Counterdiabatic, Better, Faster, Stronger: Optimal control for approximate counterdiabatic driving

Adiabatic protocols are employed across a variety of quantum technologies, from implementing state preparation and individual operations that are building blocks of larger devices, to higher-level protocols in quantum annealing and adiabatic quantum computation. The main drawback of adiabatic processes, however, is that they require prohibitively long timescales. This generally leads to losses due to decoherence and heating processes. The problem of speeding up system dynamics while retaining the adiabatic condition has garnered a large amount of interest, resulting in a whole host of diverse methods and approaches made for this purpose. This thesis is dedicated to the discovery of new ways to combine optimal control techniques with a universal method from STA: counterdiabatic driving (CD). The CD approach offers perfect suppression of all non-adiabatic effects experienced by a system driven by a time-dependent Hamiltonian regardless of how fast the process occurs. In practice, however, exact CD is difficult to derive often even more difficult to implement. The main result presented in the thesis is thus the development of a new method called counterdiabatic optimized local driving (COLD), which implements optimal control techniques in tandem with \emph{approximations} of exact CD in a way that maximises suppression of non-adiabatic effects.