Speeding up open quantum dynamics via time-rescaling engineering

The engineering of well controlled fast quantum dynamics is currently a matter of intense debate. This is because such processes may represent a way to improve the performance of noisy intermediate-scale quantum (NISQ) devices upon the realization of quantum protocols within the coherence time with increasingly more qubits. With this motivation, shortcuts to adiabaticity (STA) have been proposed as techniques to speed up adiabatic process. So far, STA have shown success in accelerating the dynamics of closed quantum systems from both theoretical and experimental perspectives. However, many limitations have precluded this advance to reach the realm of open systems. Some of these limitations are: the requirement of non Markovian dynamics, time-dependent Lindblad operators, non-local interventions, approximative methods, and a big number of controlling fields. In this work, we present a new technique to speed up open quantum dynamics, whose solutions for the fast dynamics can be derived analytically in a very simple form. Contrary to previous proposals, here the fast dynamics are Markovian and described in terms of time-independent Lindblad operators. The engineering of the fast processes is based on the time-rescaling of a reference (slow) process, which does not increase the experimental complexity. That is, for a convenient choice of the reference, the fast processes require only local interactions and the same number control fields. All these characteristics may be relevant in the design of control protocols for both closed and open many-body quantum systems. We demonstrate our framework in two cases: the driven two-level system under the action of the amplitude damping channel, and the dissipative transverse Ising model.