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

IEEE Conference on Decision and Control (CDC)

Algorithms for quantum control based on decompositions of Lie groups

Domenico D’Alessandro

Published Nov 11, 2002• 20 citations
Publisher

Abstract

Algorithms for the control of quantum mechanical systems are presented which are based on decompositions of Lie groups. The derived control laws drive the state of two and four level systems to any desired final configuration. The algorithms for the two-level case allow the use of an arbitrarily bounded control.
DOI
10.1109/cdc.2000.912898

Related papers

Algorithms for Quantum Control Based on of Lie Groups

Domenico D’Alessandro

Algorithms for the control of quantum mechanical systems are presented which are based on decompositions of Lie groups. The derived control laws drive the state of two and four level systems to any desired final configuration. The algorithms for the two-level case allow the use of an arbitrarily bounded control.

•Jan 1, 2000•0 citations

Quantum control using Lie group decompositions

S. G. Schirmer

Lie group decompositions of a desired unitary evolution operator are employed to find simple control schemes to achieve population transfers for systems initially in the ground state as well as complete inversions of the ensemble populations for systems whose initial state is an ensemble of energy eigenstates. Both completely controllable and pure-state controllable systems are considered and it is shown that the control objective can be achieved using realistic square wave pulses.

IEEE Conference on Decision and Control (CDC)•Nov 13, 2002•4 citations

Quantum control using Lie group decompositions

S. G. Schirmer

Lie group decompositions of a desired unitary evolution operator are employed to find simple control schemes to achieve population transfers for systems initially in the ground state as well as complete inversions of the ensemble populations for systems whose initial state is an ensemble of energy eigenstates. Both completely controllable and pure-state controllable systems are considered and it is shown that the control objective can be achieved using realistic square wave pulses.

IEEE Conference on Decision and Control (CDC)•Jul 10, 2003•24 citations

Quantum control by decomposition ofSU(1, 1)

Jianwu Wu, Chunwen Li, Re-Bing Wu +2 more

Constructive algorithms are presented for controlling quantum systems evolving on the SU (1, 1) Lie group. These procedures are performed via structured decomposition of SU (1, 1), which achieve precise controls without any approximations or iterative computations, under the sufficient condition that examines the existence of such decomposition. The technique is applied to controlling transitions between SU (1, 1) coherent states. These results open up new perspectives on the control design of infinite-dimensional quantum systems involving discrete or continuous spectra.

Journal of Physics A Mathematical and General•Oct 10, 2006•13 citations

Lie Group Decompositions and Control

Domenico D’Alessandro

This chapter discusses in detail the case of two-level systems and the associated Lie group. It gives an example of a general decomposition of SU(n), namely the decomposition into planar rotation, which is quite simple and can be obtained by straightforward computations. This decomposition gives a direct way to parametrize the special unitary group. The chapter presents the basics of Cartan decompositions of semisimple Lie groups. It gives some examples of applications of Lie group decompositions and introduces some notions of Lie group and Lie algebra theory. The chapter discusses Cartan decompositions of Lie groups. Cartan decompositions appear to be ubiquitous in quantum control and dynamics and in quantum information theory.

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

Constructive Decomposition of the Controllability Lie Algebra for Quantum Systems

Domenico D’Alessandro

In this technical note, we show how to use the analysis of the controllability Lie algebra of a quantum mechanical system to study its dynamics and facilitate the design of controls. We give algorithms to decompose the dynamics and describe an example of application to two coupled spin 1/2's.

IEEE Transactions on Automatic Control•Feb 17, 2010•14 citations
Constructive algorithms are presented for controlling quantum systems evolving on the SU (1, 1) Lie group. These procedures are performed via structured decomposition of SU (1, 1), which achieve precise controls without any approximations or iterative computations, under the sufficient condition that examines the existence of such decomposition. The technique is applied to controlling transitions between SU (1, 1) coherent states. These results open up new perspectives on the control design of infinite-dimensional quantum systems involving discrete or continuous spectra.
This chapter discusses in detail the case of two-level systems and the associated Lie group. It gives an example of a general decomposition of SU(n), namely the decomposition into planar rotation, which is quite simple and can be obtained by straightforward computations. This decomposition gives a direct way to parametrize the special unitary group. The chapter presents the basics of Cartan decompositions of semisimple Lie groups. It gives some examples of applications of Lie group decompositions and introduces some notions of Lie group and Lie algebra theory. The chapter discusses Cartan decompositions of Lie groups. Cartan decompositions appear to be ubiquitous in quantum control and dynamics and in quantum information theory.