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A common way to manipulate a quantum system, for example spins or artificialatoms, is to use properly tailored control pulses. In order to accomplishquantum information tasks before coherence is lost, it is crucial to implementthe control in the shortest possible time. Here we report the near time-optimalpreparation of a Bell state with fidelity higher than $99\%$ in an NMRexperiment, which is feasible by combining the synergistic capabilities ofmodelling and experiments operating in tandem. The pulses preparing the Bellstate are found by experiments that are recursively assisted with agradient-based optimization algorithm working with a model. Thus, we explorethe interplay between model-based numerical optimal design andexperimental-based learning control. Utilizing the balanced synergism betweenthe dual approaches should have broad applications for accelerating the searchfor optimal quantum controls.

Combining the synergistic control capabilities of modelling and experiments: illustration of finding a minimum time quantum objective