Square-root Time Atom Reconfiguration Plan for Lattice-shaped Mobile Tweezers

This paper proposes a scalable planning algorithm for creating defect-free atom arrays in neutral-atom systems. The algorithm generates a $\mathcal{O}(\sqrt N)$ time plan for $N$ atoms by parallelizing atom transport using a two-dimensional lattice pattern generated by acousto-optic deflectors. Our approach is based on a divide-and-conquer strategy that decomposes an arbitrary reconfiguration problem into at most three one-dimensional shuttling tasks, enabling each atom to be transported with a total transportation cost of $\mathcal{O}(\sqrt N)$. Using the Gale--Ryser theorem, the proposed algorithm provides a highly reliable solution for arbitrary target geometries. We further introduce a peephole optimization technique that improves reconfiguration efficiency for grid target geometries. Numerical simulations on a 632$\times$632 atom array demonstrate that the proposed algorithm achieves a grid configuration plan that reduces the total transportation cost to 1/7 of state-of-the-art algorithms, while resulting in 32%--35% more atom captures. We believe that our scalability improvement contributes to realizing large-scale quantum computers based on neutral atoms. Our experimental code is available from https://github.com/kotamanegi/sqrt-time-atom-reconfigure.