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

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.

21 pages, 8 figures

References in corpus (10)

• Quantum algorithm for solving linear systems of equations
• Logical quantum processor based on reconfigurable atom arrays
• Architectures for a quantum random access memory
• Encoding a magic state with beyond break-even fidelity
• Towards provably efficient quantum algorithms for large-scale machine-learning models
• Linear combination of Hamiltonian simulation for nonunitary dynamics with optimal state preparation cost
• Fault-Tolerant One-Bit Addition with the Smallest Interesting Colour Code
• Potential quantum advantage for simulation of fluid dynamics
• An Inexact Feasible Quantum Interior Point Method for Linearly Constrained Quadratic Optimization
• Early Exploration of a Flexible Framework for Efficient Quantum Linear Solvers in Power Systems