  We introduce a family of variational quantum algorithms called quantum
iterative power algorithms (QIPA) that outperform existing hybrid near-term
quantum algorithms of the same kind. We demonstrate the capabilities of QIPA as
applied to three different global-optimization numerical experiments: the
ground-state optimization of the $H_2$ molecular dissociation, search of the
transmon qubit ground-state, and biprime factorization. Since our algorithm is
hybrid, quantum/classical technologies such as error mitigation and adaptive
variational ansatzes can easily be incorporated into the algorithm. Due to the
shallow quantum circuit requirements, we anticipate large-scale implementation
and adoption of the proposed algorithm across current major quantum hardware.
