Classical and quantum physics mix

Shi Wang, Hendra I. Nurdin, Guofeng Zhang +1 more

The purpose of this paper is to formulate and solve a synthesis problem for a class of linear quantum equations that may describe mixed quantum-classical systems. A general model and a standard model for mixed quantum-classical linear stochastic systems are proposed for our design processes and then we show how the former may be transformed into the latter, which can clearly present the internal structure of a mixed quantum-classical system. Physical realizability conditions are derived separately for the two models to ensure that they can correspond to physical systems. Furthermore, a network synthesis theory is developed for a mixed quantum-classical system of the standard form and an example is given to illustrate the theory. Index Terms — linear stochastic system, mixed quantum-classical linear stochastic system, quantum system, network synthesis theory, physical realizability condition. I.

Marmo, G, David Martı́n de Diego, Lecanda, Miguel

R. Asokamani

Shi Wang, Hendra I. Nurdin, Guofeng Zhang +1 more

The purpose of this paper is to formulate and solve a synthesis problem for a class of linear quantum equations that may describe mixed quantum-classical systems. We propose a standard model for mixed quantum-classical linear stochastic systems for the design process, which can present the internal structure of a mixed quantum-classical system. Physical realizability conditions are derived for the standard model to ensure that it can correspond to a physical system. Furthermore, a network synthesis theory for a mixed quantum-classical system of the standard form has been developed. An example is given to illustrate the results.

Shi Wang

This thesis makes some theoretical contributions towards mixed quantum feedback network synthesis, quantum optical realization of classical linear stochastic systems and quantum feedback control designs. A mixed quantum-classical feedback network is an interconnected system consisting of a quantum system and a classical system connected by interfaces that convert quantum signals to classical signal (using homodyne detectors), and vice versa (using electro-optic modulators). In the area of mixed quantum-classical feedback networks, we present a network synthesis theory, which provides a natural framework for analysis and design for mixed linear systems. Physical realizability conditions are derived for linear stochastic differential equations to ensure that mixed systems can correspond to physical systems. The mixed network synthesis theory developed based on physical realizability conditions shows that how a classical of mixed quantum-classical systems described by linear stochastic differential equations can be built as a interconnection of linear quantum systems and linear classical systems using quantum optical devices as well as electrical and electric devices. However, an important practical problem for the implementation of mixed quantum-classical systems is the relatively slow speed of classical parts implemented with standard electrical and electronic devices, since a mixed system will not work correctly unless the electronic processing of classical devices is fast enough. Therefore, another interesting work is to show how classical linear stochastic systems build using electrical and electric devices can be physically implemented using quantum optical components. A complete procedure is proposed for a stable quantum linear stochastic system realizing a given stable classical linear stochastic system. The thesis explains how it may be possible to realize certain measurement feedback loops fully at the quantum level. In the area of quantum feedback control design, two numerical procedures based on extended linear matrix inequality (LMI) approach are proposed to design a coherent quantum controller in this thesis. The extended synthesis linear matrix inequalities are, in addition to new analysis tools, less conservative in comparison to the conventional counterparts since the optimization variables related to the system parameters in extended LMIs are independent of the symmetric Lyapunov matrix. These features may be useful in the optimal design of quantum optical networks. Time delays are frequently encountered in linear quantum feedback control systems such as long transmission lines between quantum plants and linear controllers, which may have an effect on the performance of closed-loop plant controller systems. Therefore, this thesis investigates the problem of linear quantum measurement-based feedback control systems subject to feedback-loop time delay described by linear stochastic differential equations. Several numerical procedures are proposed to design classical controllers that make quantum measurement-based feedback control systems with time delay stable and also guarantee that their desired control performance specifications are satisfied.

E.L. Albuquerque