Information flow in parameterized quantum circuits

Abstract: In this work, we introduce a new way to quantify information flow in quantum systems, especially for parameterized quantum circuits. We use a graph representation of the circuits and propose a new distance metric using the mutual information between gate nodes. We then present an optimization procedure for variational algorithms using paths based on the distance measure. We explore the features of the algorithm by means of the variational quantum eigensolver, in which we compute the ground state energies of the Heisenberg model. In addition, we employ the method to solve a binary classification problem using variational quantum classification. From numerical simulations, we show that our method can be successfully used for optimizing the parameterized quantum circuits primarily used in near-term algorithms. We further note that information-flow based paths can be used to improve convergence of existing stochastic gradient based methods.