QuKAN: A Quantum Circuit Born Machine approach to Quantum Kolmogorov Arnold Networks

TL;DR

This paper introduces QuKAN, a novel quantum machine learning architecture that implements Kolmogorov Arnold Networks using Quantum Circuit Born Machines, demonstrating its feasibility and potential advantages.

Contribution

It presents the first implementation of KANs in quantum form using QCBMs, combining classical and quantum components for enhanced expressiveness.

Findings

Feasibility of quantum KAN implementation demonstrated

Hybrid and fully quantum models show promising performance

Quantum KAN offers interpretability and efficient function approximation

Abstract

Kolmogorov Arnold Networks (KANs), built upon the Kolmogorov Arnold representation theorem (KAR), have demonstrated promising capabilities in expressing complex functions with fewer neurons. This is achieved by implementing learnable parameters on the edges instead of on the nodes, unlike traditional networks such as Multi-Layer Perceptrons (MLPs). However, KANs potential in quantum machine learning has not yet been well explored. In this work, we present an implementation of these KAN architectures in both hybrid and fully quantum forms using a Quantum Circuit Born Machine (QCBM). We adapt the KAN transfer using pre-trained residual functions, thereby exploiting the representational power of parametrized quantum circuits. In the hybrid model we combine classical KAN components with quantum subroutines, while the fully quantum version the entire architecture of the residual function is translated to a quantum model. We demonstrate the feasibility, interpretability and performance of the proposed Quantum KAN (QuKAN) architecture.