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

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.

References in corpus (13)

• Bloch vectors for qudits
• Teaching the Environment to Control Quantum Systems
• Controllability of open quantum systems with Kraus-map dynamics
• Optimal quantum control of Bose-Einstein condensates in magnetic microtraps: Comparison of GRAPE and Krotov optimization schemes
• Engineering arbitrary pure and mixed quantum states
• Control Landscapes for Observable Preparation with Open Quantum Systems
• Control landscapes for two-level open quantum systems
• Measurement-assisted Landau-Zener transitions
• Optimization search effort over the control landscapes for open quantum systems with Kraus-map evolution
• Dissipation control in cavity QED with oscillating mode-structures
• Femtosecond Photoionization of Atoms under Noise
• Incoherent control of optical signals; quantum heat engine approach
• Numerical estimation of reachable and controllability sets for a two-level open quantum system driven by coherent and incoherent controls