Multi-qubit gate configurations for quantum sensing and simulation in a Penning ion trap with three-dimensional crystals*

We summarize results obtained with two-dimensional ion crystals in the NIST Penning trap that demonstrate our capabilities for both quantum simulations and sensing of weak electric fields and forces. Repeating these experiments with larger numbers of ions in a 3D crystal could significantly improve upon these results. With 2D crystals, we drive spin-motion coupling and multi-qubit entangling gates using a light-shift (LS) gate. This gate cannot be straightforwardly extended for use in 3D crystals. A leading source of error in this gate is spontaneous emission induced by the off-resonant laser beams, so any alternative gate protocol should have spontaneous emission error rates no higher than those in our current configuration. A Mølmer-Sørensen (MS) gate, in which the laser beams are detuned from each other by approximately the qubit splitting, can be configured to enable quantum operations in three-dimensional crystals. We demonstrate theoretically that we can perform the MS gate with errors due to spontaneous emission comparable to those in the LS gate and examine multiple operating configurations to determine the most favorable parameters for experiments in the future.