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An optimal dynamical decoupling of a quantum system coupled to a noisyenvironment must take into account also the imperfections of the controlpulses. We present a new formalism which describes, in a closed-formexpression, the evolution of the system, including the spectral function ofboth the environment and control noise. We show that by measuring thesespectral functions, our expression can be used to optimize the decoupling pulsesequence. We demonstrate this approach with an ensemble of optically trappedultra-cold Rubidium atoms, and use quantum process tomography to identify theeffect of the environment and control noise. Our approach is applicable andimportant for any realistic implementation of quantum information processing.

Optimal dynamical decoupling in the presence of colored control noise