Quantum transfer through small networks coupled to phonons: effects of topology vs phonons

TL;DR

This paper investigates how network topology and phonon couplings influence quantum transfer efficiency, revealing that Peierls couplings can accelerate transfer in small networks but have limited effects as network size increases.

Contribution

It introduces a Bayesian optimization method to identify Hamiltonian parameters for minimal transfer time and analyzes the distinct roles of Holstein and Peierls couplings in quantum networks.

Findings

Holstein couplings do not surpass the transfer time limit of phonon-free networks.

Peierls couplings can accelerate transfer in networks with fewer than six sites.

The speed-up from Peierls couplings diminishes as network size exceeds seven sites.

Abstract

Particle or energy transfer through quantum networks is determined by network topology and couplings to environments. This study examines the combined effect of topology and external couplings on the efficiency of directional quantum transfer through quantum networks. We consider a microscopic model of qubit networks coupled to external vibrations by Holstein and Peierls couplings. By treating the positions of the network sites and the site-dependent phonon frequencies as independent variables, we determine the Hamiltonian parameters corresponding to minimum transfer time by Bayesian optimization. The results show that Holstein couplings may accelerate transfer through sub-optimal network configurations but cannot accelerate quantum dynamics beyond the limit of the transfer time in an optimal phonon-free configuration. By contrast, Peierls couplings distort the optimal networks to accelerate quantum transfer through configurations with less than six sites. However, the speed-up offered by Peierls couplings decreases with the network size and disappears for networks with more than seven sites. For networks with seven sites or more, Peierls couplings distort the optimal network configurations and change the mechanism of quantum transfer but do not affect the lower limit of the transfer time. The machine-learning approach demonstrated here can be applied to determine quantum speed limits in other applications.