Quantum Dynamics of Machine Learning

TL;DR

This paper introduces a quantum dynamic equation for machine learning based on Schrödinger's equation, establishing a theoretical framework that links quantum mechanics, thermodynamics, and machine learning processes, with potential applications in quantum computing.

Contribution

It formulates a novel quantum dynamic equation for machine learning, connecting quantum physics with iterative learning processes and validating it through key functions.

Findings

Reformulates machine learning iterations as a quantum dynamic PDE

Establishes relationship between quantum dynamics and thermodynamics

Validates the equations with diffusion, Softmax, and Sigmoid functions

Abstract

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.