Minimizing irreversible losses in quantum systems by local counterdiabatic driving

Significance Losses are ubiquitous in manipulating complex systems. They arise from our lack of control on the microscopic degrees of freedom of the system. A universal way to minimize losses is to consider adiabatic processes. These processes are, however, very slow, which significantly limits their power. In this work, we show how to speed up these protocols for general complex (quantum) systems. Although dissipation cannot be avoided, we show how it can be reduced significantly with only local access to the system. Applications range from quantum information technologies to preparing experiments and even controlling complicated classical systems, such as those found in nature. Counterdiabatic driving protocols have been proposed [Demirplak M, Rice SA (2003) J Chem Phys A 107:9937–9945; Berry M (2009) J Phys A Math Theor 42:365303] as a means to make fast changes in the Hamiltonian without exciting transitions. Such driving in principle allows one to realize arbitrarily fast annealing protocols or implement fast dissipationless driving, circumventing standard adiabatic limitations requiring infinitesimally slow rates. These ideas were tested and used both experimentally and theoretically in small systems, but in larger chaotic systems, it is known that exact counterdiabatic protocols do not exist. In this work, we develop a simple variational approach allowing one to find the best possible counterdiabatic protocols given physical constraints, like locality. These protocols are easy to derive and implement both experimentally and numerically. We show that, using these approximate protocols, one can drastically suppress heating and increase fidelity of quantum annealing protocols in complex many-particle systems. In the fast limit, these protocols provide an effective dual description of adiabatic dynamics, where the coupling constant plays the role of time and the counterdiabatic term plays the role of the Hamiltonian.