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arXiv · 2201.00427

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

Vitaly V. Kocharovsky·Vladimir V. Kocharovsky·Sergey V. Tarasov
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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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Vitaly V. Kocharovsky, Vladimir V. Kocharovsky, Sergey V. Tarasov. 2022-01-02. Quantum supremacy of the many-body fluctuations in the occupations of the excited particle states in a Bose-Einstein-condensed gas. https://doi.org/10.1103/physreva.106.063312

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