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

arXiv:1501.05044 · IEEE Transactions on Automatic Control

Quantum Noises, Physical Realizability and Coherent Quantum Feedback Control

Shanon L. Vuglar, Ian R. Petersen

Published May 30, 2016• 27 citations
arXivHTMLPDF

Abstract

Arbitrary linear time invariant systems can be implemented as quantum systems if additional quantum noises are permitted in the implementation. We give several results concerning how many additional quantum noise channels are necessary to implement state space realizations and transfer functions as quantum systems. We also give algorithms to do so. We demonstrate the utility of these results with an algorithm for obtaining a suboptimal solution to a coherent quantum LQG control problem.

DOI
10.1109/tac.2016.2574641

Related papers

When do additional quantum noises affect controller performance?

Rebbecca TY Thien, Shanon L. Vuglar, Ian R. Petersen

The introduction of quantum noise in a system is necessary for realizing it as physical quantum system. In general, quantum noise can be detrimental to the performance of a coherent quantum feedback control system. This paper gives a necessary and sufficient condition for when a quantum system corresponding to a given Linear Time Invariant (LTI) controller can be made physically realizable in the presence of both direct feedthrough quantum vacuum noise and additional quantum vacuum noise such that the additional quantum noise has no effect on the controller output. Furthermore, an example is presented to illustrate our result.

IEEE Conference on Decision and Control (CDC)•Dec 14, 2020•1 citation

Optimal Quantum Realization of a Classical Linear System

Rebbecca TY Thien, Shanon L. Vuglar, Ian R. Petersen

Additional noise in a quantum system can be detrimental to the performance of a quantum coherent feedback control system. This paper proposes a Linear Matrix Inequality (LMI) approach to construct an optimal quantum realization of a given Linear Time Invariant (LTI) system. The quantum realization problem is useful in designing coherent quantum feedback controllers. An optimal method is proposed for solving this problem in terms of a finite horizon quadratic performance index, which is related to the amount of quantum noise appearing at the system’s output. This cost function provides a measure of how much the additional quantum noise in the coherent controller will alter the feedback control system.

IFAC-PapersOnLine•Jan 1, 2020•3 citations

How many quantum noises need to be added to make an LTI system physically realizable

Shanon L. Vuglar, Ian R. Petersen

In M. R. James, H. I. Nurdin, and I. R. Petersen, “H∞ control of linear quantum stochastic systems,” IEEE Transactions on Automatic Control, vol. 53, no. 8, pp. 1787–1803, 2008, the authors showed that an arbitrary LTI system can be made physically realizable if additional quantum noise components are permitted in the implementation. However, incorporating additional noise is undesirable, and this paper refines their method in order to provide a concrete expression for the number of additional quantum noise components needed to guarantee physical realizability.

Australian Control Conference•Jan 1, 2011•8 citations

Quantum implemention of an LTI System with the minimal number of additional quantum noise inputs

Shanon L. Vuglar, Ian R. Petersen

Physical Realizability addresses the question of whether it is possible to implement a given LTI system as a quantum system. It is in general not true that a given synthesized quantum controller described by a set of stochastic differential equations is equivalent to some physically meaningful quantum system. However, if additional quantum noises are permitted in the implementation it is always possible to implement an arbitrary LTI system as a quantum system. In this paper we give an expression for the exact number of noises required to implement a given LTI system as a quantum system. Furthermore, we focus our attention on proving that this is a minimum, that is, it is not possible to implement the system as a quantum system with a smaller number of additional quantum noises.

arXiv:1304.6815•European Control Conference (ECC)•Jul 1, 2013•4 citations

A Frequency Domain Condition for the Physical Realizability of Linear Quantum Systems

A. J. Shaiju, Ian R. Petersen

A recently emerging approach to the feedback control of linear quantum systems involves the use of a controller which itself is a quantum linear system. This approach to quantum feedback control, referred to as coherent quantum feedback control, has the advantage that it does not destroy quantum information, is fast, and has the potential for efficient implementation. An important issue which arises both in the synthesis of linear coherent quantum controllers and in the modeling of linear quantum systems, is the issue of physical realizability. This issue relates to the property of whether a given set of linear quantum stochastic differential equations corresponds to a physical quantum system satisfying the laws of quantum mechanics. Under suitable assumptions, the paper shows that the question of physical realizability is equivalent to a frequency domain (J,J) -unitary condition. This is important in controller synthesis since it is the transfer function matrix of the controller which determines the closed loop system behavior.

IEEE Transactions on Automatic Control•Jul 19, 2012•81 citations

Quantum limits to feedback control of linear systems

Andrew C. Doherty, Howard M. Wiseman

In many optical and atomic systems it is now possible to monitor an individual quantum system with high signal to noise and feed back by altering the system dynamics in real time. This motivates further development of quantum mechanical descriptions of feedback control. We discuss recent work on closed loop control of open quantum systems, focusing on general linear systems for which the statistics of the problem are Gaussian. Such systems may be realized with linear optics, parametric amplifiers and homodyne detection. This problem allows a direct comparison with the classical linear, quadratic cost, Gaussian noise (LQG) optimal control problem. This highlights the key distinction between the quantum and classical theories for linear systems: that increased measurement sensitivity may run counter to the control objectives since it increases the backaction noise. While in an idealized classical control problem it is always preferable to obtain a better sensor, quantum mechanical problems generically have an optimal sensitivity since quantum mechanical measurements irreducibly disturb the system. The general theory will be illustrated by reference to specific simple examples.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 25, 2004•1 citation
Arbitrary linear time invariant systems can be implemented as quantum systems if additional quantum noises are permitted in the implementation. We give several results concerning how many additional quantum noise channels are necessary to implement state space realizations and transfer functions as quantum systems. We also give algorithms to do so. We demonstrate the utility of these results with an algorithm for obtaining a suboptimal solution to a coherent quantum LQG control problem.
The introduction of quantum noise in a system is necessary for realizing it as physical quantum system. In general, quantum noise can be detrimental to the performance of a coherent quantum feedback control system. This paper gives a necessary and sufficient condition for when a quantum system corresponding to a given Linear Time Invariant (LTI) controller can be made physically realizable in the presence of both direct feedthrough quantum vacuum noise and additional quantum vacuum noise such that the additional quantum noise has no effect on the controller output. Furthermore, an example is presented to illustrate our result.
Additional noise in a quantum system can be detrimental to the performance of a quantum coherent feedback control system. This paper proposes a Linear Matrix Inequality (LMI) approach to construct an optimal quantum realization of a given Linear Time Invariant (LTI) system. The quantum realization problem is useful in designing coherent quantum feedback controllers. An optimal method is proposed for solving this problem in terms of a finite horizon quadratic performance index, which is related to the amount of quantum noise appearing at the system’s output. This cost function provides a measure of how much the additional quantum noise in the coherent controller will alter the feedback control system.
In M. R. James, H. I. Nurdin, and I. R. Petersen, “H∞ control of linear quantum stochastic systems,” IEEE Transactions on Automatic Control, vol. 53, no. 8, pp. 1787–1803, 2008, the authors showed that an arbitrary LTI system can be made physically realizable if additional quantum noise components are permitted in the implementation. However, incorporating additional noise is undesirable, and this paper refines their method in order to provide a concrete expression for the number of additional quantum noise components needed to guarantee physical realizability.
Physical Realizability addresses the question of whether it is possible to implement a given LTI system as a quantum system. It is in general not true that a given synthesized quantum controller described by a set of stochastic differential equations is equivalent to some physically meaningful quantum system. However, if additional quantum noises are permitted in the implementation it is always possible to implement an arbitrary LTI system as a quantum system. In this paper we give an expression for the exact number of noises required to implement a given LTI system as a quantum system. Furthermore, we focus our attention on proving that this is a minimum, that is, it is not possible to implement the system as a quantum system with a smaller number of additional quantum noises.
A recently emerging approach to the feedback control of linear quantum systems involves the use of a controller which itself is a quantum linear system. This approach to quantum feedback control, referred to as coherent quantum feedback control, has the advantage that it does not destroy quantum information, is fast, and has the potential for efficient implementation. An important issue which arises both in the synthesis of linear coherent quantum controllers and in the modeling of linear quantum systems, is the issue of physical realizability. This issue relates to the property of whether a given set of linear quantum stochastic differential equations corresponds to a physical quantum system satisfying the laws of quantum mechanics. Under suitable assumptions, the paper shows that the question of physical realizability is equivalent to a frequency domain (J,J) -unitary condition. This is important in controller synthesis since it is the transfer function matrix of the controller which determines the closed loop system behavior.
In many optical and atomic systems it is now possible to monitor an individual quantum system with high signal to noise and feed back by altering the system dynamics in real time. This motivates further development of quantum mechanical descriptions of feedback control. We discuss recent work on closed loop control of open quantum systems, focusing on general linear systems for which the statistics of the problem are Gaussian. Such systems may be realized with linear optics, parametric amplifiers and homodyne detection. This problem allows a direct comparison with the classical linear, quadratic cost, Gaussian noise (LQG) optimal control problem. This highlights the key distinction between the quantum and classical theories for linear systems: that increased measurement sensitivity may run counter to the control objectives since it increases the backaction noise. While in an idealized classical control problem it is always preferable to obtain a better sensor, quantum mechanical problems generically have an optimal sensitivity since quantum mechanical measurements irreducibly disturb the system. The general theory will be illustrated by reference to specific simple examples.