  Mixed Integer Linear Programming (MILP) can be considered the backbone of the
modern power system optimization process, with a large application spectrum,
from Unit Commitment and Optimal Transmission Switching to verifying Neural
Networks for power system applications. The main issue of these formulations is
the computational complexity of the solution algorithms, as they are considered
NP-Hard problems. Quantum computing has been tested as a potential solution
towards reducing the computational burden imposed by these problems, providing
promising results, motivating the can be used to speedup the solution of MILPs.
In this work, we present a general framework for solving power system
optimization problems with a Quantum Computer (QC), which leverages
mathematical tools and QCs' sampling ability to provide accelerated solutions.
Our guiding applications are the optimal transmission switching and the
verification of neural networks trained to solve a DC Optimal Power Flow.
Specifically, using an accelerated version of Benders Decomposition , we split
a given MILP into an Integer Master Problem and a linear Subproblem and solve
it through a hybrid ``quantum-classical'' approach, getting the best of both
worlds. We provide 2 use cases, and benchmark the developed framework against
other classical and hybrid methodologies, to demonstrate the opportunities and
challenges of hybrid quantum-classical algorithms for power system mixed
integer optimization problems.
