# Time-optimal purification of a qubit in contact with a structured environment

## TL;DR

This paper explores the fastest methods to purify a qubit interacting with a structured environment, revealing that resonance strategies optimize the process and coherence can accelerate purification.

## Contribution

It introduces a geometric approach to determine time-optimal control strategies for qubit purification in structured environments, highlighting the role of resonance and coherence.

## Key findings

- Resonance with the reservoir mode optimizes purification speed.
- Weak and strong coupling regimes both favor resonance control strategies.
- Qubit coherence and system-environment correlations can enhance control efficiency.

## Abstract

We investigate the time-optimal control of the purification of a qubit interacting with a structured environment, consisting of a strongly coupled two-level defect in interaction with a thermal bath. On the basis of a geometric analysis, we show for weak and strong interaction strengths that the optimal control strategy corresponds to a qubit in resonance with the reservoir mode. We investigate when qubit coherence and correlation between the qubit and the environment speed-up the control process.