Time-optimal navigation through quantum wind

TL;DR

This paper addresses the problem of finding the fastest way to control a quantum system under external influences by deriving a universal speed limit and providing a complete solution, especially illustrated for two-level systems.

Contribution

It introduces a universal quantum speed limit for time-optimal quantum navigation and offers a complete solution applicable to arbitrary quantum systems, simplifying the problem via the interaction picture.

Findings

Derived a universal quantum speed limit for navigation.

Provided a complete solution for arbitrary quantum systems.

Illustrated the solution with a two-level system example.

Abstract

The quantum navigation problem of finding the time-optimal control Hamiltonian that transports a given initial state to a target state through quantum wind, that is, under the influence of external fields or potentials, is analysed. By lifting the problem from the state space to the space of unitary gates realising the required task, we are able to deduce the form of the solution to the problem by deriving a universal quantum speed limit. The expression thus obtained indicates that further simplifications of this apparently difficult problem are possible if we switch to the interaction picture of quantum mechanics. A complete solution to the navigation problem for an arbitrary quantum system is then obtained, and the behaviour of the solution is illustrated in the case of a two-level system.