Individual qubit addressing of rotating ion crystals in a Penning trap

Trapped ions boast long coherence times and excellent gate fidelities, making them a useful platform for quantum information processing. Penning traps offer the possibility of trapping large two-dimensional crystals of several hundred ions. The ions are confined by controlling the rotation of the ion crystal in the presence of a strong magnetic field. However, the rotation of the ion crystal makes single ion addressability a significant challenge. We propose a protocol that takes advantage of a deformable mirror to introduce AC Stark shift patterns that are static in the rotating frame of the crystal. Through numerical simulations we validate the potential of this protocol to perform high-fidelity single-ion gates in crystalline arrays of hundreds of ions.