Graph attention-based neural embedding for atom placement optimization in neutral atom quantum computing

Neutral-atom quantum computing has emerged as a promising platform for programmable quantum systems due to its flexible geometry and controllable interactions between qubits. In these architec- tures, the spatial arrangement of atoms plays a crucial role, as it directly determines the interaction graph that can be realized on hardware. This thesis investigates the fundamentals of neutral-atom quantum computing and explores the use of machine learning to optimize atom placement in quantum registers. Starting from the method proposed in the paper "Neural-powered unit disk graph embedding qubits connectivity for some QUBO problems", which employs a neural network to generate spatial embeddings compatible with hardware constraints, this work develops an enhanced architecture aimed at improving the quality and generalization of the learned embeddings. In particular, the original approach is extended by introducing a Graph Neural Network capable of explicitly modeling the structure of the interaction graph. The proposed model leverages Graph Attention layers to learn adaptive importance weights between nodes, allowing the network to better capture relational dependencies and structural patterns in the graph during the embedding process. The improved architecture is evaluated on a simplified formulation of a quantum molecular docking problem, where molecular interaction constraints must be translated into feasible atom placements on a neutral-atom quantum device. The resulting toy model demonstrates how graph-based neural ar- chitectures, especially attention-based mechanisms, can improve the optimization of atom positions by iteratively adjusting graph node coordinates to satisfy the physical constraints of neutral-atom quantum registers.