Time limited optimal dynamics beyond the Quantum Speed Limit

Abstract

The quantum speed limit sets the minimum time required to transfer a quantum system completely into a given target state. At shorter times the higher operation speed has to be paid with a loss of fidelity. Here we quantify the trade-off between the fidelity and the duration in a system driven by a time-varying control. The problem is addressed in the framework of Hilbert space geometry offering an intuitive interpretation of optimal control algorithms. This approach is applied to non-uniform time variations which leads to a necessary criterion for control optimality applicable as a measure of algorithm convergence. The time fidelity trade-off expressed in terms of the direct Hilbert velocity provides a robust prediction of the quantum speed limit and allows to adapt the control optimization such that it yields a predefined fidelity. The results are verified numerically in a multilevel system with a constrained Hamiltonian, and a classification scheme for the control sequences is proposed based on their optimizability.

7 pages, 4 figures

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Cited by in corpus (11)

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• Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
• Exploring the Quantum Speed Limit with Computer Games
• Mechanism for quantum speedup in open quantum systems
• Introduction to Theoretical and Experimental aspects of Quantum Optimal Control
• Quantum Optimal Control: Landscape Structure and Topology
• Quantum Control in Open and Periodically Driven Systems
• Global optimization for quantum dynamics of few-fermion systems
• Optimal entanglement generation in optomechanical systems via Krotov control of covariance matrix dynamics
• Analysis of lower bounds for quantum control times and their relation to the quantum speed limit
• Effect of two-qutrit entanglement on quantum speed limit time of a bipartite V-type open system