Minimal Time Generation of Density Matrices for a Two-Level Quantum System Driven by Coherent and Incoherent Controls

TL;DR

This paper develops a method to rapidly control a two-level quantum system's state using combined coherent and incoherent controls, optimizing the process in minimal time through numerical techniques.

Contribution

It introduces a novel approach to optimize control strategies for two-level quantum systems by reformulating the problem in the Bloch ball and applying Pontryagin's maximum principle.

Findings

Successfully computed minimal control times for various state transitions.

Demonstrated the effectiveness of combined coherent and incoherent controls.

Provided a general numerical framework for optimal quantum control.

Abstract

The article considers a two-level open quantum system whose dynamics is driven by a combination of coherent and incoherent controls. Coherent control enters into the Hamiltonian part of the dynamics whereas incoherent control enters into the dissipative part. The goal is to find controls which move the system from an initial density matrix to a given target density matrix as fast as possible. To achieve this goal, we reformulate the optimal control problem in terms of controlled evolution in the Bloch ball and then apply Pontryagin maximum principle and gradient projection method to numerically find minimal time and optimal coherent and incoherent controls. General method is provided and several examples of initial and target states are explicitly considered.