Details of Classical Optimization in ADAPT-VQE

Variational quantum eigensolvers (VQEs) have come to represent a diverse and powerful family of methods for computing chemical energies, where measurements of a quantum circuit are paired with classical parameter optimization to variationally minimize a cost function. Our team has recently introduced the concept of a dynamical ansatz in VQE (which we call ADAPT-VQE), which grows a unique circuit for each problem with the goal of minimizing the circuit depth. While ADAPT-VQE has been very successful at decreasing the circuit depth, the problem of classical parameter optimization persists. In general, VQEs appear to suffer from certain numerical difficulties during parameter optimization, such as exponential suppression of the gradient (barren plateaus) and large numbers of local minima. In this work, we discuss numerical problems in the context of ADAPT-VQE and how to modify the algorithm to avoid them.