Quantum Speed Limit and optimal evolution time in a two-level system
arXiv:1308.1709 · doi:10.1209/0295-5075/104/40005
Abstract
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.
(6 pages, 5 figures). The paper has been modified after discussion with peers, which revealed misconceptions about the ideas of quantum speed limit and optimal evolution time. The focus of the article has been moved to the relation between both concepts in a quantum control scenario
References in corpus (7)
- Quantum speed limit for physical processes
- Quantum speed limit for non-Markovian dynamics
- Quantum speed limits in open system dynamics
- High-fidelity quantum driving
- Transient energy excitation in shortcuts to adiabaticity for the time dependent harmonic oscillator
- Comment on "Geometric derivation of the quantum speed limit"
- Controlling open quantum systems using fast transitions
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- Hybrid quantum-classical simulation of quantum speed limits in open quantum systems
- Reachable Set Characterization of Open Quantum System by Quantum Speed Limit
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- An automated geometric space curve approach for designing dynamically corrected gates
- Attainable quantum speed limit for N-dimensional quantum systems
- Nonlinear speed-ups in ultracold quantum gases