Abstract

Quantum computers are unnecessary for exponentially-efficient computation or simulation if the Extended Church-Turing thesis---a foundational tenet of computer science---is correct. The thesis would be directly contradicted by a physical device that efficiently performs a task believed to be intractable for classical computers. Such a task is BosonSampling: obtaining a distribution of n bosons scattered by some linear-optical unitary process. Here we test the central premise of BosonSampling, experimentally verifying that the amplitudes of 3-photon scattering processes are given by the permanents of submatrices generated from a unitary describing a 6-mode integrated optical circuit. We find the protocol to be robust, working even with the unavoidable effects of photon loss, non-ideal sources, and imperfect detection. Strong evidence against the Extended Church-Turing thesis will come from scaling to large numbers of photons, which is a much simpler task than building a universal quantum computer.