  Quantum technology resorts to efficient utilization of quantum resources to
realize technique innovation. The systems are controlled such that their states
follow the desired manners to realize different quantum protocols. However, the
decoherence caused by the system-environment interactions causes the states
deviating from the desired manners. How to protect quantum resources under the
coexistence of active control and passive decoherence is of significance.
Recent studies have revealed that the decoherence is determined by the feature
of the system-environment energy spectrum: Accompanying the formation of bound
states in the energy spectrum, the decoherence can be suppressed. It supplies a
guideline to control decoherence. Such idea can be generalized to systems under
periodic driving. By virtue of manipulating Floquet bound states in the
quasienergy spectrum, coherent control via periodic driving dubbed as Floquet
engineering has become a versatile tool not only in controlling decoherence,
but also in artificially synthesizing exotic topological phases. We will review
the progress on quantum control in open and periodically driven systems.
Special attention will be paid to the distinguished role played by the bound
states and their controllability via periodic driving in suppressing
decoherence and generating novel topological phases.
