Implementation of the HHL Algorithm for Solving the Poisson Equation on Quantum Simulators
Daribayev B. Mukhanbet A. Imankulov T.
October 2023Multidisciplinary Digital Publishing Institute (MDPI)
Applied Sciences (Switzerland)
2023#13Issue 20
The Poisson equation is a fundamental equation of mathematical physics that describes the potential distribution in static fields. Solving the Poisson equation on a grid is computationally intensive and can be challenging for large grids. In recent years, quantum computing has emerged as a potential approach to solving the Poisson equation more efficiently. This article uses quantum algorithms, particularly the Harrow–Hassidim–Lloyd (HHL) algorithm, to solve the 2D Poisson equation. This algorithm can solve systems of equations faster than classical algorithms when the matrix A is sparse. The main idea is to use a quantum algorithm to transform the state vector encoding the solution of a system of equations into a superposition of states corresponding to the significant components of this solution. This superposition is measured to obtain the solution of the system of equations. The article also presents the materials and methods used to solve the Poisson equation using the HHL algorithm and provides a quantum circuit diagram. The results demonstrate the low error rate of the quantum algorithm when solving the Poisson equation.
HHL algorithm , Poisson equation , QFT , quantum algorithms , quantum computing
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Department of Computer Science, Faculty of Information Technology, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Department of Computer Science
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