Hybrid boson sampling

TL;DR

This paper introduces a hybrid boson sampling approach using coupled photons and Bose-Einstein condensates in a multi-mode cavity, demonstrating a quantum advantage potential by sampling from a #P-hard distribution.

Contribution

It proposes a novel hybrid boson sampling system combining cavity-QED and quantum-gas technologies, enabling complex quantum sampling beyond classical capabilities.

Findings

Joint probability distribution involves a hafnian of an extended covariance matrix.

Sampling statistics are #P-hard to compute even for photon-only sampling.

Hybrid system can potentially surpass limitations of separate photon or atom sampling schemes.

Abstract

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 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 interaction creating quasiparticles and exciting atoms, photons into squeezed entangled states orthogonal, respectively, to the atomic condensate and classical field driving the two-level transition. 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 hybrid boson sampling setup has the potential to overcome limitations of separate, photon or atom, sampling schemes and reveal quantum advantage.