Variational Gibbs State Preparation on Trapped-Ion Devices

TL;DR

This paper demonstrates a variational quantum algorithm for preparing Gibbs states on trapped-ion quantum computers, revealing how fidelity varies with temperature and system size, and highlighting hardware-induced thermal effects.

Contribution

It introduces a variational approach for Gibbs state preparation on ion-trap devices and analyzes the impact of hardware imperfections on fidelity.

Findings

Fidelity decreases non-monotonically with inverse temperature.

Fidelity decreases as system size increases.

Hardware induces thermal fluctuations, effectively heating the system.

Abstract

We implement a variational quantum algorithm for Gibbs state preparation of a transverse-field Ising model on IonQ's quantum computers. To this end, we train the variational parameters via classical simulation and perform state tomography on the quantum devices to evaluate the fidelity of the prepared Gibbs state. As a main result, we find that fidelity decreases (non-monotonically) as a function of the inverse temperature $\beta$ of the system. Fidelity also decreases as a function of the size of the system. Interestingly, we find that a Gibbs state prepared for a specified $\beta$ is a better representative of a Gibbs state prepared for a $\textit{lower}$ $\beta$; or in other words, thermal fluctuations in the quantum hardware lead to digital heating, that is, an increase in the temperature of the prepared Gibbs state above what was intended.