Investigating methods to solve large windfarm optimization problems with a minimum number of qubits using circuit-based quantum computers

TL;DR

The paper tackles windfarm layout optimization by casting WFLO as a QUBO and developing two quantum encodings, Pauli correlation encoding (PCE) and single-qubit operator encoding (SQOE), to dramatically reduce qubit requirements. It demonstrates through toy and real-world windfarm models (including Alltwalis, on grids up to 9×9) that SQOE generally yields higher-quality solutions and more favorable time scaling than PCE, while requiring shallower circuits. Across power-output tests and scaling analyses, the quantum approaches show competitive performance relative to a classical solver (Gurobi) and exhibit promising scaling, though full hardware demonstrations with quantum error mitigation remain for future work. The results suggest a viable path for applying circuit-based quantum optimization to WFLO and, more broadly, to other NP-hard combinatorial problems in energy systems and beyond.

Abstract

This study investigates quantum computing approaches for solving the windfarm layout optimization (WFLO) problems formulated as a quadratic unconstrained binary optimization (QUBO) problem. We investigate two encoding methods that require fewer than one qubit per grid point: the previously developed Pauli correlation encoding (PCE) and a novel single-qubit operator encoding (SQOE). These methods are tested on three windfarm configurations - two from prior WFLO scaling studies and a new real-world model based on an existing windfarm in Wales. The improved encoding methods allow us to solve WFLO problems on $9\times 9$ grids using up to 20 qubits on a quantum computer simulator. The results show that both encoding methods perform competitively and demonstrate favorable scaling characteristics across the tested systems.

Figures (30)

• Figure 1: Rose diagrams showing windspeed and probability distributions for the second Mosetti benchmark wind regime.
• Figure 2: Heatmaps of problem QUBO matrix with constraint weight (a) $\lambda=0$ and (b) $\lambda=250$.
• Figure 3: Labelling of sites on a $L=10$ windfarm grid. There is a turbine located at position 15. The wind regime is $D=\{\{0,v,1\}\}$, with capped wake length $3$ and wake radius $1$. These values are not realistic, but show the connections that occur due to wakes. More realistic wake patterns are shown in appendix \ref{['appen:Wakes']}.
• Figure 4: Heatmaps of QUBO matrix for (a) $M=4.0$ constraint and (b) $E=465.0\text{m}$, both with $\lambda = 200$.
• Figure 5: (a) On grid diagram to show how minimum spacing constraint causes $O(L)$-length connections in QUBO matrix. (b) Heatmaps of QUBO matrix for (a) $\vec{P}$ constraint with $\lambda = 200$.