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

Mathematics and its applications. Soviet series

The Problem of Control on the Quantum Level

Anatoliy G. Butkovskiy, Yu. I. Samoilenko

Published Jan 1, 1990• 0 citations
Publisher
DOI
10.1007/978-94-009-1994-5_1

Related papers

Time-optimal control of a 3-level quantum system and its generalization to an n-level system

Dong Eui Chang, Rodolphe J. Sepulchre

We solve the problem of steering a three-level quantum system from one eigen-state to another in minimum time and study its possible extension to the time-optimal control problem for a general n-level quantum system. For the three- level system we find all optimal controls by finding two types of symmetry in the problem: Z2x S3discrete symmetry and S1continuous symmetry, and exploiting them to solve the problem through discrete reduction and symplectic reduction. We then study the geometry, in the same framework, which occurs in the time-optimal control of a general n-level quantum system.

Proceedings of the ... American Control Conference/Proceedings of the American Control Conference•Jul 1, 2007•2 citations

Directions in the Theory of Quantum Control

Domenico D’Alessandro

Springer eBooks•Aug 10, 2007•7 citations

TIME-OPTIMAL CONTROL OF A 3-LEVEL QUANTUM SYSTEM AND ITS GENERALIZATION

Dong Eui Chang, Rodolphe J. Sepulchre

Abstract. We solve the problem of steering a three-level quantum system from one eigen-state to another in minimum time and study its possible extension to the time-optimal control problem for a general n-level quantum system. For the three-level system we find all optimal controls by finding two types of symmetry in the problems: Z2×S3 discrete sym-metry and S1 continuous symmetry, and exploiting them to solve the problem through discrete reduction and symplectic reduction. We then study the geometry, in the same framework, which occurs in the time-optimal control of a general n-level quantum system.

•Aug 1, 2007•4 citations

LIMITATIONS ON QUANTUM CONTROL

A. I. Solomon, Sonia G. Schirmer

APCTP-Nankai Joint Symposium on Lattice Statistics and Mathematical Physics•Nov 1, 2002•0 citations

Optimal control of two-level quantum systems

Domenico D’Alessandro, M. Dahleh

We study the manipulation of two-level quantum systems. This research is motivated by the design of quantum mechanical logic gates which perform prescribed logic operations on a two-level quantum system, a quantum bit. We consider the problem of driving the evolution operator to a desired state, while minimizing the energy-type cost. Mathematically, this problem translates into an optimal control problem for systems varying on the Lie group of special unitary matrices, with cost that is quadratic in the control. We develop a comprehensive theory of optimal control for two-level quantum systems. In particular, we prove the 'normality' of the given problem and the 'regularity' of the optimal control functions. The impact of the results of the paper on nuclear magnetic resonance experiments and quantum computation is discussed.

Proceedings of the ... American Control Conference/Proceedings of the American Control Conference•Jan 1, 2000•32 citations

Problems of quantum control and measurement

H. Ezawa

•Jan 1, 1993•0 citations
We solve the problem of steering a three-level quantum system from one eigen-state to another in minimum time and study its possible extension to the time-optimal control problem for a general n-level quantum system. For the three- level system we find all optimal controls by finding two types of symmetry in the problem: Z2x S3discrete symmetry and S1continuous symmetry, and exploiting them to solve the problem through discrete reduction and symplectic reduction. We then study the geometry, in the same framework, which occurs in the time-optimal control of a general n-level quantum system.
Abstract. We solve the problem of steering a three-level quantum system from one eigen-state to another in minimum time and study its possible extension to the time-optimal control problem for a general n-level quantum system. For the three-level system we find all optimal controls by finding two types of symmetry in the problems: Z2×S3 discrete sym-metry and S1 continuous symmetry, and exploiting them to solve the problem through discrete reduction and symplectic reduction. We then study the geometry, in the same framework, which occurs in the time-optimal control of a general n-level quantum system.
We study the manipulation of two-level quantum systems. This research is motivated by the design of quantum mechanical logic gates which perform prescribed logic operations on a two-level quantum system, a quantum bit. We consider the problem of driving the evolution operator to a desired state, while minimizing the energy-type cost. Mathematically, this problem translates into an optimal control problem for systems varying on the Lie group of special unitary matrices, with cost that is quadratic in the control. We develop a comprehensive theory of optimal control for two-level quantum systems. In particular, we prove the 'normality' of the given problem and the 'regularity' of the optimal control functions. The impact of the results of the paper on nuclear magnetic resonance experiments and quantum computation is discussed.