Abstract
We propose and analyze a method to engineer effective interactions in an ensemble of d-level systems (qudits) driven by global control fields. In particular, we present (i)a necessary and sufficient condition under which a given interaction can be decoupled, (ii)the existence of a universal sequence that decouples any (cancelable) interaction, and (iii)an efficient algorithm to engineer a target Hamiltonian from an initial Hamiltonian (if possible). We illustrate the potential of this method with two examples. Specifically, we present a 6-pulse sequence that decouples effective spin-1 dipolar interactions and demonstrate that a spin-1 Ising chain can be engineered to study transitions among three distinct symmetry protected topological phases. Our work enables new approaches for the realization of both many-body quantum memories and programmable analog quantum simulators using existing experimental platforms.
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