Higher-Order Methods for Hamiltonian Engineering Pulse Sequence Design

We introduce a framework for designing Hamiltonian engineering pulse sequences that systematically accounts for the effects of higher-order contributions to the Floquet-Magnus expansion. Our techniques result in simple, intuitive decoupling rules, despite the higher-order contributions naively involving complicated, non-local-in-time commutators. We illustrate how these rules can be used to efficiently design improved Hamiltonian engineering pulse sequences for a wide variety of tasks, such as dynamical decoupling, quantum sensing, and quantum simulation.