Towards the Simplest Model of Quantum Supremacy: Atomic Boson Sampling in a Box Trap

Abstract

We describe boson sampling of interacting atoms from the noncondensed fraction of Bose–Einstein-condensed (BEC) gas confined in a box trap as a new platform for studying computational ♯P-hardness and quantum supremacy of many-body systems. We calculate the characteristic function and statistics of atom numbers via the newly found Hafnian master theorem. Using Bloch–Messiah reduction, we find that interatomic interactions give rise to two equally important entities—eigen-squeeze modes and eigen-energy quasiparticles—whose interplay with sampling atom states determines the behavior of the BEC gas. We infer 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.