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Journal of Physics Conference Series

Multi-qubit BEC trap for atomic boson sampling

William Shannon, Vitaly V. Kocharovsky

Published May 1, 2023• 0 citations
Publisher

Abstract

Abstract We suggest a new platform for examination of quantum statistical phenomena in many-body interacting systems – a multi-qubit Bose-Einstein-condensate (BEC) trap. Ideally, it is suitable for demonstrating manifestations of quantum supremacy of such systems through atomic boson sampling of excited-state occupations. This is wholly different than the linear-interferometer platform which uses Gaussian boson sampling of non-interacting non-equilibrium photons rather than interacting atoms in equilibrium. We present a basic model of the multi-qubit BEC trap and illustrate its essential properties by means of numerical simulations.

DOI
10.1088/1742-6596/2494/1/012001

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Abstract We suggest a new platform for examination of quantum statistical phenomena in many-body interacting systems – a multi-qubit Bose-Einstein-condensate (BEC) trap. Ideally, it is suitable for demonstrating manifestations of quantum supremacy of such systems through atomic boson sampling of excited-state occupations. This is wholly different than the linear-interferometer platform which uses Gaussian boson sampling of non-interacting non-equilibrium photons rather than interacting atoms in equilibrium. We present a basic model of the multi-qubit BEC trap and illustrate its essential properties by means of numerical simulations.
We propose a multi-qubit Bose-Einstein-condensate (BEC) trap as a platform for studies of quantum statistical phenomena in many-body interacting systems. In particular, it could facilitate testing atomic boson sampling of the excited-state occupations and its quantum advantage over classical computing in a full, controllable and clear way. Contrary to a linear interferometer enabling Gaussian boson sampling of non-interacting non-equilibrium photons, the BEC trap platform pertains to an interacting equilibrium many-body system of atoms. We discuss a basic model and the main features of such a multi-qubit BEC trap.
We consider quantum statistical physics of many-body equilibrium fluctuations in an interacting Bose-Einstein-condensed (BEC) 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 discuss $\ensuremath{\sharp}\mathrm{P}$-hardness of computing this distribution. The latter is done by means of the Hafnian master theorem generalizing the classical permanent master theorem of MacMahon. We suggest an atomic boson sampling in the many-body interacting systems as an alternative to a widely studied Gaussian boson sampling of photons. We outline a multiqubit BEC trap, formed by a set of the single-qubit potential wells, as a convenient model for studying atomic boson sampling.
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.
We propose boson sampling from a system of coupled photons and Bose-Einstein condensed atoms placed inside a multi-mode cavity as a simulation process testing the quantum advantage of quantum systems over classical computers. Consider a two-level atomic transition far-detuned from photon frequency. An atom-photon scattering and interatomic collisions provide interactions that create quasiparticles and excite atoms and photons into squeezed entangled states, orthogonal to the atomic condensate and classical field driving the two-level transition, respectively. We find a joint probability distribution of atom and photon numbers within a quasi-equilibrium model via a hafnian of an extended covariance matrix. It shows a sampling statistics that is ♯P-hard for computing, even if only photon numbers are sampled. Merging cavity-QED and quantum-gas technologies into a hybrid boson sampling setup has the potential to overcome the limitations of separate, photon or atom, sampling schemes and reveal quantum advantage.
Abstract Recently, atomic boson sampling of excited atom occupations in an equilibrium interacting gas with a Bose-Einstein condensate (BEC) has been suggested as a process that could be #P-hard for classical computing. Here we consider this process within the simplest possible model of a BEC trap – the box with the periodic boundary conditions. Remarkably, this model remains pertained to #P-hardness and quantum supremacy. We evince two-mode squeezing and entanglement in the statistics of sampling from (i) a single eigen-squeeze mode or (ii) two counter-propagating waves. Although not complex enough on its own to show #P-hard behavior, such a sampling reveals the basic mechanism of the #P-hardness – an interplay between two intrinsic entities existing in the BEC gas, the eigen-energy quasiparticles and eigen-squeeze modes, that causes the interference and squeezing of the sampled excited atom states.