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Quantum mechanics establishes a fundamental bound for the minimum evolution time between two states of a given system. Known as the quantum speed limit (QSL), it is a useful tool in the context of quantum control, where the speed of some control protocol is usually intended to be as large as possible. While QSL expressions for time-independent hamiltonians have been well studied, the time-dependent regime has remained somewhat unexplored, albeit being usually the relevant problem to be compared with when studying systems controlled by external fields. In this paper we explore the relation between optimal times found in quantum control and the QSL bound, in the (relevant) time-dependent regime, by discussing the ubiquitous two-level Landau-Zener type hamiltonian.
A remarkably simple result is derived for the minimal time $T_{rm min}$ required to drive a general initial state to a final target state by a Landau-Zener type Hamiltonian or, equivalently, by time-dependent laser driving. The associated protocol is
One of the fundamental physical limits on the speed of time evolution of a quantum state is known in the form of the celebrated Mandelshtam-Tamm inequality. This inequality gives an answer to the question on how fast an isolated quantum system can ev
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 stre
We investigate if physical laws can impose limit on computational time and speed of a quantum computer built from elementary particles. We show that the product of the speed and the running time of a quantum computer is limited by the type of fundame
We investigate the roles of the relativistic effect on the speed of evolution of a quantum system coupled with amplitude damping channels. We find that the relativistic effect speed-up the quantum evolution to a uniform evolution speed of open quantu