Quantum supremacy of the many-body fluctuations in the occupations of the excited particle states in a Bose-Einstein-condensed gas

• URL: http://arxiv.org/abs/2201.00427v2
• Date: Wed, 16 Feb 2022 17:25:07 GMT
• Title: Quantum supremacy of the many-body fluctuations in the occupations of the excited particle states in a Bose-Einstein-condensed gas
• Authors: Vitaly V. Kocharovsky, Vladimir V. Kocharovsky, Sergey V. Tarasov
• Abstract summary: We suggest a multi-qubit BEC trap formed by a set of qubit potential wells. The process of many-body fluctuations in a BEC trap is #P-hard for computing.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 the Hafnian Master Theorem generalizing the famous Permanent Master Theorem of MacMahon. We suggest an appealing model, a multi-qubit BEC trap formed by a set of qubit potential wells, and discuss specifics of such an atomic boson-sampling system vs a photonic one. Finally, the process of many-body fluctuations in a BEC trap is #P-hard for computing. It could serve as a basis for demonstrating quantum supremacy of the many-body interacting systems over classical simulators.

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