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Chinese Automation Congress

Design of coherent quantum observers in the presence of unknown inputs

Dong He, Zibo Miao

Published Nov 6, 2020• 1 citation
Publisher

Abstract

In this paper, we proceed with our research on coherent quantum observers, with a focus on the scenario where there exist unknown inputs to the quantum plant. In our previous studies, we were mainly concerned with linear quantum plants in the absence of unknown inputs. However, when there are unmodeled dynamics or disturbances in quantum systems, the quantum version of Luenberger observers or Kalman filters might not be adequate. Given that no prior knowledge is assumed for the unknown inputs, we take advantage of the Hautus lemma to improve the robustness in observing a quantum system. More precisely, we consider linear quantum stochastic systems with unknown inputs involved whose dynamics correspond to open quantum harmonic oscillators. We show the procedure regarding synthesis of coherent observers for such systems that accomplish the task of simultaneously estimating system variables together with the unknown inputs, which is also illustrated by a simulation example.

DOI
10.1109/cac51589.2020.9327864

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Design of Coherent Observers

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Abstract. Quantum versions of control problems are often more difficult than their classical counterparts because of the additional constraints imposed by quantum dynamics. For example, the quantum LQG and quantumH ∞ optimal control problems remain open. To make further progress, new, systematic and tractable methods need to be developed. This paper gives three algorithms for designing coherent observers, i.e., quantum systems that are connected to a quantum plant and their outputs provide information about the internal state of the plant. Importantly, coherent observers avoid measurements of the plant outputs. We compare our coherent observers with a classical (measurement-based) observer by way of an example involving an optical cavity with thermal and vacuum noises as inputs. ar X iv

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In this paper, we proceed with our research on coherent quantum observers, with a focus on the scenario where there exist unknown inputs to the quantum plant. In our previous studies, we were mainly concerned with linear quantum plants in the absence of unknown inputs. However, when there are unmodeled dynamics or disturbances in quantum systems, the quantum version of Luenberger observers or Kalman filters might not be adequate. Given that no prior knowledge is assumed for the unknown inputs, we take advantage of the Hautus lemma to improve the robustness in observing a quantum system. More precisely, we consider linear quantum stochastic systems with unknown inputs involved whose dynamics correspond to open quantum harmonic oscillators. We show the procedure regarding synthesis of coherent observers for such systems that accomplish the task of simultaneously estimating system variables together with the unknown inputs, which is also illustrated by a simulation example.
This paper proposes a direct coupling coherent quantum observer for a quantum plant which consists of a two level quantum system. The quantum observer, which is a quantum harmonic oscillator, includes homodyne detection measurements. It is shown that the observer can be designed so that it does not affect the quantum variable of interest in the quantum plant and that measured output converges in a given sense to the plant variable of interest. Also, the plant variable of interest-observer system can be described by a set of linear quantum stochastic differential equations. A minimum variance unbiased estimator form of the Kalman filter is derived for linear quantum systems and applied to the direct coupled coherent quantum observer.
The purpose of this paper is to investigate the extension of the Luenberger observer design approach to linear quantum stochastic systems to obtain coherent quantum observers. We show how a physically realizable quantum observer can be designed, consistent with the laws of quantum mechanics. The quantum observer has the property that the mean values of the observer variables asymptotically track the corresponding mean values of the plant. In addition, we discuss entanglement of the joint plant-observer state, as well as the implications of the no-cloning theorem. Several examples are considered.
The paper is concerned with a problem of coherent (measurement-free) filtering for physically realizable (PR) linear quantum plants. The state variables of such systems satisfy canonical commutation relations and are governed by linear quantum stochastic differential equations, dynamically equivalent to those of an open quantum harmonic oscillator. The problem is to design another PR quantum system, connected unilaterally to the output of the plant and playing the role of a quantum filter, so as to minimize a mean square discrepancy between the dynamic variables of the plant and the output of the filter. This coherent quantum filtering (CQF) formulation is a simplified feedback-free version of the coherent quantum LQG control problem which remains open despite recent studies. The CQF problem is transformed into a constrained covariance control problem which is treated by using the Frechet differentiation of an appropriate Lagrange function with respect to the matrices of the filter.
Quantum versions of control problems are often more difficult than their classical counterparts because of the additional constraints imposed by quantum dynamics. For example, the quantum LQG and quantum optimal control problems remain open. To make further progress, new, systematic and tractable methods need to be developed. This paper gives three algorithms for designing coherent quantum observers, i.e., quantum systems that are connected to a quantum plant and their outputs provide information about the internal state of the plant. Importantly, coherent quantum observers avoid measurements of the plant outputs. We compare our coherent quantum observers with a classical (measurement-based) observer by way of an example involving an optical cavity with thermal and vacuum noises as inputs.
Abstract In this paper, the synthesis of robust memory modes for linear quantum passive systems in the presence of unknown inputs has been studied, aimed at facilitating secure storage and communication of quantum information. In particular, we can switch on decoherence-free (DF) modes in the storage stage by placing the poles on the imaginary axis via a coherent feedback control scheme, and these memory modes can further be simultaneously made robust against perturbations to the system parameters by minimizing the condition number associated with imaginary poles. The DF modes can also be switched off by tuning the controller parameters to place the poles in the left half of the complex plane in the writing/reading stage. We develop explicit algebraic conditions guiding the design of such a coherent quantum controller, which involves employing an augmented system model to counter the influence of unknown inputs. Examples are provided to illustrate the procedure of synthesizing robust memory modes for linear optical quantum systems.
Abstract. Quantum versions of control problems are often more difficult than their classical counterparts because of the additional constraints imposed by quantum dynamics. For example, the quantum LQG and quantumH ∞ optimal control problems remain open. To make further progress, new, systematic and tractable methods need to be developed. This paper gives three algorithms for designing coherent observers, i.e., quantum systems that are connected to a quantum plant and their outputs provide information about the internal state of the plant. Importantly, coherent observers avoid measurements of the plant outputs. We compare our coherent observers with a classical (measurement-based) observer by way of an example involving an optical cavity with thermal and vacuum noises as inputs. ar X iv