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

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 mu...

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Bibliographic Details
Published in:arXiv.org 2022-02
Main Authors: Kocharovsky, Vitaly V, Kocharovsky, Vladimir V, Tarasov, Sergey V
Format: Article
Language:English
Subjects:
Characteristic functions
Fourier transforms
Probability distribution functions
Qubits (quantum computing)
Simulators
Theorems
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2201.00427