  Pointer states are long-lasting high-fidelity states in open quantum systems.
We show how any pure state in a non-Markovian open quantum system can be made
to behave as a pointer state by suitably engineering the coupling to the
environment via open-loop periodic control. Engineered pointer states are
constructed as approximate fixed points of the controlled open-system dynamics,
in such a way that they are guaranteed to survive over a long time with a
fidelity determined by the relative precision with which the dynamics is
engineered. We provide quantitative minimum-fidelity bounds by identifying
symmetry and ergodicity conditions that the decoherence-inducing perturbation
must obey in the presence of control, and develop explicit pulse sequences for
engineering any desired set of orthogonal states as pointer states. These
general control protocols are validated through exact numerical simulations as
well as semi-classical approximations in realistic single and two qubit
dissipative systems. We also examine the role of control imperfections, and
show that while pointer-state engineering protocols are highly robust in the
presence of systematic pulse errors, the latter can also lead to unintended
pointer-state generation in dynamical decoupling implementations, explaining
the initial-state selectivity observed in recent experiments.
