Filtering noise through quantum control in high-dimensional systems

Engineering-inspired filter functions are a powerful heuristic for the development of noise-robust quantum logic operations. We expand on existing single-qubit approaches and present a generalized, computationally efficient framework to calculate filter functions for operations performed on D-dimensional manifolds such as pairs of interacting qubits (including spectator levels), and qudits. We describe the computational approach and illustrate application in both systems. Filter function predictions for noise susceptibility in Molmer-Sorensen entangling gates are experimentally validated via experiments on trapped ions, showing good agreement with no free parameters.