Genesis of quantum supremacy of atomic boson sampling

Atomic boson sampling [V.V. Kocharovsky et al., PRA 106, 063312 (2022)] from the noncondensed fraction of Bose-Einstein-condensed (BEC) gas confined in a box trap is presented as a new platform for studying computational ♯P-hardness and quantum supremacy of many-body systems. The joint probability distribution of atom numbers is calculated by means of a newly found hafnian master theorem. The Bloch-Messiah reduction of the Bogoliubov transformation for an interacting BEC gas is explicitly calculated. It shows that interatomic interactions give rise to two equally important entities – eigen-squeeze modes and eigen-energy quasiparticles – whose interplay with sampling atom states determines behavior of the BEC gas. It is proven that two necessary ingredients of ♯P-hardness, squeezing and interference, are self-generated in the gas and, contrary to Gaussian boson sampling in linear interferometers, external sources of squeezed bosons are not required. In conclusion, the analysis of the box BEC trap reveals genesis of quantum supremacy of atomic boson sampling over classical computing.