Felix Motzoi

The Mølmer-Sørensen gate is a widely used entangling gate for ion platforms with inherent robustness to trap heating. The gate performance is limited by coherent errors, arising from the Lamb-Dicke (LD) approximation and sideband errors. Here, we provide explicit analytical formulas for errors up to fourth order in the LD parameter, by using the Magnus expansion to match numerical precision, and overcome significant, orders-of-magnitude underestimation of errors by previous theory methods. We show that fourth order Magnus expansion terms are unavoidable, being in fact leading order in LD, and are therefore critical to include for typical experimental fidelity ranges. We show how these errors can be dramatically reduced compared to previous theory by using analytical renormalization of the drive strength, by calibration of the Lamb-Dicke parameter, and by the use of smooth pulse shaping.

Shortening quantum circuits is crucial to reducing the destructive effect of environmental decoherence and enabling useful algorithms. Here, we demonstrate an improvement in such compilation tasks via a combination of using hybrid discrete-continuous optimization across a continuous gate set, and architecture-tailored implementation. The continuous parameters are discovered with a gradient-based optimization algorithm, while in tandem the optimal gate orderings are learned via a deep reinforcement learning algorithm, based on projective simulation. To test this approach, we introduce a framework to simulate collective gates in trapped-ion systems efficiently on a classical device. The algorithm proves able to significantly reduce the size of relevant quantum circuits for trapped-ion computing. Furthermore, we show that our framework can also be applied to an experimental setup whose goal is to reproduce an unknown unitary process.