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arXiv:2511.13572 · Entropy

Qudit-native simulation of the Potts model

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

quant-phSubmitted Nov 17, 2025• Announced Nov 18, 2025• 0 citations
v1 · Nov 17, 2025v2 · Nov 23, 2025
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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.

Journal reference
Entropy 28, 160 (2026)
DOI
10.3390/e28020160
Comments
7 pages, 3 figures

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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.
The Fermi-Hubbard model, a fundamental framework for studying strongly correlated phenomena could significantly benefit from quantum simulations when exploring non-trivial settings. However, simulating this problem requires twice as many qubits as the physical sites, in addition to complicated on-chip connectivities and swap gates required to simulate the physical interactions. In this work, we introduce a novel quantum simulation approach utilizing qudits to overcome such complexities. Leveraging on the symmetries of the Fermi-Hubbard model and their intrinsic relation to Clifford algebras, we first demonstrate a Qudit Fermionic Mapping (QFM) that reduces the encoding cost associated with the qubit-based approach. We then describe the unitary evolution of the mapped Hamiltonian by interpreting the resulting Majorana operators in terms of physical single- and two-qudit gates. While the QFM can be used for any quantum hardware with four accessible energy levels, we demonstrate the specific reduction in overhead resulting from utilizing the native Controlled-SUM gate (equivalent to qubit CNOT) for a fixed-frequency ququart transmon. We further transpile the resulting two transmon-qudit gates by demonstrating a qudit operator Schmidt decomposition using the Controlled-SUM gate. Finally, we demonstrate the efficacy of our proposal by numerical simulation of local observables such as the filling factor and Green's function for various Trotter steps. The compatibility of our approach with different qudit platforms paves the path for achieving quantum advantage in simulating non-trivial quantum many-body systems.
The Suzuki-Trotter decomposition, which digitalizes quantum time evolution, provides a promising framework for simulating quantum dynamics on quantum hardware and exploring quantum advantage over classical computation. However, conventional Trotter circuits require a large number of non-local gates, lowering their faithfulness to the ideal dynamics when implemented on current noisy quantum hardware. While most previous studies have focused on circuit optimization, we instead propose a new Trotter decomposition that is intrinsically circuit-efficient for simulating quantum dynamics on near-term devices. Our method substantially reduces both the residual error by Trotter decomposition and the number of CNOT operations compared to conventional Trotter decompositions by exploiting the symmetry of the target model to construct an effective Hamiltonian with fewer two-qubit gates. We demonstrate the noise robustness of the proposed approach through numerical simulations of a nine-site Heisenberg model under realistic noise, and further validate its experimental practicality on the IBM superconducting device, achieving a state fidelity exceeding 0.980.980.98 when combined with quantum error mitigation in the three-site case. The proposed circuit design is also compatible with existing circuit optimization techniques. Our results establish a practical route toward noise-resilient quantum simulation in many-body dynamics.
Accurately simulating long-time dynamics of many-body systems is a challenge in both classical and quantum computing due to the accumulation of Trotter errors. While low-order Trotter-Suzuki decompositions are straightforward to implement, their rapidly growing error limits access to long-time observables. We present a framework for constructing efficient high-order Trotter-Suzuki schemes by identifying their structure and directly optimizing their parameters over a high-dimensional space. This method enables the discovery of new schemes with significantly improved efficiency compared to traditional constructions, such as those by Suzuki and Yoshida. Based on the theoretical efficiency and practical performance, we recommend two novel highly efficient schemes at 4th4^{\textrm{th}}4th and 6th6^{\textrm{th}}6th order. We also demonstrate the effectiveness of these decompositions on the Heisenberg model and the quantum harmonic oscillator, and find that for a fixed final time they perform better across the computational cost. Even when using large time steps, they surpass established low-order schemes like the Leapfrog. Finally, we investigate the in-practice performance of different Trotter schemes and find the decompositions with more uniform coefficients tend to feature improved error accumulation over long times. We have included this observation into our choice of recommended schemes.
The Suzuki–Trotter decomposition, which digitalizes quantum time evolution, provides a promising framework for simulating quantum dynamics on quantum hardware and exploring quantum advantage over classical computation. However, conventional Trotter circuits require a large number of non-local gates, lowering their faithfulness to the ideal dynamics when implemented on current noisy quantum hardware. While most previous studies have focused on circuit optimization, we instead propose a new Trotter decomposition that is intrinsically circuit-efficient for simulating quantum dynamics on near-term devices. Our method substantially reduces both the residual error by Trotter decomposition and the number of CNOT operations compared to conventional Trotter decompositions by exploiting the symmetry of the target model to construct an effective Hamiltonian with fewer two-qubit gates. We demonstrate the noise robustness of the proposed approach through numerical simulations of a nine-site Heisenberg model under realistic noise and further validate its experimental practicality on the IBM superconducting device, achieving a state fidelity exceeding 0.98 when combined with quantum error mitigation in the three-site case. The proposed circuit design is also compatible with existing circuit optimization techniques. Our results establish a practical route toward noise-resilient quantum simulation in many-body dynamics.
Hamiltonian formulations of lattice field theories provide access to real-time dynamics, but their simulation is difficult to implement efficiently. Trotter-Suzuki decompositions are at the center of time evolution computation, either on quantum hardware or classically, for instance with the use of tensor networks. While low-order Trotterizations remain the standard choice due to their simplicity, higher-order schemes offer the potential for improved efficiency. In this work we outline a short guide to Trotter-Suzuki schemes and their implementations in general. To help with this, we highlight new efficient schemes found by our optimization framework, and demonstrate their performance on the Heisenberg model.
We present an algorithmic method for the digital quantum simulation of many-body locally indivisible non-Markovian open quantum systems. It consists of two parts: first, a Suzuki-Lie-Trotter decomposition of the global system propagator into the product of subsystem propagators, which may not be quantum channels, and second, an algorithmic procedure for the implementation of the subsystem propagators through unitary operations and measurements on a dilated space. By providing rigorous error bounds for the relevant Suzuki-Lie-Trotter decomposition, we are able to analyze the efficiency of the method, and connect it with an appropriate measure of the local indivisibility of the system. In light of our analysis, the proposed method is expected to be experimentally achievable for a variety of interesting cases.