Time limited optimal dynamics beyond the Quantum Speed Limit

TL;DR

This paper investigates the fundamental limits of quantum system control speed, quantifying the fidelity-time trade-off and proposing a geometric framework for optimizing control protocols beyond the traditional quantum speed limit.

Contribution

It introduces a Hilbert space geometric approach to analyze and optimize quantum control speed and fidelity trade-offs, providing a criterion for control optimality and a classification scheme for control sequences.

Findings

Predicts the quantum speed limit using Hilbert velocity.

Provides a method to adapt control for desired fidelity.

Verifies results numerically in multilevel systems.

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.