High-Speed Driving of a Two-Level System

Abstract

A remarkably simple result is found for the optimal protocol of drivings for a general two-level Hamiltonian which transports a given initial state to a given final state in minimal time. If one of the three possible drivings is unconstrained in strength the problem is analytically completely solvable. A surprise arises for a class of states when one driving is bounded by a constant $c$ and the other drivings are constant. Then, for large $c$, the optimal driving is of type bang-off-bang and for increasing $c$ one recovers the unconstrained result. However, for smaller $c$ the optimal driving can suddenly switch to bang-bang type. It is also shown that for general states one may have a multistep protocol. The present paper explicitly proves and considerably extends the author's results contained in Phys. Rev. Lett. {\bf 111}, 260501 (2013).

10 pages, 4 figures, typos corrected

References in corpus (4)

• Quantum speed limit for physical processes
• Quantum speed limits in open system dynamics
• Optimal control of a qubit in an optical cavity
• Control of conditional quantum beats in cavity QED: amplitude decoherence and phase shifts

Cited by in corpus (6)

• Classical-driving-assisted quantum speed-up
• Quantum-speed-limit time for multiqubit open systems
• Time-optimal control of a dissipative qubit
• Reverse engineering protocols for controlling spin dynamics
• Resonant shortcuts for adiabatic rapid passage with only $z$-field control
• Hybrid quantum-classical simulation of quantum speed limits in open quantum systems