Enhanced Variational Quantum Kolmogorov-Arnold Network

Abstract

The Kolmogorov-Arnold Network (KAN) is a novel multi-layer network model recognized for its efficiency in neuromorphic computing, where synapses between neurons are trained linearly. Computations in KAN are performed by generating a polynomial vector from the state vector and layer-wise trained synapses, enabling efficient processing. While KAN can be implemented on quantum computers using block encoding and Quantum Signal Processing, these methods require fault-tolerant quantum devices, making them impractical for current Noisy Intermediate-Scale Quantum (NISQ) hardware. We propose the Enhanced Variational Quantum Kolmogorov-Arnold Network (EVQKAN) to overcome this limitation, which emulates KAN through variational quantum algorithms. The EVQKAN ansatz employs a tiling technique to emulate layer matrices, leading to significantly higher accuracy compared to conventional Variational Quantum Kolmogorov-Arnold Network (VQKAN) and Quantum Neural Networks (QNN), even with a smaller number of layers. EVQKAN achieves superior performance with a single-layer architecture, whereas QNN and VQKAN typically struggle. Additionally, EVQKAN eliminates the need for Quantum Signal Processing, enhancing its robustness to noise and making it well-suited for practical deployment on NISQ-era quantum devices.