Title: Quantum Kolmogorov–Arnold Networks
Primary area: learning theory
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, this architecture has remained confined to classical implementations. In this work, we introduce Quantum Kolmogorov-Arnold Networks (QKANs), a quantum implementation that leverages parameterized quantum circuits to realize the learnable activation functions central to KANs. 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.