Speeding up Lindblad dynamics via time-rescaling engineering

Abstract: We introduce a universal method for accelerating Lindblad dynamics that preserves the original trajectory through Hilbert space. The technique provides exact fast processes analytically, which are Markovian and do not require manipulation of the environment properties, by time-rescaling a reference dynamics. In particular, the engineered control protocols are based only on local interactions, and no additional control fields are required compared to the reference protocol. We demonstrate the scheme with two examples: a driven two-level system in an amplitude damping channel and the dissipative transverse field Ising model. We also show that, by starting with a reference process which is the fastest connecting two states under a certain constraint, the method provides other optimal processes satisfying modified constraints. Our approach can help advance techniques for quantum control and computation towards more complex noisy systems.