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

2025-06-27

AI Summary

Existing quantum machine learning models suffer from limited expressive power, poor interpretability, and high quantum resource overhead. Method: This work introduces Kolmogorov–Arnold Networks (KANs) into quantum machine learning for the first time, proposing two novel architectures—hybrid and fully quantum QuKANs. QuKANs enhance function approximation and interpretability under low qubit overhead via learnable edge weights, residual function transfer, and Born-rule-based quantum state encoding. The approach integrates parameterized quantum circuits, classical-quantum co-training, and quantum-state encoding of classical data. Contribution/Results: Experiments demonstrate that QuKANs achieve faster convergence and superior generalization across multiple benchmark tasks, outperforming both conventional quantum neural networks and classical KAN baselines. QuKANs establish a new paradigm for interpretable, efficient, and resource-frugal quantum machine learning.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Search and Optimization: Learning to Search

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• Exploring KANs potential in quantum machine learning
• Implementing hybrid and fully quantum KAN architectures
• Demonstrating feasibility and performance of Quantum KANs

Innovation

• Quantum Circuit Born Machine for KANs
• Hybrid classical-quantum KAN architecture
• Fully quantum residual function translation