QuKAN: A Quantum Circuit Born Machine approach to Quantum Kolmogorov Arnold Networks
This work addresses the integration of KANs into quantum computing for potential efficiency gains, but it appears incremental as it adapts existing KAN architectures to quantum forms without clear broad impact.
The paper tackled the problem of implementing Kolmogorov Arnold Networks (KANs) in quantum machine learning by developing hybrid and fully quantum versions using Quantum Circuit Born Machines, demonstrating feasibility, interpretability, and performance.
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.