The notion of moving objects through time the same way that we move them through space has been present in popular culture since the publication in 1895 of H.G. Well’s The Time Machine. The topic of time manipulation or time warping is, however, much older: it already features in Indian texts from year 400 B.C., and was the subject of a number of theological discussions in Europe during the Middle Ages.
In  we investigate this question from the point of view of non-relativistic quantum theory. Surprisingly, we find that one can engineer particle beams with the property to make any quantum system they scatter with leap backwards in time!
The scenario we consider is as follows: a closed system has been following a unitary evolution for a time T. Our goal is to reset its quantum state to the state it had at time t=0, way long before we started interacting with it in the first place. Moreover, this system, the target, is uncontrolled: that means that we not only ignore how the target evolves by itself, but also with other quantum systems we may use to manipulate it.
In order to interact with the target, we send a quantum system (a probe) close to it and back to a controlled lab, see the figure above. We assume no knowledge on the interaction between the target and the probe. We then wait for time T and repeat these above steps a number of times. At the end of the protocol, we measure the returned probes in the lab.
Under these conditions, we show that there exists a way to prepare and process the quantum probes such that, if the final measurement is successful, the target system is projected to its past quantum state at time t=0. The probability of success of this quantum resetting protocol is non-zero for all possible (unitary) interactions between the target and the probe, save a subset of measure zero. Moreover, if the protocol fails, we can still run a second protocol that undoes both the effect of the prior evolution of the target and the failed resetting protocol. If that second protocol also fails, we can carry out a third one to undo both protocols and the past evolution, etcetera, etcetera.
The simplest quantum resetting protocols exhibit an average probability of success of 22% when the interaction between probe and target is completely random and just require manipulating four two-level system probes. This is already within reach of current quantum technologies, so an experimental realization of quantum time-warping is around the corner.
„Translating Uncontrolled Systems in Time“, David Trillo, Benjamin Dive, and Miguel Navascués, Quantum, 2020
 M. Navascués, Resetting uncontrolled quantum systems, Phys. Rev. X 031008 (2018).