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

Journal of the Nigerian Association of Mathematical Physics

Hamilton-Jacobi-Bellman equations for quantum control

MO Ogundiran, Philip Oladapo Olanrewaju

Published Jun 13, 2008• 0 citations
Publisher

Abstract

The aim of this work is to study Hamilton-Jacobi-Bellman equation for quantum control driven by quantum noises. These noises are annhihilation, creation and gauge processes. We shall consider the solutions of Hamilton-Jacobi-Bellman equation via the Hamiltonian system measurable in time. JONAMP Vol. 11 2007: pp. 525-528
DOI
10.4314/jonamp.v11i1.40254

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

Optimal control equation for quantum stochastic differential equations

Javad Sharifi, Hamidreza Momeni

Interaction of open quantum systems with fundamental noncommutative quantum noises can be described by quantum stochastic differential equations (QSDE). These equations have a key role in quantum network analysis and design, especially for quantum information processing. Hence, in this paper, we derive a Hamilton-Jacobi-Bellman equation for quantum stochastic differential equations. The Bellman optimality principle is developed for open quantum systems. The cost functional of quantum observable to be minimized is considered to be general noncommutative polynomial of quantum operator. Since the method directly deals with QSDE, then it is a useful tool for optimal control of quantum optical networks. In addition, we will exhibit some electro-optical and all-optical feedback control schematics for implementation of quantum control based on QSDEs.

IEEE Conference on Decision and Control (CDC)•Dec 1, 2010•2 citations

Quantum demolition filtering and optimal control of unstable systems

V. P. Belavkin

A brief account of the quantum information dynamics and dynamical programming methods for optimal control of quantum unstable systems is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme, we exploit the separation theorem of filtering and control aspects as in the usual case of quantum stable systems with non-demolition observation. This allows us to start with the Belavkin quantum filtering equation generalized to demolition observations and derive the generalized Hamilton-Jacobi-Bellman equation using standard arguments of classical control theory. This is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term if the control is restricted to Hamiltonian terms in the filtering equation. An unstable controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure quantum qubit state from a mixed one.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Oct 22, 2012•2 citations

Quantum version of Hamilton-Jacobi theory for Time-dependent Systems

Seiji Sakocia, Minoru Omote, S. Kamefuchi

By constructing a quantum conserved quantity even for a system with timedependent Hamiltonian, we develop the quantum version of Hamilton-Jacobi theory, that is applicable for non-conserved systems as well as conserved ones. A novel viewpoint, Hamilton-Jacobi picture, of the quantum mechanics will be introduced.

CRC Press eBooks•Nov 30, 2003•0 citations

Doing quantum mechanics with control theory

H.H. Rosenbrock

Bellman and Dreyfus (1964) showed how classical mechanics can be obtained from Hamilton's principle by dynamic programming. If we add noise in a particular way, we obtain Schrodinger's equation and many other results from the elementary theory of quantum mechanics. Some new results can also be obtained, and there are important consequences for the philosophy of science.

IEEE Transactions on Automatic Control•Jan 1, 2000•28 citations
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.
Interaction of open quantum systems with fundamental noncommutative quantum noises can be described by quantum stochastic differential equations (QSDE). These equations have a key role in quantum network analysis and design, especially for quantum information processing. Hence, in this paper, we derive a Hamilton-Jacobi-Bellman equation for quantum stochastic differential equations. The Bellman optimality principle is developed for open quantum systems. The cost functional of quantum observable to be minimized is considered to be general noncommutative polynomial of quantum operator. Since the method directly deals with QSDE, then it is a useful tool for optimal control of quantum optical networks. In addition, we will exhibit some electro-optical and all-optical feedback control schematics for implementation of quantum control based on QSDEs.
A brief account of the quantum information dynamics and dynamical programming methods for optimal control of quantum unstable systems is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme, we exploit the separation theorem of filtering and control aspects as in the usual case of quantum stable systems with non-demolition observation. This allows us to start with the Belavkin quantum filtering equation generalized to demolition observations and derive the generalized Hamilton-Jacobi-Bellman equation using standard arguments of classical control theory. This is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term if the control is restricted to Hamiltonian terms in the filtering equation. An unstable controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure quantum qubit state from a mixed one.