Structure-Aware Compilation for Scalable Neutral-Atom Quantum Computing

We study the compilation of structured quantum gate families on two-dimensional neutral-atom arrays, aiming to reduce addressing and transport overhead under realistic hardware constraints. For single-qubit gates, we exploit the algebraic structures of gate families at the matrix level, enabling efficient rank-one decompositions over appropriate algebraic structures and thereby reducing the number of addressing layers. For controlled-Z (C-Z) gates, we formulate the transport scheduling problem using graph-theoretic models, leading to efficient compilation algorithms under realistic transport constraints. We provide provable performance guarantees for the proposed methods and validate them through extensive numerical experiments. Across representative single-qubit gate families, our methods reduce the number of addressing layers by up to a factor of two compared with na\"ive row- or column-wise implementations. For C-Z gates, our scheduling strategy reduces the required number of atom transport operations by approximately 50\%. When applied to QAOA circuits for MaxCut, the proposed framework reduces transport cost by more than 30\% on average. These results show that the physical constraints of neutral-atom hardware can be converted into algebraic and graph-theoretic structure, turning a hardware-level scheduling bottleneck into tractable decomposition and coloring problems.