Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Control and Decision Conference (CCDC)

Optimal control of population inversion in open quantum systems

Wei Cui

Published May 1, 2015• 0 citations
Publisher

Abstract

We consider an optimal control problem for the quantum population transfer in open quantum systems. Quantum optimal control using the Pontryagin maximum principle is specifically derived. The influences of surrounding environment are analytically and numerically studied. In particular, we demonstrate that the quantum optimal control ability remarkablely dependents on temperatures. Only at low temperatures, the derived control laws have active performance and the quantum decoherence time can be extended.

DOI
10.1109/ccdc.2015.7162489

Related papers

Optimal decoherence control of non-Markovian open quantum systems

Wei Cui, Zairong Xi, Yu Pan

We investigate the optimal control problem in non-Markovian open, dissipative quantum system. Optimal control using Pontryagin maximum principle of this problem has been specifically derived. The influences of Ohmic reservoir with Lorentz-Drude regularization are numerically studied in a two-level system under the following three conditions w0Lt wc, w0ap wcor w0Gt wcrespectively. The optimal control process shows its remarkable influences to the decoherence dynamics. The temperature is a key factor in the decoherence dynamics. We analysis the optimal decoherence control in high temperature, intermediate temperature, and low temperature reservoirs respectively. It implies that designing some engineered reservoirs with the controlled coupling and state of the environment can slow down the decoherence rate and delay the decoherence time. Moreover, we compared the non-Markovian optimal decoherence control with the Markovian one, we find that with non-Markovian the engineered artificial reservoirs are better than with the Markovian approximate in controlling the open, dissipative quantum systempsilas decoherence.

Chinese Control Conference (CCC)•Jul 1, 2008•0 citations

Optimal control of population transfer in Markovian open quantum systems

Wei Cui, Zairong Xi, Yu Pan

There has long been interest to control the transfer of population between specified quantum states. Recent work has optimized the control law for closed system population transfer by using a gradient ascent pulse engineer- ing algorithm [1]. Here, a spin-boson model consisting of two-level atoms which interact with the dissipative environment, is investigated. With opti- mal control, the quantum system can invert the populations of the quantum logic states. The temperature plays an important role in controlling popula- tion transfer. At low temperatures the control has active performance, while at high temperatures it has less erect. We also analyze the decoherence be- havior of open quantum systems with optimal population transfer control, and we find that these controls can prolong the coherence time. We hope that active optimal control can help quantum solid-state-based engineering.

arXiv:1004.4301•Apr 24, 2010•0 citations

Optimal decoherence control in non-Markovian open dissipative quantum systems

Wei Cui, Zairong Xi, Yu Pan

We investigate the optimal control problem for a non-Markovian open, dissipative quantum system. Optimal control using the Pontryagin maximum principle is specifically derived. The influences of ohmic reservoir with Lorentz-Drude regularization are numerically studied in a two-level system under the following three conditions: ${\ensuremath{\omega}}_{0}⪡{\ensuremath{\omega}}_{c}$, ${\ensuremath{\omega}}_{0}\ensuremath{\approx}{\ensuremath{\omega}}_{c}$, or ${\ensuremath{\omega}}_{0}⪢{\ensuremath{\omega}}_{c}$, where ${\ensuremath{\omega}}_{0}$ is the characteristic frequency of the quantum system of interest, and ${\ensuremath{\omega}}_{c}$ the cutoff frequency of the ohmic reservoir. The optimal control process shows its remarkable influences on the decoherence dynamics. The temperature is a key factor in the decoherence dynamics. We analyze the optimal decoherence control in high temperature, intermediate temperature, and low temperature reservoirs, respectively. It implies that designing some engineered reservoirs with the controlled coupling and state of the environment can slow down the decoherence rate and delay the decoherence time. Moreover, we compare the non-Markovian optimal decoherence control with the Markovian one and find that with non-Markovian the engineered artificial reservoirs are better than with the Markovian approximation in controlling the open, dissipative quantum system's decoherence.

arXiv:0910.5208•Physical Review A•Mar 26, 2008•88 citations

Optimal Control of Quantum Systems by Pontryagin Maximum Principle

Nahid Binandeh Dehaghani, Фернандо Лобо Перейра

Optimal control provides powerful tools and concepts that can be applied to control quantum systems. It has been used extensively to improve the performance of quantum processes in a variety of active areas in quantum technologies. This paper reviews the necessary conditions of optimality in the form of a Pontryagin Maximum Principle (PMP), and introduces its formulations for quantum systems. After formulating an optimal control problem for a two-level quantum system, we then study the application of PMP to obtain an optimal control strategy.

U Porto Journal of Engineering•Apr 28, 2022•9 citations

Optimal Control of Quantum Systems

Domenico D’Alessandro

Optimal control theory provides a powerful set of tools and concepts that can be applied to quantum control systems. This chapter presents the general formulation of optimal control problems and gives the basic necessary conditions of optimality, the Pontryagin maximum principle (PMP). It presents an outline of the derivation of the PMP in the case of a fixed final time and free final state. One of the major problems in the context is that quantum systems are very sensitive to the presence of the environment which often destroys the main features of quantum dynamics. The chapter examines how the problem of minimum time control for system specializes in the case where eL/eK is a symmetric space.

Chapman & Hall/CRC eBooks•Jul 13, 2021•0 citations

Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control

Ugo Boscain, Mario Sigalotti, Dominique Sugny

Optimal Control Theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum technologies by means of highly efficient control of quantum dynamics. This tutorial aims at providing an introduction to key concepts of optimal control theory which is accessible to physicists and engineers working in quantum control or in related fields. The different mathematical results are introduced intuitively, before being rigorously stated. This tutorial describes modern aspects of optimal control theory, with a particular focus on the Pontryagin Maximum Principle, which is the main tool for determining open-loop control laws without experimental feedback. The different steps to solve an optimal control problem are discussed, before moving on to more advanced topics such as the existence of optimal solutions or the definition of the different types of extremals, namely normal, abnormal, and singular. The tutorial covers various quantum control issues and describes their mathematical formulation suitable for optimal control. The connection between the Pontryagin Maximum Principle and gradient-based optimization algorithms used for high-dimensional quantum systems is described. The optimal solution of different low-dimensional quantum systems is presented in detail, illustrating how the mathematical tools are applied in a practical way.

arXiv:2010.09368•PRX Quantum•Sep 14, 2021•207 citations
We consider an optimal control problem for the quantum population transfer in open quantum systems. Quantum optimal control using the Pontryagin maximum principle is specifically derived. The influences of surrounding environment are analytically and numerically studied. In particular, we demonstrate that the quantum optimal control ability remarkablely dependents on temperatures. Only at low temperatures, the derived control laws have active performance and the quantum decoherence time can be extended.
We investigate the optimal control problem in non-Markovian open, dissipative quantum system. Optimal control using Pontryagin maximum principle of this problem has been specifically derived. The influences of Ohmic reservoir with Lorentz-Drude regularization are numerically studied in a two-level system under the following three conditions w0Lt wc, w0ap wcor w0Gt wcrespectively. The optimal control process shows its remarkable influences to the decoherence dynamics. The temperature is a key factor in the decoherence dynamics. We analysis the optimal decoherence control in high temperature, intermediate temperature, and low temperature reservoirs respectively. It implies that designing some engineered reservoirs with the controlled coupling and state of the environment can slow down the decoherence rate and delay the decoherence time. Moreover, we compared the non-Markovian optimal decoherence control with the Markovian one, we find that with non-Markovian the engineered artificial reservoirs are better than with the Markovian approximate in controlling the open, dissipative quantum systempsilas decoherence.
There has long been interest to control the transfer of population between specified quantum states. Recent work has optimized the control law for closed system population transfer by using a gradient ascent pulse engineer- ing algorithm [1]. Here, a spin-boson model consisting of two-level atoms which interact with the dissipative environment, is investigated. With opti- mal control, the quantum system can invert the populations of the quantum logic states. The temperature plays an important role in controlling popula- tion transfer. At low temperatures the control has active performance, while at high temperatures it has less erect. We also analyze the decoherence be- havior of open quantum systems with optimal population transfer control, and we find that these controls can prolong the coherence time. We hope that active optimal control can help quantum solid-state-based engineering.
We investigate the optimal control problem for a non-Markovian open, dissipative quantum system. Optimal control using the Pontryagin maximum principle is specifically derived. The influences of ohmic reservoir with Lorentz-Drude regularization are numerically studied in a two-level system under the following three conditions: ${\ensuremath{\omega}}_{0}⪡{\ensuremath{\omega}}_{c}$, ${\ensuremath{\omega}}_{0}\ensuremath{\approx}{\ensuremath{\omega}}_{c}$, or ${\ensuremath{\omega}}_{0}⪢{\ensuremath{\omega}}_{c}$, where ${\ensuremath{\omega}}_{0}$ is the characteristic frequency of the quantum system of interest, and ${\ensuremath{\omega}}_{c}$ the cutoff frequency of the ohmic reservoir. The optimal control process shows its remarkable influences on the decoherence dynamics. The temperature is a key factor in the decoherence dynamics. We analyze the optimal decoherence control in high temperature, intermediate temperature, and low temperature reservoirs, respectively. It implies that designing some engineered reservoirs with the controlled coupling and state of the environment can slow down the decoherence rate and delay the decoherence time. Moreover, we compare the non-Markovian optimal decoherence control with the Markovian one and find that with non-Markovian the engineered artificial reservoirs are better than with the Markovian approximation in controlling the open, dissipative quantum system's decoherence.
Optimal control provides powerful tools and concepts that can be applied to control quantum systems. It has been used extensively to improve the performance of quantum processes in a variety of active areas in quantum technologies. This paper reviews the necessary conditions of optimality in the form of a Pontryagin Maximum Principle (PMP), and introduces its formulations for quantum systems. After formulating an optimal control problem for a two-level quantum system, we then study the application of PMP to obtain an optimal control strategy.
Optimal control theory provides a powerful set of tools and concepts that can be applied to quantum control systems. This chapter presents the general formulation of optimal control problems and gives the basic necessary conditions of optimality, the Pontryagin maximum principle (PMP). It presents an outline of the derivation of the PMP in the case of a fixed final time and free final state. One of the major problems in the context is that quantum systems are very sensitive to the presence of the environment which often destroys the main features of quantum dynamics. The chapter examines how the problem of minimum time control for system specializes in the case where eL/eK is a symmetric space.
Optimal Control Theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum technologies by means of highly efficient control of quantum dynamics. This tutorial aims at providing an introduction to key concepts of optimal control theory which is accessible to physicists and engineers working in quantum control or in related fields. The different mathematical results are introduced intuitively, before being rigorously stated. This tutorial describes modern aspects of optimal control theory, with a particular focus on the Pontryagin Maximum Principle, which is the main tool for determining open-loop control laws without experimental feedback. The different steps to solve an optimal control problem are discussed, before moving on to more advanced topics such as the existence of optimal solutions or the definition of the different types of extremals, namely normal, abnormal, and singular. The tutorial covers various quantum control issues and describes their mathematical formulation suitable for optimal control. The connection between the Pontryagin Maximum Principle and gradient-based optimization algorithms used for high-dimensional quantum systems is described. The optimal solution of different low-dimensional quantum systems is presented in detail, illustrating how the mathematical tools are applied in a practical way.