  An important issue in developing quantum technology is that quantum states
are so sensitive to noise. We propose a protocol that introduces reverse
dynamics, in order to precisely control quantum systems against noise described
by the Lindblad master equation. The reverse dynamics can be obtained by
constructing the Petz recovery map in continuous time. By providing the exact
form of the Hamiltonian and jump operators for the reverse dynamics, we explore
the potential of utilizing the near-optimal recovery of the Petz map in
controlling noisy quantum dynamics. While time-dependent dissipation
engineering enables us to fully recover a single quantum trajectory, we also
design a time-independent recovery protocol to protect encoded quantum
information against decoherence. Our protocol can efficiently suppress only the
noise part of dynamics thereby providing an effective unitary evolution of the
quantum system.
