Energy shortcut of N-level quantum protocols by optimal control

Abstract

We introduce an energetically-optimal method inspired from Shortcut-To-Adiabaticity (STA) processes, named Quantum-Optimal-Shortcut-To-Energetics (QOSTE). QOSTE produces the same transformation as STA for a given protocol used in quantum technologies or thermodynamics, but at the lowest possible energy cost. In the general case of a N- level quantum system, we derive the QOSTE controls using geometrical and optimal control tools, and show that the minimal energy cost is determined by the length of the geodesic in the rotating frame given by the original protocol. For long control times, the scaling of the ratio between the two energy costs of STA and QOSTE is quadratic in time. We benchmark our results with the Landau-Zener protocol for qubits and STIRAP for three-level systems. We observe a drastic reduction in energy with respect to standard STA methods. Finally, using gradient-based optimization algorithms and highlighting the emerging trade-off between robustness and energy cost, we design robust QOSTE outperforming STA both in robustness and energy efficiency.