  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).
