Evolving quantum circuits at the gate level with a hybrid quantum-inspired evolutionary algorithm

This paper proposes an approach to evolve quantum circuits at the gate level, based on a hybrid quantum-inspired evolutionary algorithm. This approach encodes quantum gates as integers and combines the cost and correctness of quantum circuits into the fitness function. A fast algorithm of matrix multiplication with Kronecker product has been proposed to speed up the calculation of matrix multiplication in individuals evaluation. This algorithm is shown to be better than the known best algorithm for matrix multiplication when a certain condition holds. The approach of evolving quantum circuits is validated by some experiments and the effects of some parameters are investigated. And finally, some features of the approach are also discussed.