# Quantum phase transition with inhomogeneous driving in the Lechner-Hauke-Zoller model

## TL;DR

This paper investigates the phase diagram of the Lechner-Hauke-Zoller model, deriving analytic expressions for free energy and critical points, and proposes an inhomogeneous driving method to avoid first-order transitions, enhancing quantum annealing efficiency.

## Contribution

It introduces an inhomogeneous transverse field with a time-dependent parameter to evade first-order quantum phase transitions in the model.

## Key findings

- Analytic expressions for free energy and critical coefficients derived.
- Inhomogeneous driving improves ground-state preparation efficiency.
- Numerical verification confirms theoretical predictions.

## Abstract

We study the zero-temperature phase diagram of the Lechner-Hauke-Zoller model. An analytic expression for the free-energy and critical coefficients for finite-size systems and in the thermodynamic limit are derived and numerically verified. With the aim to improve standard quantum annealing, we introduce an inhomogeneously driven transverse field with an additional time-dependent parameter that allows one to evade the first-order quantum phase transition and, thus, improve the efficiency of the ground-state preparation considerably.