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)

Low frequency approximation for a class of linear complex quantum systems using cascade cavity realization

Ian R. Petersen

Published Dec 1, 2010• 1 citation
Publisher

Abstract

This paper presents a method for approximating a class of complex transfer function matrices corresponding to physically realizable complex linear quantum systems. The class of complex linear quantum systems under consideration includes interconnections of passive optical components such as cavities, beam-splitters, phase-shifters and interferometers. This approximation method builds on a previous result for the cascade realization of these transfer function matrices and gives good approximations at low frequencies.

DOI
10.1109/cdc.2010.5716984

Related papers

Cascade cavity realization for a class of complex transfer functions arising in coherent quantum feedback control

Ian R. Petersen

This paper presents a realization algorithm for a class of complex transfer functions corresponding to physically realizable complex linear quantum systems. The class of complex linear quantum systems under consideration includes interconnections of passive optical components such as cavities, beam-splitters, phase-shifters and interferometers. It is shown that for almost all quantum optical systems within this class, the corresponding transfer function can be realized as a cascade connection involving only cavities and phase-shifters.

European Control Conference (ECC)•Aug 1, 2009•14 citations

Singular perturbation approximations for a class of linear complex quantum systems

Ian R. Petersen

This paper considers the use of singular perturbation approximations for a class of linear complex quantum systems arising in the area of quantum optics. The class of linear complex quantum systems under consideration arises in systems consisting of interconnections of passive optical components such as cavities, beams splitters and phase shifters. The main result of the paper shows that for a class of singular perturbations of such systems, the approximate reduced dimension quantum system and guaranteed to be physically realizable.

Proceedings of the ... American Control Conference/Proceedings of the American Control Conference•Jun 1, 2010•10 citations

Factorization of Linear Quantum Systems with Delayed Feedback

Gil Tabak, Ryan Hamerly, Hideo Mabuchi

We consider the transfer functions describing the input-output relation for a class of linear open quantum systems involving feedback with nonzero time delays. We show how such transfer functions can be factorized into a product of terms which are transfer functions of canonical physically realizable components. We prove under certain conditions that this product converges, and can be approximated on compact sets. Thus our factorization can be interpreted as a (possibly infinite) cascade. Our result extends past work where linear open quantum systems with a state-space realization have been shown to have a pure cascade realization [Nurdin, H. I., Grivopoulos, S., & Petersen, I. R. (2016). The transfer function of generic linear quantum stochastic systems has a pure cascade realization. Automatica, 69, 324-333.]. The functions we consider are inherently non-Markovian, which is why in our case the resulting product may have infinitely many terms.

arXiv:1803.01539•Mar 5, 2018•1 citation

Low frequency approximation for a class of linear quantum systems using cascade cavity realization

Ian R. Petersen

arXiv:1107.5607•Systems & Control Letters•Dec 4, 2011•16 citations

On synthesis of linear quantum stochastic systems by pure cascading

Hendra I. Nurdin

Recently, it has been demonstrated that an arbitrary linear quantum stochastic system can be realized as a cascade connection of simpler one degree of freedom quantum harmonic oscillators together with a direct interaction Hamiltonian which is bilinear in the canonical operators of the oscillators. However, from an experimental point of view, realizations by pure cascading, without a direct interaction Hamiltonian, would be much simpler to implement and this raises the natural question of what class of linear quantum stochastic systems are realizable by cascading alone. This paper gives a precise characterization of this class of linear quantum stochastic systems and then it is proved that, in the weaker sense of transfer function realizability, all passive linear quantum stochastic systems belong to this class. A constructive example is given to show the transfer function realization of a two degrees of freedom passive linear quantum system by pure cascading.

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

On transfer function realizations for Linear Quantum Stochastic Systems

Symeon Grivopoulos, Hendra I. Nurdin, Ian R. Petersen

The realization of transfer functions of Linear Quantum Stochastic Systems (LQSSs) is an issue of fundamental importance for the practical applications of such systems, especially as coherent controllers for other quantum systems. In this paper, we review two realization methods proposed by the authors in [1], [2], [3], [4]. The first one uses a cascade of a static linear quantum-optical network and single-mode optical cavities, while the second uses a feedback network of such cavities, along with static linear quantum-optical networks that pre- and post-process the cavity network inputs and outputs.

arXiv:1609.01843•IEEE Conference on Decision and Control (CDC)•Dec 1, 2016•2 citations
This paper presents a method for approximating a class of complex transfer function matrices corresponding to physically realizable complex linear quantum systems. The class of complex linear quantum systems under consideration includes interconnections of passive optical components such as cavities, beam-splitters, phase-shifters and interferometers. This approximation method builds on a previous result for the cascade realization of these transfer function matrices and gives good approximations at low frequencies.
This paper presents a realization algorithm for a class of complex transfer functions corresponding to physically realizable complex linear quantum systems. The class of complex linear quantum systems under consideration includes interconnections of passive optical components such as cavities, beam-splitters, phase-shifters and interferometers. It is shown that for almost all quantum optical systems within this class, the corresponding transfer function can be realized as a cascade connection involving only cavities and phase-shifters.
This paper considers the use of singular perturbation approximations for a class of linear complex quantum systems arising in the area of quantum optics. The class of linear complex quantum systems under consideration arises in systems consisting of interconnections of passive optical components such as cavities, beams splitters and phase shifters. The main result of the paper shows that for a class of singular perturbations of such systems, the approximate reduced dimension quantum system and guaranteed to be physically realizable.
We consider the transfer functions describing the input-output relation for a class of linear open quantum systems involving feedback with nonzero time delays. We show how such transfer functions can be factorized into a product of terms which are transfer functions of canonical physically realizable components. We prove under certain conditions that this product converges, and can be approximated on compact sets. Thus our factorization can be interpreted as a (possibly infinite) cascade. Our result extends past work where linear open quantum systems with a state-space realization have been shown to have a pure cascade realization [Nurdin, H. I., Grivopoulos, S., & Petersen, I. R. (2016). The transfer function of generic linear quantum stochastic systems has a pure cascade realization. Automatica, 69, 324-333.]. The functions we consider are inherently non-Markovian, which is why in our case the resulting product may have infinitely many terms.
Recently, it has been demonstrated that an arbitrary linear quantum stochastic system can be realized as a cascade connection of simpler one degree of freedom quantum harmonic oscillators together with a direct interaction Hamiltonian which is bilinear in the canonical operators of the oscillators. However, from an experimental point of view, realizations by pure cascading, without a direct interaction Hamiltonian, would be much simpler to implement and this raises the natural question of what class of linear quantum stochastic systems are realizable by cascading alone. This paper gives a precise characterization of this class of linear quantum stochastic systems and then it is proved that, in the weaker sense of transfer function realizability, all passive linear quantum stochastic systems belong to this class. A constructive example is given to show the transfer function realization of a two degrees of freedom passive linear quantum system by pure cascading.
The realization of transfer functions of Linear Quantum Stochastic Systems (LQSSs) is an issue of fundamental importance for the practical applications of such systems, especially as coherent controllers for other quantum systems. In this paper, we review two realization methods proposed by the authors in [1], [2], [3], [4]. The first one uses a cascade of a static linear quantum-optical network and single-mode optical cavities, while the second uses a feedback network of such cavities, along with static linear quantum-optical networks that pre- and post-process the cavity network inputs and outputs.