
MTSU Computational and Data Science Ph.D. student, Yuan Chen, presents elements from his dissertation proposal on Quantum Algorithms for Differential Equations.

This talk presents a collection of works on quantum and hybrid quantum–classical methods for differential equations, with emphasis on the two directions: learning-based quantum models for dynamical systems and lightweight quantum recurrent architectures. Differential equations are central to modeling complex phenomena across science and engineering, yet many important problems remain challenging because of oscillatory behavior, chaos, and multiscale structure. The first part studies quantum recurrent neural networks for predicting the dynamics of ordinary differential equations and extends them through an encoder–decoder framework to time-dependent partial differential equations. The second part focuses on architectural efficiency by introducing minimal quantum recurrent models that retain only the most essential quantum components while shifting the remaining operations to classical layers. These works demonstrate how quantum recurrent models can be used to learn differential-equation dynamics while discussing the trade-offs among predictive accuracy, parameter efficiency, runtime, and trainability.
















