A Hybrid Quantum Algorithm for Load Flow

TL;DR

This work introduces a hybrid quantum approach to load-flow analysis by substituting the classical Jacobian inversion in Newton-Raphson with the HHL quantum linear solver to obtain the Newton direction. It details the theoretical components of HHL, including QFT and QPE, and integrates them into the NR framework to solve $Jx=\Delta\beta$ iteratively. Experimental results on small IEEE cases indicate that, in simulation, the HHL-based method is significantly slower than classical NR due to overheads, though convergence is achieved and the direction vectors become increasingly consistent across iterations. The study highlights the potential for quantum accelerations in large-scale load-flow problems and points to preconditioning and QPE refinements as key avenues to realize practical speedups on future quantum devices.

Abstract

The goal of the load flow study is to ensure that electrical power is delivered efficiently and reliably to end-users while maintaining the stability and security of the power system. Newton-Raphson is a numerical method used widely for load flow analysis. One of the most computationally expensive steps in this method is an equation-solving step. We propose to replace this step with HHL, a quantum algorithm for solving linear systems of equations. HHL is exponentially faster, but with caveats. In this study, a hybrid quantum algorithm is proposed for solving load flow. The Newton-Raphson method is used as a benchmark to compare the performance of the hybrid quantum algorithm. Although the simulation of the hybrid quantum algorithm takes much time, these preliminary results are encouraging and point to the potential for the use of quantum algorithms to develop hybrid quantum algorithms for load flow analysis and related problems.

Figures (2)

• Figure 1: QPE Circuit
• Figure 2: HHL Circuit