Advances in Evolutionary Optimization of Quantum Operators

• https://mendel-journal.org/index.php/mendel/article/view/152/161

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.