Data classification by quantum radial basis function networks

TL;DR

This paper introduces a quantum version of the radial basis function network, leveraging quantum linear algebra and coherent states to achieve faster training while maintaining classification accuracy.

Contribution

The paper presents a novel quantum RBF network model with a new implementation approach and proves its training speed is nearly quadratic faster than classical methods.

Findings

Quantum RBF network trains almost quadratically faster.

Quantum RBF performs comparably to classical in classification accuracy.

Numerical results confirm efficiency and effectiveness.

Abstract

Radial basis function (RBF) network is a third layered neural network that is widely used in function approximation and data classification. Here we propose a quantum model of the RBF network. Similar to the classical case, we still use the radial basis functions as the activation functions. Quantum linear algebraic techniques and coherent states can be applied to implement these functions. Differently, we define the state of the weight as a tensor product of single-qubit states. This gives a simple approach to implement the quantum RBF network in the quantum circuits. Theoretically, we prove that the training is almost quadratic faster than the classical one. Numerically, we demonstrate that the quantum RBF network can solve binary classification problems as good as the classical RBF network. While the time used for training is much shorter.