Quantum Kolmogorov–Arnold Networks

Yongchen Zhou, Qiang Ni, Richard Jiang

Keywords: Quantum Computing, Kolmogorov–Arnold Networks

Abstract: The pursuit of quantum advantage in machine learning drives the exploration of quantum analogues of powerful classical architectures. The recent introduction of Kolmogorov-Arnold Networks (KANs) provides a mathematically grounded framework for enhanced expressivity and accuracy in function approximation. However, KANs and their variants fundamentally rely on predefined basis functions. In this work, we introduce Quantum Kolmogorov-Arnold Networks (QKANs), which leverage parameterized quantum circuits to implement learnable activation functions without predefined bases. We establish the theoretical foundations of QKANs and demonstrate their effectiveness through numerical experiments, showing superior performance on function approximation tasks. QKANs accurately model complex nonlinear relationships and establish a new benchmark for expressive power in quantum machine learning. This work bridges KANs with quantum computation, providing a new paradigm for expressive quantum machine learning.

Primary Area: learning theory

Submission Number: 8971