Adaptive Variational Quantum Kolmogorov-Arnold Network

Abstract: Kolmogorov-Arnold Network (KAN) is a novel multi-layer neuromorphic network. Many groups worldwide have studied this network, including image processing, time series analysis, solving physical problems, and practical applications such as medical use. Therefore, we propose an Adaptive Variational Quantum Kolmogorov-Arnold Network (VQKAN) that takes advantage of KAN for Variational Quantum Algorithms in an adaptive manner. The Adaptive VQKAN is VQKAN that uses adaptive ansatz as the ansatz and repeat VQKAN growing the ansatz just like Adaptive Variational Quantum Eigensolver (VQE). The scheme inspired by Adaptive VQE is promised to ascend the accuracy of VQKAN to practical value. As a result, Adaptive VQKAN has been revealed to calculate the fitting problem more accurately and faster than Quantum Neural Networks by far less number of parametric gates.