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Qudit-native simulation of the Potts model

Maksim A. Gavreev, Evgeniy O. Kiktenko, Aleksey K. Fedorov, Anastasiia S. Nikolaeva

TL;DR

This paper addresses the difficulty of simulating high-dimensional quantum spin models by introducing qudit-native Suzuki–Trotter decompositions tailored to the $q$-state Potts model. It provides two gate-decomposition schemes—one based on light-shift (LS) gates and another using an auxiliary level to emulate projectors—yielding hardware-efficient mappings onto qudit gate sequences, with trapped-ion architectures as a primary target. Numerical results for $q=3$ demonstrate that second-order Suzuki–Trotter dynamics reproduce dynamical quantum phase transitions as seen in exact simulations, validating the approach for non-equilibrium phenomena. The work offers a practical framework for digital quantum simulation of multi-level models on near-term quantum processors, enabling exploration of rich critical dynamics and entanglement structures in high-dimensional systems.

Abstract

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.

Qudit-native simulation of the Potts model

TL;DR

This paper addresses the difficulty of simulating high-dimensional quantum spin models by introducing qudit-native Suzuki–Trotter decompositions tailored to the -state Potts model. It provides two gate-decomposition schemes—one based on light-shift (LS) gates and another using an auxiliary level to emulate projectors—yielding hardware-efficient mappings onto qudit gate sequences, with trapped-ion architectures as a primary target. Numerical results for demonstrate that second-order Suzuki–Trotter dynamics reproduce dynamical quantum phase transitions as seen in exact simulations, validating the approach for non-equilibrium phenomena. The work offers a practical framework for digital quantum simulation of multi-level models on near-term quantum processors, enabling exploration of rich critical dynamics and entanglement structures in high-dimensional systems.

Abstract

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.

Paper Structure

This paper contains 10 sections, 24 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Quantum Potts model
  3. Suzuki--Trotter Decomposition
  4. Gate decompositions
  5. Single-qudit gate decomposition
  6. Two-qudit gate decompositions
  7. LS-gate-based decomposition
  8. Decomposition based on an additional level
  9. Qudit simulation of the Potts model: dynamical quantum phase transition
  10. Conclusion

Figures (3)

  • Figure 1: Two-qudit time-evolution operator implementation using light shift (LS) gate.
  • Figure 2: Two-qudit time-evolution operator implementation using ancilla level.
  • Figure 3: Rate function for the simulated dynamics with the qutrit Potts Hamiltonian. The inset shows the infidelity caused by Trotterization error.