Efficient algorithms to solve atom reconfiguration problems. I. Redistribution-reconfiguration algorithm

We propose the redistribution-reconfiguration~(red-rec) algorithm to efficiently compute control protocols assemble compact-centered configurations of atoms in two-dimensional arrays optical traps with lattice geometries. The red-rec redistributes among pairs donor-receiver columns and reconfigures each column using an exact displacement-minimizing algorithm, harnessing parallel operations that simultaneously actuate multiple reduce execution time. numerically quantify performance both absence presence loss, realistic physical parameters operational constraints. show number required prepare a configuration on grid mean success probability one half scales as 3/2 power desired atoms, highlighting challenges assembling tens thousands atoms. further demonstrate faster preparation times can be achieved by rejecting containing fewer than given threshold. admits efficient implementation readily deployed real-time systems large high fast times.