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Programmable arrays of optical traps enable the assembly of configurations ofsingle atoms to perform controlled experiments on quantum many-body systems.Finding the sequence of control operations to transform an arbitraryconfiguration of atoms into a predetermined one requires solving an atomreconfiguration problem quickly and efficiently. A typical approach to solveatom reconfiguration problems is to use an assignment algorithm to determinewhich atoms to move to which traps. This approach results in control protocolsthat exactly minimize the number of displacement operations; however, thisapproach does not optimize for the number of displaced atoms nor the number oftimes each atom is displaced, resulting in unnecessary control operations thatincrease the execution time and failure rate of the control protocol. In thiswork, we propose the assignment-rerouting-ordering (aro) algorithm to improvethe performance of assignment-based algorithms in solving atom reconfigurationproblems. The aro algorithm uses an assignment subroutine to minimize the totaldistance traveled by all atoms, a rerouting subroutine to reduce the number ofdisplaced atoms, and an ordering subroutine to guarantee that each atom isdisplaced at most once. The ordering subroutine relies on the existence of apartial ordering of moves that can be obtained using a polynomial-timealgorithm that we introduce within the formal framework of graph theory. Wenumerically quantify the performance of the aro algorithm in the presence andin the absence of loss, and show that it outperforms the exact, approximation,and heuristic algorithms that we use as benchmarks. Our results are useful forassembling large configurations of atoms with high success probability and fastpreparation time, as well as for designing and benchmarking novel atomreconfiguration algorithms.

Efficient algorithms to solve atom reconfiguration problems. II. The assignment-rerouting-ordering (aro) algorithm