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.
Comment: 12+10 pages, 6 figures, see accompanying paper "Robust Higher-Order Hamiltonian Engineering for Quantum Sensing with Strongly Interacting Systems" for application of these techniques to quantum sensing