Atomic boson sampling in a Bose-Einstein-condensed gas

Kocharovsky, V. V.; Kocharovsky, Vl. V.; Tarasov, S. V.

doi:10.1103/physreva.106.063312

Cited by 6 publications

(14 citation statements)

References 114 publications

(60 reference statements)

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“…The next logical exploration in this design is to see how the ground state is affected by the interpatricle interactions through solving the Gross-Pitaevskii equation for the condensate (We use standard notations [3].) The strength g of interaction depends on the healing length…”

Section: Condensate Wave Function Versus Single-particle Ground Statementioning

confidence: 99%

“…Statistics of atomic boson sampling and its computational ♯P-hardness are determined by a covariance matrix G which is expressed via the matrix R of the Bogoliubov transformation [3]:…”

Section: Bogoliubov Couplings and Quasiparticles -Causes For Squeezin...mentioning

confidence: 99%

“…Here we present a new platform suitable for such research; a multi-qubit BEC trap [2]. It stems from the fact of computational ♯P-hardness of atomic boson sampling of excited-atom numbers in a Bose-Einstein-condensed interacting equilibrium gas proven in [3]. This comes as an alternative to the well-known optical interferometer platform which makes use of non-interacting photons, supplied in squeezed states by external sources, rather than massive atoms in equilibrium [4,5,6,7].…”

Section: Introductionmentioning

confidence: 99%

“…Computational ♯P-hardness and quantum supremacy of photonic boson sampling in a linear interferometer Both boson sampling problems, photonic in the linear interferometer and atomic in the BEC trap, are ♯P-hard for computing. This stems from the fact that both derive their complexity from the hafnian (or indeed the permanent) of some n×n matrix composed from a correlation matrix G of the creation and annihilation operators of associated bosons [3,8]. The hafnian and permanent constitute a universal tool for studying nature's complexities [9] and their computation is a ♯P-hard problem [10], requiring ∼ n 3 2 n/2 and ∼ n 2 2 n operations, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Multi-qubit BEC trap for atomic boson sampling

Shannon

Kocharovsky

2023

J. Phys.: Conf. Ser.

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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.

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Section: Condensate Wave Function Versus Single-particle Ground Statementioning

confidence: 99%

“…Statistics of atomic boson sampling and its computational ♯P-hardness are determined by a covariance matrix G which is expressed via the matrix R of the Bogoliubov transformation [3]:…”

Section: Bogoliubov Couplings and Quasiparticles -Causes For Squeezin...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multi-qubit BEC trap for atomic boson sampling

Shannon

Kocharovsky

2023

J. Phys.: Conf. Ser.

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“…The analysis of various quantum many-body systems capable of simulating P-hard computational problems is one of the main topics of modern research in quantum physics and computing (see, for example, [1][2][3][4][5][6][7][8] and references therein). Recently, an atomic boson sampling of excited atom occupations in an equilibrium gas with a Bose-Einstein condensate (BEC) has been suggested as a process that could be P-hard for classical computing [9]. An example of a multi-qubit BEC trap [10] shows that it could serve as a rich and, at the same time, convenient platform for studies of various phenomena associated with atomic boson sampling and quantum supremacy.…”

Section: Introduction: the Simplest Quantum Many-body Model Showing P...mentioning

confidence: 99%

Towards the Simplest Model of Quantum Supremacy: Atomic Boson Sampling in a Box Trap

Kocharovsky,

Shannon

et al. 2023

Entropy

Self Cite

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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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Universal nature of quantum supremacy

Kocharovsky

2024

J. Phys.: Conf. Ser.

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We disclose the universal nature of computational #P-hardness and quantum supremacy of quantum many-body systems. We do so by means of the new powerful technique (the hafnian master theorem) that allows one to address the #P-hard problems systematically. We consider a generic example of many-body interacting systems – a trapped BEC-gas of interacting Bose atoms, apply the hafnian master theorem and refer to the Toda’s theorem on a #P-complete oracle.

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Atomic boson sampling in a Bose-Einstein-condensed gas

Cited by 6 publications

References 114 publications

Multi-qubit BEC trap for atomic boson sampling

Multi-qubit BEC trap for atomic boson sampling

Towards the Simplest Model of Quantum Supremacy: Atomic Boson Sampling in a Box Trap

Universal nature of quantum supremacy

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