Squeezing in atomic boson sampling
ORAL
Abstract
Recently, atomic boson sampling of excited atom occupations in an equilibrium interacting gas with a
Bose-Einstein condensate (BEC) has been suggested [V.V. Kocharovsky et al., PRA 106, 063312 (2022),
Entropy 24, 1771 (2022)] 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
calculate, analytically and numerically, the effect of single- and two-mode squeezing on the statistics of
sampling from a single eigen-squeeze mode and two counter-propagating waves. Although not complex
enough on its own to show ♯P-hard behavior, single- or two-mode sampling reveals the basic
mechanism for the emergence of the computational ♯P-hardness in a many-body quantum system of
interacting atoms.
Bose-Einstein condensate (BEC) has been suggested [V.V. Kocharovsky et al., PRA 106, 063312 (2022),
Entropy 24, 1771 (2022)] 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
calculate, analytically and numerically, the effect of single- and two-mode squeezing on the statistics of
sampling from a single eigen-squeeze mode and two counter-propagating waves. Although not complex
enough on its own to show ♯P-hard behavior, single- or two-mode sampling reveals the basic
mechanism for the emergence of the computational ♯P-hardness in a many-body quantum system of
interacting atoms.
* The support from the Herman F. Heep and Minnie Belle Heep Texas A&MUniversity Endowed Fund held/administered by the Texas A&M Foundation is acknowledged.
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Publication: V.V. Kocharovsky, Vl.V. Kocharovsky, W.D. Shannon, S.V. Tarasov, Towards the simplest model of
quantum supremacy: Atomic boson sampling in a box trap, arXiv:2305.08320v1 [cond-mat.quant-gas] 15
May 2023 (submitted to Entropy).
V. V. Kocharovsky, Vl. V. Kocharovsky, W. D. Shannon, and S. V. Tarasov, Multi-Qubit Bose–Einstein
Condensate Trap for Atomic Boson Sampling, Entropy 24, 1771 (2022); DOI: 10.3390/e24121771.
Presenters
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William D Shannon
Texas A&M University
Authors
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William D Shannon
Texas A&M University
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Vitaly V Kocharovsky
Texas A&M University