  A quantum memory interacts with its environment and loses information via
decoherence as well as incoherence. A robust quantum control that prepares,
preserves, and manipulates nonclassical correlations even in the presence of
environmental influence is of paramount importance in quantum information
processing. A well-known technique to suppress decoherence, namely Dynamical
Decoupling (DD), consists of a sequence of rapid flips applied to the system in
order to refocus the system-environment interactions. In this work, we
integrate DD with quantum gates using optimal control techniques to realize
robust quantum gates which offer protection against decoherence. To investigate
the protection of non-classical correlation, we study the evolution of quantum
discord in Grover's search algorithm implemented with dynamically protected
gates. Using a two-qubit NMR system, we experimentally demonstrate a
significant protection against decoherence and incoherence. We find better
performances by phase alternating DD sequences with suitable spacings between
the DD pulses. Interestingly, we also find that DD sequences based on $\pi/2$
pulses perform as well as or even better than those with $\pi$ pulses in
protecting the non-classical correlation. We also support the experimental
results by analyzing the robustness of various DD schemes.
