Multi-Qubit Bose–Einstein Condensate Trap for Atomic Boson Sampling

Abstract

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.

Atomic boson sampling in a Bose-Einstein-condensed gas

“…The purpose of the present paper is somewhat opposite to that of 9 . Namely, we aim at the simplest possible model of the BEC trap that would allow us to greatly simplify the general theory outlined in 8,9 and explicitly disclose the mechanisms behind the ♯P-hard computational complexity of quantum many-body systems.…”

“…The purpose of the present paper is somewhat opposite to that of 9 . Namely, we aim at the simplest possible model of the BEC trap that would allow us to greatly simplify the general theory outlined in 8,9 and explicitly disclose the mechanisms behind the ♯P-hard computational complexity of quantum many-body systems. In a result, many general formulas and the entire theory, based on the method of characteristic function and hafnian master theorem, acquire an explicit, transparent form clearly revealing the origin of the ♯Phardness of computing the joint probability distribution of the excited-atom occupations.…”

“…Their normal and anomalous correlations are given by the corresponding (2M × 2M)-submatrix of the covariance matrix in Eq. (9). Suppose the preselected wave functions are coupled via the Bogoliubov Hamiltonian only between themselves, that is, their off-diagonal couplings ∆ ll ′ , ∆ll ′ , and ε ll ′ in Eq.…”

“…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 8 . A multi-qubit BEC trap that could serve as a rich and, at the same time, convenient platform for experimental studies of various phenomena associated with atomic boson sampling has been discussed in 9 .…”

Multi-qubit BEC trap for atomic boson sampling

“…Various techniques have been discussed and employed to try to achieve this goal which has so far been elusive [1]. 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].…”