  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.

Quantum Physics