KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search

Quantum architecture search (QAS) is a promising direction for optimization and automated design of quantum circuits towards quantum advantage. Recent techniques in QAS focus on machine learning-based approaches from reinforcement learning, like deep Q-network. While multi-layer perceptron-based deep Q-networks have been applied for QAS, their interpretability remains challenging due to the high number of parameters. In this work, we evaluate the practicality of Kolmogorov-Arnold Networks (KANs) in QAS problems, analyzing their efficiency in the task of quantum state preparation and quantum chemistry. In quantum state preparation, our results show that in a noiseless scenario, the probability of success and the number of optimal quantum circuit configurations to generate the multi-qubit maximally entangled states are $2\times$ to $5\times$ higher than Multi-Layer perceptions (MLPs). Moreover, in noisy scenarios, KAN can achieve a better fidelity in approximating maximally entangled state than MLPs, where the performance of the MLP significantly depends on the choice of activation function. In tackling quantum chemistry problems, we enhance the recently proposed QAS algorithm by integrating Curriculum Reinforcement Learning (CRL) with a KAN structure instead of the traditional MLP. This modification allows us to design a parameterized quantum circuit that contains fewer 2-qubit gates and has a shallower depth, thereby improving the efficiency of finding the ground state of a chemical Hamiltonian. Further investigation reveals that KAN requires a significantly smaller number of learnable parameters compared to MLPs; however, the average time of executing each episode for KAN is higher.