Efficient atom rearrangements for quantum error correction primitives with a single AOD

Neutral-atom quantum computers offer arbitrary connectivity enabled by atom transport. Some logical operations can then be simplified or reduced entirely to geometric rearrangements of the atoms. Minimizing the duration of these movements is therefore essential for high logical throughput. We introduce new primitives to shear, rotate and reflect 2D arrays of atoms in a static lattice using sweeps of a single dynamic crossed acousto-optic deflector (AOD) pair. Using (nega-)binary and geometric decompositions, we achieve an AOD stroke count scaling logarithmically in the linear size of the array. In one example, we use the Paeth decomposition to implement a $90^{\circ}$ rotation for a transversal Hadamard gate in a rotated surface code of distance $d$ in $3\lfloor\log_2(d-1)\rfloor + 4$ AOD strokes and $O(d^{1/3})$ constant-jerk time, against $O(d^2)$ strokes and $O(d^{7/3})$ time for atom-by-atom rearrangement.