Quantum Optimization for Network Capacity Expansion of Microgrid Models via Grover-Enhanced QAOA

We propose a compact, application-driven instantiation of the Quantum Approximate Optimization Algorithm (QAOA) for constrained combinatorial network expansion problem for a typical microgrid. The approach pairs a Grover-style feasibility-aware mixer with an observable diagonal cost and a pragmatic grid+refine parameter search that respects the discrete nature of amplitude-amplification steps while optimising continuous phase angles. Benchmarked against a classical global solver on an instance derived from a PyPSA model and evaluated via noiseless statevector simulation and sampling, the method demonstrably elevates the quantum probability mass on the true classical optimum and improves the signal-to-noise ratio inside the feasible subspace. We discuss algorithmic trade-offs and outline promising directions for parameterisation and hardware validation.