Energy-saving fast-forward scaling

We propose energy-saving fast-forward scaling. Fast-forward scaling is a method which enables us to speed up (or slow down) given dynamics in a certain measurement basis. We introduce energy costs of fast-forward scaling, and find possibility of energy-saving speedup for time-independent measurement bases. As concrete examples, we show such energy-saving fast-forward scaling in a two-level system and quantum annealing of a general Ising spin glass. We also discuss the influence of a time-dependent measurement basis, and give a remedy for unwanted energy costs. The present results pave the way for realization of energy-efficient quantum technologies.