Quantum-Assisted Multi-Output Gaussian Processes for Line Parameter Estimation in Power Systems

IEEE Access, vol. 14, pp. 66758–66769

Abstract

A 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, a proof-of-concept demonstration of quantum-assisted multi-output Gaussian Process regression is presented, where the kernel matrix inversion during the training phase of GP is replaced by the Harrow-Hassidim-Lloyd (HHL) algorithm, a well-known quantum algorithm for solving linear systems. The presented approach uses classical kernels, but employs quantum computing for the computationally expensive matrix inversion operations. To reduce the large circuit depth of HHL, matrix conditioning and a circuit optimization technique called Approximate Quantum Compiling (AQC) is implemented, which reduces the circuit depth fromO(107) gates to approximately 250 gates. The quantum-assisted Gaussian process is then utilized for implementation of line parameter of electrical grids, a real-world problem adapted from our previous work. Using AQC, up to 13-qubit HHL circuit has been implemented for a 32×32 kernel matrix inversion on IBM Quantum hardware (IBM Auckland). The performance of quantum hardware implementation is compared against noiseless quantum simulators and classical computation results. Through this work the feasibility of implementing quantum-assisted GP on current Noisy Intermediate-Scale Quantum (NISQ) hardware is demonstrated and key bottlenecks for future improvements are identified. To the best of authors’ knowledge, this is one of the largest experimental implementations involving HHL algorithm for power system applications on IBM hardware.

Authors 7

1. Priyanka Arkalgud Ganeshamurthy Aachen E.ON Energy Research Center Institute for Automation of Complex Power Systems

   RWTH Aachen University

   Affiliation as printed

   E.ON Energy Research Center, Institute for Automation of Complex Power Systems, RWTH Aachen University, Aachen, Germany

2. Kumar Ghosh

   E.ON (Germany)

   Affiliation as printed

   E.ON Digital Technology GmbH, Hannover, Germany

3. Corey O’Meara

   E.ON (Germany)

   Affiliation as printed

   E.ON Digital Technology GmbH, Hannover, Germany

4. G. Cortiana

   E.ON (Germany)

   Affiliation as printed

   E.ON Digital Technology GmbH, Hannover, Germany

5. Jan Schiefelbein-Lach

   E.ON (Germany)

   Affiliation as printed

   E.ON Group Innovation GmbH, Essen, Germany

6. Antonello Monti Aachen E.ON Energy Research Center Institute for Automation of Complex Power Systems

   RWTH Aachen University

   Affiliation as printed

   E.ON Energy Research Center, Institute for Automation of Complex Power Systems, RWTH Aachen University, Aachen, Germany

7. Ferdinanda Ponci Aachen E.ON Energy Research Center Institute for Automation of Complex Power Systems

   RWTH Aachen University

   Affiliation as printed

   E.ON Energy Research Center, Institute for Automation of Complex Power Systems, RWTH Aachen University, Aachen, Germany