No abstract

No abstract

We propose a new method to construct an optimal linear coherent quantum controller based on an evolutionary optimization method, namely a differential evolution algorithm. The aim is to provide a straightforward approach to deal with both nonlinear and nonconvex constraints arising in the coherent quantum controller synthesis. The solution to this control problem involves a complex algebraic Riccati equation, which corresponds to a physical realizability condition for the coherent quantum controller. The proposed method is demonstrated through an example of an entanglement control problem for a quantum network comprising two cascaded optical parametric amplifiers.Index Terms-Coherent quantum control, differential evolution, entanglement control. I. INTRODUCTIONDeveloping reliable computational methods has been an important aspect of solving quantum control problems. In this regard, we particularly refer to [1]- [3] where it is shown that a dynamic coherent quantum controller must satisfy a physical realizability condition in order to exhibit a meaningful quantum dynamic. This requirement leads to a quantum controller synthesis problem with a nonconvex nonlinear constraint, which is often difficult to solve numerically. This issue has indeed been addressed in [2] where a rank constrained LMI approach (see [4]) is used to synthesize a physically realizable coherent quantum LQG controller. The approach of [2], however, is applied only to solve a relaxed feasibility version of the original quantum LQG control problem, which is a nonconvex nonlinear optimization problem and remains to be solved. Also, there is a concern about the success of the rank constrained LMI approach, which is dependent on a suitable initial point to begin the numerical iteration. Moreover, when dealing with higher order quantum control systems, the approach of [2] will lead to complicated rank constrained LMI problems.These concerns provide our impetus to present in this technical note a tractable algorithm to solve a coherent quantum feedback control problem for a class of non-commutative linear quantum stochastic systems. Inspired by [2] and [5], we thus propose to use an evolutionary optimization approach, that is the differential evolution (DE) algorithm (see [6]), to solve the quantum feedback control problem. The aims are to obtain a straightforward algorithm and to avoid a critical dependence on a suitable initial point to start the numerical iteration. Consequently, we reformulate the given quantum control problem as a constrained nonlinear optimization problem. In this case, the Manuscript

No abstract