An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications

TL;DR

This paper investigates the application of the HHL quantum linear solver to scientific problems like power-grid management and climate modeling, analyzing accuracy, resource costs, and error correction in simulated quantum environments.

Contribution

It provides an early assessment of the HHL algorithm's feasibility and resource requirements for scientific applications using quantum simulation tools.

Findings

Quantum phase estimation accuracy impacts solution quality.

Resource costs grow exponentially with problem size.

Quantum error correction can reduce physical qubit demands.

Abstract

In this paper, we explore using the Harrow-Hassidim-Lloyd (HHL) algorithm to address scientific and engineering problems through quantum computing, utilizing the NWQSim simulation package on a high-performance computing platform. Focusing on domains such as power-grid management and climate projection, we demonstrate the correlations of the accuracy of quantum phase estimation, along with various properties of coefficient matrices, on the final solution and quantum resource cost in iterative and non-iterative numerical methods such as the Newton--Raphson method and finite difference method, as well as their impacts on quantum error correction costs using the Microsoft Azure Quantum resource estimator. We summarize the exponential resource cost from quantum phase estimation before and after quantum error correction and illustrate a potential way to reduce the demands on physical qubits. This work lays down a preliminary step for future investigations, urging a closer examination of quantum algorithms' scalability and efficiency in domain applications.