Title: Numerical solution of boundary value problems using quantum computing system

Authors: Ajanta Das; Debabrata Datta; S. Suman Rajest; Varun Kumar Nomula; R. Dharani; K. Danesh

Addresses: Department of Physics, Heritage Institute of Technology, Kolkata, 700107, West Bengal, India ' Department of Information Technology, Heritage Institute of Technology, Kolkata, 700107, West Bengal, India ' Department of Research and Development (R&D) and International Student Affairs (ISA), Dhaanish Ahmed College of Engineering, Chennai, 601301, Tamil Nadu, India ' Department of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, 30332, USA ' Department of Information Technology, Panimalar Engineering College, Chennai, 600123, Tamil Nadu India ' Department of Electronics and Communication Engineering, SRM Institute of Science and Technology, Ramapuram Campus, Chennai, 600089, Tamil Nadu India

Abstract: Boundary value problems (BVPs) arise in various scientific and engineering disciplines, including physics, finance, and biology. Classical computers may not be able to solve these problems quickly or accurately due to their computational complexity. Quantum Fourier transform (QFT) may efficiently solve differential equations including the Schrödinger equation and Helmholtz equation, according to recent quantum computing research. Quantum annealing determines a Hamiltonian's ground state using quantum fluctuation. The quantum computing BVP approach is novel to numerical methods. Quantum methods like quantum phase estimation have not been employed to solve BVPs in heat transfer, groundwater modelling, or advection diffusion response. The Harrow-Hassidim-Lloyd (HHL) quantum algorithm solves steady-state heat and radon-diffusion equations in this research study. The BVP linear operator eigenvalues are computed using the quantum phase estimation approach. We used IBM's 'Qiskit' package to compute in Python. IBM Qiskit's 'Linear Solver' program provided the quantum computing numerical solution. Tridiagonal Toeplitz matrix role is shown. Comparisons with traditional results and future applications were made.

Keywords: BVPs; boundary value problems; quantum computing; HHL algorithm; quantum phase; estimation algorithm; linear solver; QFT; quantum Fourier transform.

DOI: 10.1504/IJSSE.2025.151321

International Journal of System of Systems Engineering, 2025 Vol.15 No.6, pp.561 - 579

Received: 12 Jun 2023
Accepted: 26 Aug 2023
Published online: 23 Jan 2026 *

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