Qudit-native simulation of the Potts model

Simulating entangled, many-body quantum systems is notoriously hard, especially in the case of high-dimensional nature of physical underlying 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 Molmer-Sorensen gate and additional local levels to encode the Potts interactions, while (ii) the second employs an 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 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.