Global optimization in variational quantum algorithms via dynamic tunneling method

We present a global optimization routine for the variational quantum algorithms, which utilizes the dynamic tunneling flow. Originally designed to leverage information gathered by a gradient-based optimizer around local minima, we adapt the conventional dynamic tunneling flow to exploit the distance measure of quantum states, resolving issues of extrinsic degeneracy arising from the parametrization of quantum states. Our global optimization algorithm is applied to the variational quantum eigensolver for the transverse-field Ising model to demonstrate the performance of our routine while comparing it with the conventional dynamic tunneling method, which is based on the Euclidean distance measure on the parameter space.