Abstract

Boson sampling is a quantum mechanical task involving Fock basis state preparation and detection and evolution using only linear interactions. A classical algorithm for producing samples from this quantum task cannot be efficient unless the polynomial hierarchy of complexity classes collapses, a situation believed to be highly implausible. We present a method for constructing a device which uses Fock state preparations, linear interactions, and Gaussian continuous-variable measurements for which one can show that exact sampling would be hard for a classical algorithm in the same way as boson sampling. The detection events used from this arrangement do not allow a similar conclusion to be drawn for the classical hardness of approximate sampling. We discuss the details of this result outlining some specific properties required by approximate sampling hardness.