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

Quantum Information and Computation

Controllable Subsystems of Quantum Dynamical Systems

Mingyi Zhang, Hui Dai, G.-H. Dong, H.-W. Xie, D.-W. Hu

Published Jul 1, 2007• 4 citations
Publisher

Abstract

This paper proposes the concept of subsystem controllability for both closed and open quantum dynamical systems, and the existence conditions of controllable subsystems are derived accordingly. It is demonstrated that a controllable subsystem may exist for a closed quantum dynamical system even if the overall system is not controllable. Furthermore, we also demonstrate that, for a class of decoherence-free subsystems of Markovian open quantum dynamical systems, the subsystems are controllable under open-loop coherent control if the initial states of the open systems are factorized. To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subsystems are useful for quantum computation.

DOI
10.26421/qic7.5-6-4

Related papers

Controllable Subspaces of Open Quantum Dynamical Systems

Ming Zhang, Hong‐Yi Dai, Gong Er-Ling +2 more

This paper discusses the concept of controllable subspace for open quantum dynamical systems.It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable.This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable.To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation.

Communications in Theoretical Physics•Jan 1, 2008•5 citations

Controllable subsystems of quantum dynamical systems

ZhangMing, DAIHong-Yi, DongGuo-Hua +2 more

This paper proposes the concept of subsystem controllability for both closed and open quantum dynamical systems, and the existence conditions of controllable subsystems are derived accordingly. It ...

Quantum Information and Computation•Jul 1, 2007•0 citations

Control of Open Quantum Dynamical Systems

Ming Zhang, Wei Kang Zhu, Dewen Hu

This paper demonstrates that the decoherence-free subsystem of open quantum dynamical system is open-loop controllable if the suitable coherent controls are permitted. This result is in marked contrast to the fact that open quantum dynamical systems are not open-loop controllable. In other words, combining the decoherence-free subsystem condition with coherent control on the open quantum dynamical systems will enhance the ability to suppress the decoherence and to manipulate open quantum dynamical systems.

Chinese Control Conference (CCC)•Aug 1, 2006•0 citations

Decoherence-Free Linear Quantum Subsystems

Naoki Yamamoto

This paper provides a general theory for characterizing and constructing a decoherence-free (DF) subsystem for an infinite dimensional linear open quantum system. The main idea is that, based on the Heisenberg picture of the dynamics rather than the commonly-taken Schrödinger picture, the notions of controllability and observability in control theory are employed to characterize a DF subsystem. A particularly useful result is a general if and only if condition for a linear system to have a DF component; this condition is used to demonstrate how to actually construct a DF dynamics in some specific examples. It is also shown that, as in the finite dimensional case, we are able to do coherent manipulation and preservation of a state of a DF subsystem.

arXiv:1210.2632•IEEE Transactions on Automatic Control•Mar 25, 2014•32 citations

Quantum Markovian Subsystems: Invariance, Attractivity, and Control

Francesco Ticozzi, Lorenza Viola

We characterize the dynamical behavior of continuous-time, Markovian quantum systems with respect to a subsystem of interest. Markovian dynamics describes a wide class of open quantum systems of relevance to quantum information processing, subsystem encodings offering a general pathway to faithfully represent quantum information. We provide explicit linear-algebraic characterizations of the notion of invariant and noiseless subsystem for Markovian master equations, under different robustness assumptions for model-parameter and initial-state variations. The stronger concept of an attractive quantum subsystem is introduced, and sufficient existence conditions are identified based on Lyapunov's stability techniques. As a main control application, we address the potential of output-feedback Markovian control strategies for quantum pure state-stabilization and noiseless-subspace generation. In particular, explicit results for the synthesis of stabilizing semigroups and noiseless subspaces in finite-dimensional Markovian systems are obtained.

arXiv:0705.1372•May 9, 2007•0 citations

Quantum Markovian Subsystems: Invariance, Attractivity, and Control

Francesco Ticozzi, Lorenza Viola

We characterize the dynamical behavior of continuous-time, Markovian quantum systems with respect to a subsystem of interest. Markovian dynamics describes a wide class of open quantum systems of relevance to quantum information processing, subsystem encodings offering a general pathway to faithfully represent quantum information. We provide explicit linear-algebraic characterizations of the notion of invariant and noiseless subsystem for Markovian master equations, under different robustness assumptions for model-parameter and initial-state variations. The stronger concept of an attractive quantum subsystem is introduced, and sufficient existence conditions are identified based on Lyapunov's stability techniques. As a main control application, we address the potential of output-feedback Markovian control strategies for quantum pure state-stabilization and noiseless-subspace generation. In particular, explicit results for the synthesis of stabilizing semigroups and noiseless subspaces in finite-dimensional Markovian systems are obtained.

IEEE Transactions on Automatic Control•Oct 1, 2008•167 citations
This paper proposes the concept of subsystem controllability for both closed and open quantum dynamical systems, and the existence conditions of controllable subsystems are derived accordingly. It is demonstrated that a controllable subsystem may exist for a closed quantum dynamical system even if the overall system is not controllable. Furthermore, we also demonstrate that, for a class of decoherence-free subsystems of Markovian open quantum dynamical systems, the subsystems are controllable under open-loop coherent control if the initial states of the open systems are factorized. To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subsystems are useful for quantum computation.
This paper discusses the concept of controllable subspace for open quantum dynamical systems.It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable.This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable.To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation.
This paper demonstrates that the decoherence-free subsystem of open quantum dynamical system is open-loop controllable if the suitable coherent controls are permitted. This result is in marked contrast to the fact that open quantum dynamical systems are not open-loop controllable. In other words, combining the decoherence-free subsystem condition with coherent control on the open quantum dynamical systems will enhance the ability to suppress the decoherence and to manipulate open quantum dynamical systems.
This paper provides a general theory for characterizing and constructing a decoherence-free (DF) subsystem for an infinite dimensional linear open quantum system. The main idea is that, based on the Heisenberg picture of the dynamics rather than the commonly-taken Schrödinger picture, the notions of controllability and observability in control theory are employed to characterize a DF subsystem. A particularly useful result is a general if and only if condition for a linear system to have a DF component; this condition is used to demonstrate how to actually construct a DF dynamics in some specific examples. It is also shown that, as in the finite dimensional case, we are able to do coherent manipulation and preservation of a state of a DF subsystem.
We characterize the dynamical behavior of continuous-time, Markovian quantum systems with respect to a subsystem of interest. Markovian dynamics describes a wide class of open quantum systems of relevance to quantum information processing, subsystem encodings offering a general pathway to faithfully represent quantum information. We provide explicit linear-algebraic characterizations of the notion of invariant and noiseless subsystem for Markovian master equations, under different robustness assumptions for model-parameter and initial-state variations. The stronger concept of an attractive quantum subsystem is introduced, and sufficient existence conditions are identified based on Lyapunov's stability techniques. As a main control application, we address the potential of output-feedback Markovian control strategies for quantum pure state-stabilization and noiseless-subspace generation. In particular, explicit results for the synthesis of stabilizing semigroups and noiseless subspaces in finite-dimensional Markovian systems are obtained.
We characterize the dynamical behavior of continuous-time, Markovian quantum systems with respect to a subsystem of interest. Markovian dynamics describes a wide class of open quantum systems of relevance to quantum information processing, subsystem encodings offering a general pathway to faithfully represent quantum information. We provide explicit linear-algebraic characterizations of the notion of invariant and noiseless subsystem for Markovian master equations, under different robustness assumptions for model-parameter and initial-state variations. The stronger concept of an attractive quantum subsystem is introduced, and sufficient existence conditions are identified based on Lyapunov's stability techniques. As a main control application, we address the potential of output-feedback Markovian control strategies for quantum pure state-stabilization and noiseless-subspace generation. In particular, explicit results for the synthesis of stabilizing semigroups and noiseless subspaces in finite-dimensional Markovian systems are obtained.