Optimization of Time-Dependent Decoherence Rates and Coherent Control for a Qutrit System

TL;DR

This paper develops optimal control strategies for a three-level quantum system (qutrit) with time-dependent decoherence, combining coherent and incoherent controls to improve state preparation accuracy.

Contribution

It introduces a novel control framework that optimizes both coherent and incoherent processes in a qutrit system, including derivation of gradients and adaptation of Krotov's method.

Findings

Control methods effectively optimize state overlap and distance measures.

Incoherent control enables environment resource utilization.

Numerical results demonstrate improved control performance.

Abstract

The work considers an open qutrit system whose density matrix $\rho(t)$ evolution is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation with simultaneous coherent (in the Hamiltonian) and incoherent (in the superoperator of dissipation) controls. Incoherent control makes the decoherence rates depending on time in a specific controlled manner and within clear physical mechanics. We consider the problem of maximizing the Hilbert-Schmidt overlap between the system's final state $\rho(T)$ and a given target state $\rho_{\rm target}$ and the problem of minimizing the squared Hilbert-Schmidt distance between these states. For the both problems, we perform their realifications, derive the corresponding Pontryagin function, adjount system (with the two cases of transversality conditions in view of the two terminal objectives), and gradients of the objectives, adapt the one-, two-, three-step gradient projection methods. For the problem of maximizing the overlap, we also adapt the regularized first-order Krotov method. In the numerical experiments, we analyze, first, the methods' operation and, second, the obtained control processes, in respect to considering the environment as a resource via incoherent control.