Quantum Circuit Synthesis of an Approximate Hybrid Kolmogorov-Arnold Network

In this work, we construct a quantum circuit that instantiates an approximate version of a hybrid quantum-classical Kolmogorov-Arnold (AHQC-KAN) network. Our AHQC-KAN uses Chebyshev polynomials and a recursive operator encoding scheme. We demonstrate that our circuit requires $\mathcal{O}(\log n)$ qubits and $\mathcal{O}\left(2^{n}\right)$-2-qubit gates for n features. Simulation results show that our single-layer AHQC-KAN circuit achieves high accuracy on the highly nonlinear dataset, namely the spiral dataset with different noise levels. This work opens up several research directions for future consideration.