Numeric Optimization for Configurable, Parallel, Error-Robust Entangling Gates in Large Ion Registers

A class of entangling gates for trapped atomic ions is studied and the use of numeric optimization techniques to create a wide range of fast, error-robust gate constructions is demonstrated. A numeric optimization framework is introduced targeting maximally- and partially-entangling operations on ion pairs, multi-ion registers, multi-ion subsets of large registers, and parallel operations within a single register. Ions are assumed to be individually addressed, permitting optimization over amplitude- and phase-modulated controls. Calculations and simulations demonstrate that the inclusion of modulation of the difference phase for the bichromatic drive used in the Molmer-Sorensen gate permits approximately time-optimal control across a range of gate configurations, and when suitably combined with analytic constraints can also provide robustness against key experimental sources of error. The impact of experimental constraints such as bounds on coupling rates or modulation band-limits on achievable performance is further demonstrated. Using a custom optimization engine based on TensorFlow, for optimizations on ion registers up to 20 ions, time-to-solution of order tens of minutes using a local-instance laptop is also demonstrated, allowing computational access to system-scales relevant to near-term trapped-ion devices.