Conditions for an experimental Boson-sampling computer to disprove the Extended Church-Turing thesis

Abstract

We give a set of sufficient conditions on the experimental Boson-Sampling computer to satisfy Theorem 1.3 of Aaronson & Arkhipov (Theory of Computing \textbf{9}, 143 (2013)) stating a computational problem whose simulation on a classical computer would collapse the polynomial hierarchy of the computational complexity to the third level. This implies that such an experimental device is in conflict with the Extended Church-Turing thesis. In practical terms, we give a set of sufficient conditions for the scalability of the experimental Boson-Sampling computer beyond the power of the classical computers. The derived conditions can be also used for devising efficient verification tests of the Boson-Sampling computer.