Advances in Evolutionary Optimization of Quantum Operators

Evolution strategy, differential evolution, self-adaptation of control parameters, quantum operator, unitary matrix.

Three existing techniques (representations) which allow generating unitary matrices are used in various evolutionary algorithms in order to optimize their coefficients. The objective is to obtain as precise quantum operators (the resulting unitary matrices) as possible for given quantum transformations. Ordinary evolution strategy, self-adaptive evolution strategy and differential evolution are applied with various settings as the optimization algorithms for the quantum operators. These algorithms are evaluated on the tasks of designing quantum operators for 3- and 4-qubit maximum amplitude detector and a solver of a logic function of three variables in conjunctive normal form. These tasks require require unitary matrices of various sizes. It will be demonstrated that the self-adaptive evolution strategy and differential evolution are able to produce remarkably better results than the ordinary evolutiona strategy. Moreover, the results can be improved by selecting a proper settings for the evolution as presented by a comparative evaluation. A comparative study is presented regarding the evolutionary design of quantum operators in the form of unitary matrices.