# Qudit-Native Simulation of the Potts Model

## TL;DR

This paper introduces a new method for simulating the Potts model using qudit systems, enabling efficient quantum simulations on trapped-ion platforms.

## Contribution

The paper presents two novel qudit-native decomposition schemes for simulating the Potts model using trapped-ion platforms.

## Key findings

- Two qudit-native decomposition schemes are introduced for encoding Potts interactions using trapped-ion gates.
- A Suzuki–Trotter approximation is demonstrated for detecting dynamical quantum phase transitions.
- The approach provides a pathway for qudit-based digital simulation of many-body quantum models.

## Abstract

Simulating entangled, many-body quantum systems is notoriously hard, especially in the case of the high-dimensional nature of the underlying physical objects. In this work, we propose an approach for simulating the Potts model based on the Suzuki–Trotter decomposition that we construct for qudit systems. Specifically, we introduce two qudit-native decomposition schemes: (i) the first utilizes the Mølmer–Sørensen gate and additional local levels to encode the Potts interactions, while (ii) the second employs a light-shift gate that naturally fits qudit architectures. These decompositions enable a direct and efficient mapping of the Potts model dynamics into hardware-efficient qudit gate sequences for a trapped-ion platform. Furthermore, we demonstrate the use of a Suzuki–Trotter approximation with our evolution-into-gates framework for detecting the dynamical quantum phase transition. Our results establish a pathway toward qudit-based digital quantum simulation of many-body models and provide a new perspective on probing nonanalytic behavior in high-dimensional quantum many-body models.