Performance Comparison of Gate-Based and Adiabatic Quantum Computing for Power Flow Analysis

TL;DR

This work reframes AC power flow as a combinatorial PF problem amenable to Ising/QUBO representations and compares gate-based QAOA against adiabatic quantum computing solutions (D-Wave QA and Fujitsu QIIO) on a 4-bus system. It shows that QA and QIIO can closely reproduce NR solutions with small residuals, while QAOA achieves comparable accuracy for some components but lags in others and does not consistently meet convergence thresholds in the tested setup. The results reveal clear trade-offs: AQC methods currently offer faster convergence and higher scalability for PF, whereas GQC approaches like QAOA remain challenged by hardware limitations and optimization overhead in NISQ-era experiments. Overall, the paper provides the first QAOA PF implementation and a direct performance comparison, illustrating the practical viability and scalability prospects of quantum PF algorithms as hardware evolves.

Abstract

In this paper, we present the first direct comparison between gate-based quantum computing (GQC) and adiabatic quantum computing (AQC) for solving the AC power flow (PF) equations. Building on the Adiabatic Quantum Power Flow (AQPF) algorithm originally designed for annealing platforms, we adapt it to the Quantum Approximate Optimization Algorithm (QAOA). The PF equations are reformulated as a combinatorial optimization problem. Numerical experiments on a 4-bus test system assess solution accuracy and computational time. Results from QAOA are benchmarked against those obtained using D-Wave's Advantage system and Fujitsu's latest generation Digital Annealer, i.e., Quantum-Inspired Integrated Optimization software (QIIO). The findings provide quantitative insights into the performance trade-offs, scalability, and practical viability of GQC versus AQC paradigms for PF analysis, highlighting the potential of quantum algorithms to address the computational challenges associated with modern electricity networks in the Noisy Intermediate-Scale Quantum (NISQ).

Figures (1)

• Figure 1: Representation of $\mathbf{\mu} = [\mu_1, \mu_2, \mu_3]$ and $\mathbf{\omega} = [\omega_1, \omega_2, \omega_3]$ obtained by QA, QIIO, and QAOA for the 4-bus test system. The slack bus $i=0$ is not shown. The graphs include $\mu_i$ and $\omega_i$ obtained from the NR solver.