Quantum multi-output Gaussian Processes based Machine Learning for Line Parameter Estimation in Electrical Grids

TL;DR

This paper introduces a quantum multi-output Gaussian Process model utilizing quantum algorithms to efficiently perform kernel matrix inversion, applied to electrical grid line parameter estimation, demonstrating feasibility on IBM Quantum hardware.

Contribution

The paper develops a quantum version of multi-output Gaussian Processes using the HHL algorithm with circuit optimization, enabling practical application in real-world electrical grid analysis.

Findings

Successful implementation of 13-qubit HHL circuit on IBM Quantum hardware.

QGP demonstrates comparable performance to classical methods in line parameter estimation.

Circuit optimization via AQC reduces depth, making quantum implementation feasible.

Abstract

Gaussian process (GP) is a powerful modeling method with applications in machine learning for various engineering and non-engineering fields. Despite numerous benefits of modeling using GPs, the computational complexity associated with GPs demanding immense resources make their practical usage highly challenging. In this article, we develop a quantum version of multi-output Gaussian Process (QGP) by implementing a well-known quantum algorithm called HHL, to perform the Kernel matrix inversion within the Gaussian Process. To reduce the large circuit depth of HHL a circuit optimization technique called Approximate Quantum Compiling (AQC) has been implemented. We further showcase the application of QGP for a real-world problem to estimate line parameters of an electrical grid. Using AQC, up to 13-qubit HHL circuit has been implemented for a 32x32 kernel matrix inversion on IBM Quantum hardware for demonstrating QGP based line parameter estimation experimentally. Finally, we compare its performance against noise-less quantum simulators and classical computation results.