Quantum Computing Modules Enhance Statistical Physics Education with Simulations of Random Walks and the Ising Model

Statistical physics routinely explores complex systems exhibiting probabilistic and collective behaviours, and now, quantum computing offers a novel approach to understanding these phenomena. Zihan Li, Dan A. Mazilu, and Irina Mazilu from Washington and Lee University present two practical modules designed for undergraduate courses, integrating quantum computation into the study of the random walk and the Ising model. These modules allow students to directly simulate both classical and quantum systems, fostering a deeper grasp of fundamental concepts like superposition, interference, and statistical distributions. By providing accessible code and student activities, this work significantly enhances engagement with statistical physics and opens new avenues for exploring complex systems through the lens of quantum mechanics.

This work presents two classroom-ready modules that integrate quantum computing into the undergraduate curriculum using Qiskit, focusing on the quantum random walk and the Ising model. Both modules enable students to simulate and contrast classical and quantum systems, thereby deepening their understanding of concepts such as superposition, interference, and statistical distributions. The authors outline how these examples can be used to enhance student engagement with statistical physics, making complex topics more accessible and suitable for courses in statistical mechanics, modern physics, or introductory quantum computing.

Quantum Simulations Enhance Statistical Physics Teaching

Researchers developed a novel approach to teaching statistical physics by integrating quantum computing modules using the Qiskit platform. These modules, focused on the random walk and the Ising model, allow students to directly simulate and compare classical and quantum behaviours, fostering a deeper understanding of core concepts. The random walk module guides students from classical diffusion to quantum interference, demonstrating how superposition and unitary evolution shape probability distributions. Students construct circuits mirroring coin tosses and shifts, observing the resulting quantum randomness across multiple trials.

The Ising model module revisits the classical Metropolis algorithm and then reimplements the same model using quantum circuits. This translation requires students to carefully consider how energy, probability, and thermal behaviour can be encoded in quantum operations. Through side-by-side simulations, students gain practical skills and conceptual insights into the differences between classical and quantum approaches to modelling physical systems. Researchers detail how the quantum circuit for the two-dimensional Ising model can be optimized for efficiency. The team discovered that focusing on the probability of not flipping a spin when neighbours exhibit positive energy changes significantly reduces computation time.

This optimization stems from the observation that most spin configurations will not yield a positive energy change, thus bypassing unnecessary circuit calculations. This principle extends to three-dimensional models and other lattice structures, demonstrating the broad applicability of this approach. The work provides a step-by-step guide within an accompanying Jupyter notebook, allowing students to construct the algorithm and assemble the corresponding quantum circuits, strengthening both conceptual understanding and coding experience.

Quantum Computing Enhances Statistical Physics Education

By implementing these modules, students gain a deeper understanding of fundamental principles such as superposition, interference, and statistical distributions, extending beyond traditional analytical approaches. The modules successfully demonstrate how quantum computing can enhance engagement with statistical physics and are adaptable for use in a range of undergraduate courses, including modern physics and introductory quantum computing. The authors acknowledge that the presented modules require students to have some prior understanding of qubits and quantum measurement, and suggest tools like IBM Quantum Composer to aid visualisation of abstract concepts. Future work could explore extending these modules to encompass more complex statistical physics models and further refine the pedagogical approach to maximise student learning outcomes. These advancements offer a valuable resource for educators seeking to incorporate cutting-edge computational tools into their curriculum and provide students with a more intuitive grasp of complex physical phenomena.