Benchmarking the DC-OPF Problem on Quantum Annealers

Abstract

Combinatorial optimization problems can be naturally formulated as Quadratic Unconstrained Binary Optimization (QUBO) models and subsequently mapped onto Ising Hamiltonians, making them suitable for Quantum Annealing (QA) techniques. However, the practical implementation of these approaches is hindered by the limited connectivity of current quantum hardware and by the difficulty of accurately simulating the annealing dynamics for large-scale instances. In this work, a Direct Current Optimal Power Flow (DC-OPF) problem is formulated as a QUBO model and studied from both the embedding and annealing perspectives. Two embedding strategies, namely minorminer and the Triangular Architecture, are analyzed in terms of their physical qubit requirements. In addition, two simulation approaches, QiliSim and a variational method, are employed to investigate the annealing dynamics. To improve the annealing performance, catalyst terms previously developed for systems without local fields are extended to account for the local field contributions naturally present in the DC-OPF formulation. These additional interactions, inspired by diagonal augmentations of the Quantum Approximate Optimization Algorithm (QAOA), act as catalysts by enhancing the ground state fidelity with respect to standard quantum annealing. Different catalyst configurations are studied and their effect on the probability of obtaining low energy states is analyzed. Furthermore, qubit reduction strategies based on thresholding and spectral decomposition are investigated in order to decrease the physical resources required for implementation. The results show that the inclusion of local field contributions in the catalyst term, leads to a significant improvement in the annealing performance and that suitable thresholding techniques allow the number of physical qubits to be reduced by approximately a factor of two while preserving the quality of the obtained solutions. These findings provide further support for the catalyst framework and contribute to bringing realistic optimization problems closer to current quantum hardware