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

TL;DR

This paper explores quantum computing methods for windfarm layout optimization, introducing new encoding techniques that reduce qubit requirements and enable solving larger problems efficiently on quantum simulators.

Contribution

It presents a novel single-qubit operator encoding method and compares it with existing approaches, demonstrating improved scalability for windfarm optimization problems.

Findings

Both encoding methods perform competitively.

Problems on 9x9 grids can be solved with up to 20 qubits.

Methods show favorable scaling characteristics.

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.