Quantum Kolmogorov-Arnold networks by combining quantum signal processing circuits
Ammar Daskin
TL;DR
The paper addresses realizing Kolmogorov-Arnold Networks (KAN) on quantum hardware by leveraging Quantum Signal Processing (QSP) blocks as modular layers. A single quantum KAN layer is constructed from a diagonal block unitary $\mathcal{QL}=\bigoplus_i U_{\Vec{\phi_i}}(x_i)$ with a Hadamard-based selector that forms a linear combination of polynomial terms $P(x_i)$ to implement activations; outputs are read via standard quantum measurements or parameterized operations. To enable deep architectures, the authors propose stacking layers through qubitization of polynomial terms, initializing a multi-qubit state encoding the polynomial components and applying phase gates to realize higher-degree terms, followed by Hadamards to recover $P(x)$-type outputs. They discuss challenges in layer composition due to repeated $W$ gates and input encoding, and offer ancilla-assisted and qubitization-based strategies to address them. Overall, the work outlines a concrete path for robust quantum machine learning with KAN using QSP, including a practical approach to deep quantum networks.
Abstract
In this paper, we show that an equivalent implementation of KAN can be done on quantum computers by simply combining quantum signal processing circuits in layers. This provides a powerful and robust path for the applications of KAN on quantum computers.