Time-optimal control of a two-level dissipative quantum system

TL;DR

This paper analyzes the time-optimal control strategies for a dissipative two-level quantum system using geometric control theory, revealing how dissipation can sometimes aid in faster state transformations.

Contribution

It applies geometric control theory to construct the optimal synthesis for a dissipative quantum system, a novel approach in this context.

Findings

Dissipation can accelerate certain quantum state transformations.

Optimal trajectories for state conversion and purification are characterized.

The control synthesis provides comprehensive guidance for manipulating the system efficiently.

Abstract

We propose an analysis of the time-optimal control of a dissipative two-level quantum system whose dynamics is governed by the Lindblad equation. This simple system allows one to use tools of geometric control theory and to construct its optimal synthesis, i.e. to determine the set of all the optimal trajectories starting from a given initial point. We study different processes such as conversion of a pure state into a mixed state and purification of a mixed state. In particular cases, we show that dissipation is not undesirable and can help accelerating the control.