@MISC{Aaronson_bosonsamplingis, author = {Scott Aaronson and Alex Arkhipov}, title = {BosonSampling Is Far From Uniform}, year = {} }

Share

OpenURL

Abstract

BosonSampling, which we proposed three years ago, is a scheme for using linear-optical networks to solve sampling problems that appear to be intractable for a classical computer. In a recent manuscript, Gogolin et al. claimed that even an ideal BosonSampling device’s output would be “operationally indistinguishable ” from a purely random string, at least “without detailed a priori knowledge”—or at any rate, that telling the two apart might itself be a hard computational problem. In this paper, we first answer these claims—explaining why the first is based on a definition of “a priori knowledge ” so strange that, were it adopted, almost no quantum algorithm could be distinguished from a pure random-number source; while the second is neither new nor a practical obstacle to interesting BosonSampling experiments (for reasons discussed in our original paper, which Gogolin et al. fail to acknowledge). However, we then go further, and address some interesting research questions inspired by Gogolin et al.’s mistaken arguments. We prove that, provided the number of output modes is at least quadratically greater than the number of photons, with high probability over a Haar-random matrix A, the BosonSampling distribution induced by A is far from the uniform