Variational quantum algorithms are a promising hybrid framework for solving chemistry and physics problems with broad applicability to optimization as well. They are particularly well suited for noisy intermediate scale quantum (NISQ) computers. In this paper, we describe the unitary block optimization scheme (UBOS) and apply it to two variational quantum algorithms: the variational quantum eigensolver (VQE) and variational time evolution. The goal of VQE is to optimize a classically intractable parameterized quantum wave function to target a physical state of a Hamiltonian or solve an optimization problem. UBOS is an alternative to other VQE optimization schemes with a number of advantages including fast convergence, less sensitivity to barren plateaus, the ability to tunnel through some local minima and no hyperparameters to tune. We additionally describe how UBOS applies to real and imaginary time-evolution (TUBOS).

17 pages, 11 figures