Data classification by quantum radial basis function networks

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.