Qudit-native Simulation with Suzuki-Trotter Decomposition Efficiently Maps Potts Model Dynamics Onto Trapped-ion Platforms

Simulating the behaviour of complex, entangled systems presents a significant challenge in physics, particularly when dealing with systems possessing many interacting components. Maxim Gavreev, Evgeniy Kiktenko, and Aleksey Fedorov, along with their colleagues at National University of Science and Technology “MISIS”, now demonstrate a novel approach to modelling the Potts model, a system widely used to understand magnetic materials and complex systems. The team constructs decompositions specifically designed for qudit systems, which utilise quantum bits capable of representing more than two states, and maps the model’s dynamics onto efficient sequences of quantum gates suitable for implementation on trapped-ion platforms. This work establishes a clear pathway towards building qudit-based digital simulations of many-body models and offers a new method for identifying critical points and understanding complex behaviour in high-dimensional physical systems.

Kiktenko, Aleksey K. Fedorov, and Anastasiia S. This work proposes an approach for simulating the Potts model based on the Suzuki-Trotter decomposition, specifically constructed for qudits. The method allows for efficient representation and manipulation of the quantum states required to model the system’s behaviour, offering a potential advantage over traditional simulation techniques. Specifically, the team introduces two qudit-native decomposition schemes. The first utilises Mølmer, Sørensen gates and additional local levels to encode the Potts interactions, while 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, the researchers demonstrate the use of a Suzuki-Trotter approximation with their evolution-into-gates framework, for detecting the dynamical quantum phase transition. The results establish a pathway toward qudit-based digital quantum simulation of many-body models.

Qudits Enhance Quantum Simulation Efficiency

This document details research on simulating quantum systems, focusing on the use of qudits, quantum systems with more than two levels, to enhance computational power and efficiency. The research addresses limitations of traditional qubit-based quantum computers, proposing that qudits offer advantages for simulating systems with inherent multi-level structures. Qudits can represent complex states with fewer physical resources than qubits, potentially leading to more efficient quantum simulations, and the research targets simulating phenomena in high-energy physics, condensed matter physics, statistical mechanics, quantum chemistry, and materials science. The team explores different physical platforms for realising qudits, including trapped ions, Rydberg atoms, and superconducting circuits.

They developed techniques to decompose complex quantum gates into simpler, native gates implementable on chosen qudit platforms, optimising gate sequences based on energy level transitions and developing efficient methods for implementing crucial quantum operations. The researchers also adapted and designed quantum algorithms specifically for qudit-based computers, verifying their performance using classical simulations. This work builds upon the foundational history of quantum simulation and connects to existing quantum algorithms for solving specific problems in physics and materials science, acknowledging ongoing hardware development efforts. Tensor network methods are also used as a classical simulation technique to verify qudit-based algorithms.

The research demonstrates that qudits offer a potentially more efficient way to represent and simulate certain quantum systems compared to qubits. New techniques for decomposing quantum gates into native qudit gates have been developed, leading to more efficient quantum circuits. The team has demonstrated the feasibility of using qudits to simulate various physical phenomena, and highlights ongoing progress in building and improving qudit-based quantum computers, including trapped-ion and Rydberg atom platforms. Future research will focus on scaling up qudit systems, developing new qudit algorithms, exploring new applications, and improving qudit coherence and fidelity. In essence, this document presents a comprehensive overview of the growing field of qudit-based quantum simulation, highlighting its potential to overcome the limitations of qubit-based computers and unlock new possibilities for scientific discovery.

Qudit Simulation of Quantum Phase Transitions

This work presents a new framework for simulating complex quantum systems using qudits, quantum bits that can exist in more than two states, on quantum computing platforms. Researchers have developed methods to map the dynamics of the q-state Potts model, a system used to study magnetism and disordered materials, onto sequences of operations achievable with qudits. Two distinct decompositions were created, one utilising the Molmer-Sorensen gate and another employing a light-shift gate, both designed to efficiently translate the model’s behaviour into hardware-compatible instructions for trapped-ion systems. The team demonstrated the accuracy of their approach by successfully simulating a three-level Potts chain and accurately reproducing a dynamical quantum phase transition, a critical point where the system’s behaviour changes dramatically.

Numerical results align with exact calculations, establishing a solid foundation for scaling these simulations to larger, more complex systems where traditional computational methods become impractical. This establishes a practical pathway for implementing multi-level quantum spin models on near-term qudit platforms, leveraging the natural ability of systems like trapped ions and neutral atoms to access high-dimensional quantum spaces. The authors acknowledge that the current simulations are limited to relatively small systems and first-order approximations within the Suzuki-Trotter decomposition. Future research will focus on extending these methods to larger systems and exploring higher-dimensional Potts models, bridging the gap between theoretical quantum many-body physics and experimental realisation of multi-level quantum dynamics. This work provides a significant step towards harnessing the power of qudits for simulating complex quantum phenomena and benchmarking emerging quantum processors.