Fast-forward scaling and shortcuts to adiabaticity

Fast-forward scaling is a method to realize given dynamics within a different time, and shortcuts to adiabaticity are methods to realize adiabatic time evolution or to obtain a final result of adiabatic time evolution within a short time. Fast-forward scaling can be applied to adiabatic time evolution, and thus it is regarded as one of the methods of shortcuts to adiabaticity. Relations between different methods of shortcuts to adiabaticity have been discussed.

In this talk, we revisit a relation between fast-forward scaling and counterdiabatic driving, which is one of the methods of shortcuts to adiabaticity. By adopting expression of fast-forward scaling in [Hatomura, SciPost Physics 15, 036 (2023)], we reformulate application of fast-forward scaling to counterdiabatic driving and the procedure of regularization. Then, we find clear equivalence between fast-forward scaling of adiabatic time evolution and counterdiabatic driving. Our finding builds a bridge between fast-forward scaling and counterdiabatic driving.