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

International Conference on Control, Automation, Robotics and Vision (ICARCV)

Quantization of optimal control system & Synthesis of optimal controls of quantum diffusion process

B. C. Roy

Published Dec 1, 2010• 1 citation
Publisher

Abstract

When applied quantization to classical control system, quantum mechanics opens completely new perspectives; by exploiting quantum mechanical features, such as, time evolution of quantum state and costate (generalized momenta) of the Hamiltonian of the system, one can formulate and solve the optimal control problems of the quantum mechanical system more efficiently than the classical system. The physical perspective of quantization of the optimal feedback system is outlined by exploiting the formulation of the optimization problem of the system within the context of Hamilton-Jacobi theory and Pontryagin maximum/minimum principle in abstract Hubert space. One of the most striking example is the optimal control problem of synthesizing the feedback law of quantum diffusion process. The optimal diffusion process is shown to satisfy the Schrödinger wave equation of energy with the feedback law as potential function.

DOI
10.1109/icarcv.2010.5707902

Related papers

Hamilton-jacobi-bellman equations for quantum optimal control

John Edward Gough, V.A. Belavkin, Oleg Georgievich Smolyanov

One develops a Hamilton-Jacobi-Bellman equation and a stochastic Hamilton-Jacobi-Bellman equation for quantum optimal feedback control. In this paper we do not discuss in details how to find the optimal control functions; we would like to notice only that the corresponding generalizations of the classical Pontryagin maximum principle can be obtained and used

Days on Diffraction•Jan 1, 2006•2 citations

Hamilton–Jacobi–Bellman equations for quantum optimal feedback control

John Edward Gough, V. P. Belavkin, Oleg Georgievich Smolyanov

We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding Hamilton-Jacobi-Bellman equations using the elementary arguments of classical control theory and show that this is equivalent, in the Stratonovich calculus, to a stochastic Hamilton-Pontryagin setup. We show that, for cost functionals that are linear in the state, the theory yields the traditional Bellman equations treated so far in quantum feedback.

arXiv:quant-ph/0502155•Journal of Optics B Quantum and Semiclassical Optics•Sep 14, 2005•62 citations

An Optimal Control Perspective on Classical and Quantum Physical Systems

Mauricio Contreras González, Marcelo J. Villena, Roberto Ortiz

This paper analyzes classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open- or closed-loop feedback evolution of a control problem. Firstly, for the classical regime, when it is viewed in terms of the theory of canonical transformations, we find that a closed-loop feedback problem can describe it. Secondly, for a quantum physical system, if one realizes that the Heisenberg commutation relations themselves can be considered constraints in a non-commutative space, then the momentum must depend on the position of any generic wave function. That implies the existence of a closed-loop strategy for the quantum case. Thus, closed-loop feedback is a natural phenomenon in the physical world. By way of completeness, we briefly review control theory and the classical mechanics of constrained systems and analyze some examples at the classical and quantum levels.

Symmetry•Nov 8, 2023•4 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

An Optimal Control Perspective on Classical and Quantum Physical Systems

Mauricio Contreras G., Marcelo J. Villena

In this paper, we analyze classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open or closed-loop feedback evolution of a control problem. Firstly, for the classical regime, when it is viewed in terms of the theory of canonical transformations, we find that it can be described by a closed-loop feedback problem. Secondly, for a quantum physical system, if one realizes that the Heisenberg commutation relations themselves can be thought of as constraints in a non-commutative space, then the momentum must be dependent on the position for any generic wave function. This implies the existence of a closed-loop strategy for the quantum case. Thus, closed-loop feedback is a natural phenomenon in the physical world. For the sake of exposition, we give a short review of control theory, and some familiar examples at the classical and quantum levels are analyzed.

arXiv:2006.06162•Jun 11, 2020•0 citations
When applied quantization to classical control system, quantum mechanics opens completely new perspectives; by exploiting quantum mechanical features, such as, time evolution of quantum state and costate (generalized momenta) of the Hamiltonian of the system, one can formulate and solve the optimal control problems of the quantum mechanical system more efficiently than the classical system. The physical perspective of quantization of the optimal feedback system is outlined by exploiting the formulation of the optimization problem of the system within the context of Hamilton-Jacobi theory and Pontryagin maximum/minimum principle in abstract Hubert space. One of the most striking example is the optimal control problem of synthesizing the feedback law of quantum diffusion process. The optimal diffusion process is shown to satisfy the Schrödinger wave equation of energy with the feedback law as potential function.
We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding Hamilton-Jacobi-Bellman equations using the elementary arguments of classical control theory and show that this is equivalent, in the Stratonovich calculus, to a stochastic Hamilton-Pontryagin setup. We show that, for cost functionals that are linear in the state, the theory yields the traditional Bellman equations treated so far in quantum feedback.
This paper analyzes classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open- or closed-loop feedback evolution of a control problem. Firstly, for the classical regime, when it is viewed in terms of the theory of canonical transformations, we find that a closed-loop feedback problem can describe it. Secondly, for a quantum physical system, if one realizes that the Heisenberg commutation relations themselves can be considered constraints in a non-commutative space, then the momentum must depend on the position of any generic wave function. That implies the existence of a closed-loop strategy for the quantum case. Thus, closed-loop feedback is a natural phenomenon in the physical world. By way of completeness, we briefly review control theory and the classical mechanics of constrained systems and analyze some examples at the classical and quantum levels.
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.
In this paper, we analyze classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open or closed-loop feedback evolution of a control problem. Firstly, for the classical regime, when it is viewed in terms of the theory of canonical transformations, we find that it can be described by a closed-loop feedback problem. Secondly, for a quantum physical system, if one realizes that the Heisenberg commutation relations themselves can be thought of as constraints in a non-commutative space, then the momentum must be dependent on the position for any generic wave function. This implies the existence of a closed-loop strategy for the quantum case. Thus, closed-loop feedback is a natural phenomenon in the physical world. For the sake of exposition, we give a short review of control theory, and some familiar examples at the classical and quantum levels are analyzed.