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

Combining the QAOA and HHL Algorithm to achieve a Substantial Quantum Speedup for the Unit Commitment Problem