Nonlinear Quantum Neuron: A Fundamental Building Block for Quantum Neural Networks

TL;DR

This paper introduces a framework for constructing nonlinear quantum neurons, enabling quantum neural networks to incorporate nonlinear activation functions, which are essential for powerful learning capabilities, using quantum circuits that approximate nonlinear functions.

Contribution

The paper proposes a generalizable quantum circuit framework to realize nonlinear quantum neurons, addressing the challenge of integrating nonlinearity into quantum neural networks.

Findings

Quantum circuits can approximate nonlinear functions effectively.

The framework requires polynomial quantum resources relative to input size.

Experimental results on IBM Quantum Experience validate the approach.

Abstract

Quantum computing enables quantum neural networks (QNNs) to have great potentials to surpass artificial neural networks (ANNs). The powerful generalization of neural networks is attributed to nonlinear activation functions. Although various models related to QNNs have been developed, they are facing the challenge of merging the nonlinear, dissipative dynamics of neural computing into the linear, unitary quantum system. In this paper, we establish different quantum circuits to approximate nonlinear functions and then propose a generalizable framework to realize any nonlinear quantum neuron. We present two quantum neuron examples based on the proposed framework. The quantum resources required to construct a single quantum neuron are the polynomial, in function of the input size. Finally, both IBM Quantum Experience results and numerical simulations illustrate the effectiveness of the proposed framework.