Quantum-Inspired Neural Network Activation Functions

Jincheng Zhang

Published Sep 3, 2026• 0 citations

Abstract

This paper explores a novel approach to neural network activation functions by drawing inspiration from quantum mechanical principles. Traditional activation functions, such as sigmoid and ReLU, often exhibit limitations in terms of learning efficiency and representational capacity. We hypothesize that classical activation functions can be effectively approximated by functions derived from quantum mechanics, specifically utilizing concepts like the quantum harmonic oscillator. The proposed activation functions aim to leverage the unique properties of quantum systems—superposition, entanglement, and tunneling—to potentially enhance neural network performance. We introduce a set of new activation functions and provide a theoretical framework for their design. The core claim of this work is that classical activation functions can be accurately approximated by quantum mechanical functions. The primary mechanism involves translating quantum mechanical models into differentiable functions suitable for use within a neural network architecture. We discuss the mathematical foundations, potential benefits, and challenges associated with this approach, focusing on the approximation of the quantum harmonic oscillator and its application to neural network activation. The research contributes to a fundamental shift in activation function design, moving beyond purely classical models towards a quantum-inspired paradigm.

DOI: 10.5281/zenodo.22270854

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