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arXiv:2512.17582

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

James Hancock, Matthew Craven, Craig McNeile

quant-phSubmitted Dec 19, 2025• Announced Dec 22, 2025• 0 citations
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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.

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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 9×99\times 99×9 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.
Abstract Layout optimization problems involve finding the optimal arrangement of elements in order to maximize efficiency. For instance, the wind farm layout optimization (WFLO) problem consists of the best turbine placement to maximize energy production while minimizing wake losses. As its nonlinear and combinatorial nature makes it challenging for traditional optimization methods, alternative approaches such as quantum annealing and quantum‐classical hybrid methods offer a promising alternative for tackling such complex problems. Here, WFLO is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem using the Jensen wake model. A quantum annealer is compared, the Gurobi solver, and the Quantum Approximate Optimization Algorithm (QAOA). The quantum annealer provides solutions one order of magnitude faster than Gurobi with at most 3% lower power output, making it suitable for rapid suboptimal approximations. These findings highlight the trade‐off between the quality of the solution and the computational time and demonstrate how quantum methods, especially when combined with classical solvers, can contribute to efficient renewable energy optimization.
Recent advancements in quantum computing have demonstrated significant potential for solving combinatorial optimization problems, like the quadratic knapsack problem, a constrained binary optimization problem. How- ever, current quantum and quantum-inspired algorithms often require transforming these constrained problems into an unconstrained form, known as Quadratic Unconstrained Binary Optimization (QUBO). Such transfor- mations can significantly impact the algorithms’ speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess all nine methods using Simulated An- nealing and find that three of our approaches outperform existing methods in terms of execution time and the quality and quantity of feasible solutions found. Additionally, we tested these transformations on quantum annealers, which were unable to solve even small problem instances, due to limitations in connectivity and error rates. However, our results highlight the advantages of the new approaches, which reduce the total num- ber of variables in the QUBO representation. This is a critical factor for enhanced performance on emerging quantum hardware, since it also reduces the required number of qubits and the embedding chain lengths.
To run an algorithm on a quantum computer, one must choose an assignment from logical qubits in a circuit to physical qubits on quantum hardware. This task of initial qubit placement, or qubit allocation, is especially important on present-day quantum computers which have a limited number of qubits, connectivity constraints, and varying gate fidelities. In this work we formulate and implement the qubit placement problem as a quadratic, unconstrained binary optimization (QUBO) problem and solve it using simulated annealing to obtain a spectrum of initial placements. Compared to contemporary allocation methods available in t|ket$\rangle $ and Qiskit, the QUBO method yields allocations with improved circuit depth for $>$50% of a large set of benchmark circuits, with many also requiring fewer CX gates.
Recent advancements in quantum computing have demonstrated significant potential for solving combinatorial optimization problems, like the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum and quantum-inspired algorithms often require transforming these constrained problems into an unconstrained form, known as Quadratic Unconstrained Binary Optimization (QUBO). Such transformations can significantly impact the algorithms’ speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess all nine methods using Simulated Annealing and find that three of our approaches outperform existing methods in terms of execution time and the quality and quantity of feasible solutions found. Additionally, we tested these transformations on quantum annealers, which were unable to solve even small problem instances, due to limitations in connectivity and error rates. However, our results highlight the advantages of the new approaches, which reduce the total number of variables in the QUBO representation. This is a critical factor for enhanced performance on emerging quantum hardware, since it also reduces the required number of qubits and the embedding chain lengths.
The LogQ algorithm encodes Quadratic Unconstrained Binary Optimization (QUBO) problems with exponentially fewer qubits than the Quantum Approximate Optimization Algorithm (QAOA). The advantages of conventional LogQ are accompanied by a challenge related to the optimization of its free parameters, which requires the usage of resourceintensive evolutionary or even global optimization algorithms. We propose a newlog⁡Q\log QlogQparameterization that can be optimized with a gradient-inspired method, which is less resource-intensive and thus strengthens the advantage of LogQ over QAOA for large/industrial problems. We illustrate the features of our method on an analytical model and present larger scale numerical results on MaxCut problems.