Noise resistant quantum control using dynamical invariants

A systematic approach to design robust control protocols against the influence of different types of noise is introduced. We present control schemes which protect the decay of the populations avoiding dissipation in the adiabatic and non-adiabatic regimes and minimize the effect of dephasing. The effectiveness of the protocols is demonstrated in two different systems. Firstly we present the case of population inversion of a two level system in the presence of either one or two simultaneous noise sources. Secondly, we present an example of the expansion of coherent and thermal states in harmonic traps, subject to noise arising from monitoring and modulation of the control respectively.