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arXiv · 1405.6079

Time limited optimal dynamics beyond the Quantum Speed Limit

Miroslav Gajdacz·Kunal K. Das·Jan Arlt·Jacob F. Sherson·Tomáš Opatrný
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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.

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Miroslav Gajdacz, Kunal K. Das, Jan Arlt, Jacob F. Sherson, Tomáš Opatrný. 2014-05-23. Time limited optimal dynamics beyond the Quantum Speed Limit. https://doi.org/10.1103/physreva.92.062106

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