11 Dec 2024 | Akash Kundu*, a, Aritra Sarkar†, b, Abhishek Sadhu‡, c
The paper introduces the Kolmogorov-Arnold Network (KAN) for Quantum Architecture Search (QAS), aiming to address the challenges of interpretability and parameter growth in Multi-Layer Perceptron (MLP)-based deep Q-networks. KAN, inspired by the Kolmogorov-Arnold representation theorem, uses spline-based univariate functions to approximate complex functions, enhancing accuracy and interpretability. The authors evaluate KAN's performance in quantum state preparation and quantum chemistry problems, demonstrating that KAN outperforms MLPs in terms of success probability, optimal solutions, and circuit design. In noiseless scenarios, KAN achieves higher success probabilities and fewer optimal solutions compared to MLPs. In noisy environments, KAN shows better fidelity in approximating quantum states. For quantum chemistry, KAN constructs more compact parameterized quantum circuits with fewer 2-qubit gates and reduced circuit depth, while requiring fewer learnable parameters. However, KAN has a higher execution time per episode compared to MLPs. The study suggests that KAN is a promising alternative to MLPs in QAS, particularly in scenarios with noise and limited parameter budgets.The paper introduces the Kolmogorov-Arnold Network (KAN) for Quantum Architecture Search (QAS), aiming to address the challenges of interpretability and parameter growth in Multi-Layer Perceptron (MLP)-based deep Q-networks. KAN, inspired by the Kolmogorov-Arnold representation theorem, uses spline-based univariate functions to approximate complex functions, enhancing accuracy and interpretability. The authors evaluate KAN's performance in quantum state preparation and quantum chemistry problems, demonstrating that KAN outperforms MLPs in terms of success probability, optimal solutions, and circuit design. In noiseless scenarios, KAN achieves higher success probabilities and fewer optimal solutions compared to MLPs. In noisy environments, KAN shows better fidelity in approximating quantum states. For quantum chemistry, KAN constructs more compact parameterized quantum circuits with fewer 2-qubit gates and reduced circuit depth, while requiring fewer learnable parameters. However, KAN has a higher execution time per episode compared to MLPs. The study suggests that KAN is a promising alternative to MLPs in QAS, particularly in scenarios with noise and limited parameter budgets.