  The quantum dynamic equation (QDE) of machine learning is obtained based on
Schr\"odinger equation and potential energy equivalence relationship. Through
Wick rotation, the relationship between quantum dynamics and thermodynamics is
also established in this paper. This equation reformulates the iterative
process of machine learning into a time-dependent partial differential equation
with a clear mathematical structure, offering a theoretical framework for
investigating machine learning iterations through quantum and mathematical
theories. Within this framework, the fundamental iterative process, the
diffusion model, and the Softmax and Sigmoid functions are examined, validating
the proposed quantum dynamics equations. This approach not only presents a
rigorous theoretical foundation for machine learning but also holds promise for
supporting the implementation of machine learning algorithms on quantum
computers.
