A framework for the benchmarking of transport-induced excitations in shuttling-based ion-trap quantum processors
We develop a theoretical and numerical framework to analyze the effect of transport on the motional states of ions in a trapped-ion quantum processor. We decompose the shuttling protocol into primitive operations and characterize these in terms of their heating performance. Instead of having to simulate the whole transport protocol for each complete ion trajectory, the method allows us to determine the heating properties of each primitive operation separately and obtain the global result through an algebraic expression. We demonstrate our method by applying it to an 8-qubit quantum processor design based on linear transport and swap operations for all-to-all connectivity. We show how to incorporate the price of motional operations at the level of the compiler as a cost function.