Fast quantum control via adiabatic resonance

As a major technique to realize quantum gates in superconducting and semiconductor qubits, adiabatic passage (AP) is robust but slow. Here we propose a universal requirement for all schemes aiming at accelerating AP, that we call the "adiabatic resonance" (AR) condition. In essence, the evolution in the adiabatic frame should be cyclic. Furthermore, we design a scheme to realize fast AP by extending the AR condition to multiple AR, namely letting the evolution path periodically return to the adiabatic path. We have applied the AR condition to two- and three-level examples. In particular, we derive the most general condition of AR for an arbitrary two-level system, and apply it in a double quantum dot system to realize rapid adiabatic Landau-Zener transition. The robustness of the scheme is analyzed for low- and high-frequency noises. We also show an example in three-level system to accelerate the adiabatic manipulation and discuss the possibility of optimizing the pulses and the robustness against noisy pulses.