Optimal control for state preparation in two-qubit open quantum systems driven by coherent and incoherent controls via GRAPE approach

TL;DR

This paper develops a GRAPE-based optimal control method for two-qubit open quantum systems driven by both coherent and incoherent controls, focusing on state preparation with analytical gradient derivation and analysis of entropy and purity evolution.

Contribution

It introduces an analytical gradient expression for the control problem involving incoherent controls and compares different interaction classes in two-qubit systems.

Findings

Optimized controls significantly affect entropy and purity dynamics.

Different interaction classes exhibit distinct behaviors under GRAPE optimization.

Analytical gradient facilitates efficient control optimization in open quantum systems.

Abstract

In this work, we consider a model of two qubits driven by coherent and incoherent time-dependent controls. The dynamics of the system is governed by a Gorini-Kossakowski-Sudarshan-Lindblad master equation, where coherent control enters into the Hamiltonian and incoherent control enters into both the Hamiltonian (via Lamb shift) and the dissipative superoperator. We consider two physically different classes of interaction with coherent control and study the optimal control problem of state preparation formulated as minimization of the Hilbert-Schmidt distance's square between the final density matrix and a given target density matrix at some fixed target time. Taking into account that incoherent control by its physical meaning is a non-negative function of time, we derive an analytical expression for the gradient of the objective and develop optimization approaches based on adaptation for this problem of GRadient Ascent Pulse Engineering (GRAPE). We study evolution of the von Neumann entropy, purity, and one-qubit reduced density matrices under optimized controls and observe a significantly different behavior of GRAPE optimization for the two classes of interaction with coherent control in the Hamiltonian.