Abstract
We consider quantum statistical physics of many-body equilibrium fluctuations in an interacting Bose-Einstein-condensed (BEC) gas. We find a universal analytic formula for a characteristic function (Fourier transform) of a joint probability distribution for the particle occupation numbers in a BEC gas and discuss $\ensuremath{\sharp}\mathrm{P}$-hardness of computing this distribution. The latter is done by means of the Hafnian master theorem generalizing the classical permanent master theorem of MacMahon. We suggest an atomic boson sampling in the many-body interacting systems as an alternative to a widely studied Gaussian boson sampling of photons. We outline a multiqubit BEC trap, formed by a set of the single-qubit potential wells, as a convenient model for studying atomic boson sampling.
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