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While quantum devices rely on interactions between constituent subsystems andwith their environment to operate, native interactions alone often fail todeliver targeted performance. Coherent pulsed control provides the ability totailor effective interactions, known as Hamiltonian engineering. We propose aHamiltonian engineering method that maximizes desired interactions whilemitigating deleterious ones by conducting a pulse sequence search usingconstrained optimization. The optimization formulation incorporates pulsesequence length and cardinality penalties consistent with linear or integerprogramming. We apply the general technique to magnetometry with solid statespin ensembles in which inhomogeneous interactions between sensing spins limitcoherence. Defining figures of merit for broadband Ramsey magnetometry, wepresent novel pulse sequences which outperform known techniques for homonuclearspin decoupling in both spin-1/2 and spin-1 systems. When applied to nitrogenvacancy (NV) centers in diamond, this scheme partially preserves the Zeemaninteraction while zeroing dipolar coupling between negatively chargedNV$^{\text -}$ centers. Such a scheme is of interest for NV$^\text{-}$magnetometers which have reached the NV$^\text{-}$-NV$^\text{-}$ couplinglimit. We discuss experimental implementation in NV ensembles, as well asapplicability of the current approach to more general spin bath decoupling andsuperconducting qubit control.

Hamiltonian Engineering with Constrained Optimization for Quantum Sensing and Control