Numerical estimation of reachable and controllability sets for a two-level open quantum system driven by coherent and incoherent controls

TL;DR

This paper develops numerical methods to estimate the reachable and controllability sets of a two-level open quantum system using Bloch parametrization and optimization techniques, accounting for control constraints.

Contribution

It introduces an adapted section method combined with differential evolution and dual annealing to estimate reachable sets in quantum control systems with constraints.

Findings

Reachable sets depend on initial state distance and control constraints.

Estimation accuracy varies with final time and control variation limits.

Numerical results demonstrate the method's effectiveness in quantum control analysis.

Abstract

The article considers a two-level open quantum system, whose evolution is governed by the Gorini--Kossakowski--Lindblad--Sudarshan master equation with Hamiltonian and dissipation superoperator depending, correspondingly, on piecewise constant coherent and incoherent controls with constrained magnitudes. Additional constraints on controls' variations are also considered. The system is analyzed using Bloch parametrization of the system's density matrix. We adapt the section method for obtaining outer parallelepipedal and pointwise estimations of reachable and controllability sets in the Bloch ball via solving a number of problems for optimizing coherent and incoherent controls with respect to some objective criteria. The differential evolution and dual annealing optimization methods are used. The numerical results show how the reachable sets' estimations depend on distances between the system's initial states and the Bloch ball's center point, final times, constraints on controls' magnitudes and variations.