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

• URL: http://arxiv.org/abs/2211.02517v1
• Date: Fri, 4 Nov 2022 15:20:18 GMT
• Title: Optimal control for state preparation in two-qubit open quantum systems driven by coherent and incoherent controls via GRAPE approach
• Authors: Vadim Petruhanov and Alexander Pechen
• Abstract summary: 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. We study evolution of the von Neumann entropy, purity, and one-qubit reduced density matrices under optimized controls.
• Score: 77.34726150561087
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Incoherent GRAPE (inGRAPE) for optimization of quantum systems with environmentally assisted control [51.3422222472898]
  We discuss applications of incoherent GRAPE method to high fidelity gate generation for open one- and two-qubit systems. For a qutrit, a formulation of the environment-assisted incoherent control with time-dependent decoherence rates is provided.
  arXiv  Detail & Related papers  (2024-03-26T05:13:26Z)
• Generation of C-NOT, SWAP, and C-Z Gates for Two Qubits Using Coherent and Incoherent Controls and Stochastic Optimization [56.47577824219207]
  We consider a general form of the dynamics of open quantum systems determined by the Gorini-Kossakowsky-Sudarchhan-Lindblad type master equation. We analyze the control problems of generating two-qubit C-NOT, SWAP, and C-Z gates using piecewise constant controls and optimization.
  arXiv  Detail & Related papers  (2023-12-09T17:55:47Z)
• Optimization of Time-Dependent Decoherence Rates and Coherent Control for a Qutrit System [77.34726150561087]
  Incoherent control makes the decoherence rates depending on time in a specific controlled manner. 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.
  arXiv  Detail & Related papers  (2023-08-08T01:28:50Z)
• Optimal State Manipulation for a Two-Qubit System Driven by Coherent and Incoherent Controls [77.34726150561087]
  State preparation is important for optimal control of two-qubit quantum systems. We exploit two physically different coherent control and optimize the Hilbert-Schmidt target density matrices.
  arXiv  Detail & Related papers  (2023-04-03T10:22:35Z)
• On optimization of coherent and incoherent controls for two-level quantum systems [77.34726150561087]
  This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr"odinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
  arXiv  Detail & Related papers  (2022-05-05T09:08:03Z)
• Optimal solutions to quantum annealing using two independent control functions [0.0]
  We show that an optimal solution consists of both controls tuned at their upper bound for the whole evolution time. We propose the use of a quantum optimal control technique adapted to limit the amplitude of the controls. We show that the scheme with two-control functions yields a higher fidelity than the other schemes for the same evolution time.
  arXiv  Detail & Related papers  (2021-10-26T16:54:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.