single-photon states is fed through a Haar-random linear optics network and sampled at the output by using coincidence photodetection. This problem is strongly believed to be classically hard to simulate. We show that an analogous procedure implements the same problem, using photon-added or -subtracted squeezed vacuum states (with arbitrary squeezing), where sampling at the output is performed via parity measurements. The equivalence is exact and independent of the squeezing parameter, and hence provides an entire class of quantum states of light in the same complexity class as boson sampling.