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

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