  In this paper, we propose a quantum algorithm to solve the unit commitment
(UC) problem at least cubically faster than existing classical approaches. This
is accomplished by calculating the energy transmission costs using the HHL
algorithm inside a QAOA routine. We verify our findings experimentally using
quantum circuit simulators in a small case study. Further, we postulate the
applicability of the concepts developed for this algorithm to be used for a
large class of optimization problems that demand solving a linear system of
equations in order to calculate the cost function for a given solution.
