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Towards the Simplest Model of Quantum Supremacy: Atomic Boson Sampling in a Box Trap
Vitaly V Kocharovsky1, Vladimir V Kocharovsky1, William D Shannon1
1Department of Physics and Astronomy, Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX 77843, USA.
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.
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