KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search

TL;DR

KANQAS reframes quantum architecture search by substituting a Kolmogorov-Arnold Network for the traditional MLP in a DDQN-based reinforcement learning loop. Across quantum state preparation and quantum chemistry tasks, KAQN achieves higher or comparable performance with drastically fewer trainable parameters, and shows robustness to hardware-like noise, albeit with longer episode runtimes. The work demonstrates more compact parameterized quantum circuits for molecular ground-state problems and highlights the interpretability and efficiency gains offered by KAN in quantum AI design. Together, these findings suggest KAN is a promising path toward practical, hardware-aware quantum architecture search and design.

Abstract

Quantum architecture Search (QAS) is a promising direction for optimization and automated design of quantum circuits towards quantum advantage. Recent techniques in QAS emphasize Multi-Layer Perceptron (MLP)-based deep Q-networks. However, their interpretability remains challenging due to the large number of learnable parameters and the complexities involved in selecting appropriate activation functions. In this work, to overcome these challenges, we utilize the Kolmogorov-Arnold Network (KAN) in the QAS algorithm, 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 is 2 to 5 times higher than MLPs. In noisy environments, KAN outperforms MLPs in fidelity when approximating these states, showcasing its robustness against noise. In tackling quantum chemistry problems, we enhance the recently proposed QAS algorithm by integrating curriculum reinforcement learning with a KAN structure. This facilitates a more efficient design of parameterized quantum circuits by reducing the number of required 2-qubit gates and circuit depth. 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.

Figures (6)

• Figure 1: The schematic for the KANQAS algorithm illustrates how the Kolmogorov-Arnold network replaces the traditional multi-layer perceptron in the reinforcement learning subroutine for quantum architecture search. In this setup, the environment, which incorporates a quantum algorithm, interacts with the RL-agent powered by a KAN-driven double deep-Q network, referred to as KAQN. Following an $\epsilon$-greedy policy, the agent selects its next action based on the reward function and the RL-state received from the environment. For the details of the reward function construction and quantum circuit encoding into an RL-state check the Sec. \ref{['sec:methods']} and Appendix \ref{['appndix:tensor_based_encoding']} respectively.
• Figure 2: In (a) the probability of successful circuits and in (b) the probability of optimal successful circuits in finding a 2-qubit maximally entangled state is slightly higher with KAN than MLP. A total of 10000 episodes are divided into 4 separate intervals where each interval contains 2500 episodes. In (a), each point in an interval corresponds to the probability of occurrence of a successful episode (see Eq. \ref{['eq:success_equation']}). Similarly, (b) corresponds to the number of occurrences of an optimal successful episode. The results are averaged over 20 random seeds (i.e. initialization) of the networks.
• Figure 3: In (a) the probability of successful circuits and in (b) the total number of optimal successful circuits in finding a 3-qubit maximally entangled state are noticeably higher with KAN than MLP. A total of 8000 episodes are divided into 4 separate intervals, where each interval contains 2000 episodes. In (a), each point in an interval corresponds to the probability of occurrence of a successful episode (see Eq. \ref{['eq:success_equation']}). The results are averaged over 15 random seeds (i.e. initialization) of the networks. The range defines the best performance of each interval for both networks. The range defines the region between the best and the worst performance in each interval for both networks.
• Figure 4: The number of splines ($k$) has more impact in improving and stabilizing the performance of the KAN than the grid size ($G$). Here we measure the improvement of the KAN while constructing the GHZ state by calculating the average number of gates and depth in each setting. Each point is marked as $(a,b)$ where $a$ is the total number of successful episodes and $b$ total optimal successful episodes.
• Figure 5: KAN outperforms MLP in finding a parameterized quantum circuit that solves the 4-qubit $\texttt{LiH}$ and $\texttt{H}_2$ molecule. We solve a molecule when its energy goes below the chemical accuracy, i.e., $1.6\times10^{-3}$ Hartree. In the plot, the average corresponds to the average performance of the neural networks over three distinct initializations, and the minimum is the best-performing seed among the three. We consider $\text{KAN}_{4,3}$ that corresponds to a KAN of depth 4 and 3 neurons, whereas $\text{MLP}_{6,1000}$ and $\text{MLP}_{4,100}$ defines MLP of depth 6 with 1000 neurons and MLP of depth 4 with 100 neurons respectively. It should be noted that an MLP of configuration $\text{MLP}_{6,1000}$ outperforms KAN in the number of 2-qubit gates, depth, and the total number of parameters, but the number of trainable parameters required for the MLP is $5.15\times10^6$ which is very large compared to $5.52\times10^4$ parameters of KAN.