Reversing Lindblad Dynamics via Continuous Petz Recovery Map

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.