Quantum Information & Computation
Volume 25, Issue 3
RESEARCH ARTICLE Open access

Variational Quantum Algorithm for Solving Second-Order Linear Differential Equations

Ryo Sugaya, Tomohiro Sogabe, Tomoya Kemmochi, Shao-Liang Zhang

Author affiliations
  • Ryo Sugaya1
  • Tomohiro Sogabe1
  • Tomoya Kemmochi1
  • Shao-Liang Zhang1
  1. Department of Applied Physics, Graduate School of Engineering, Nagoya University, Nagoya 464-8601, Japan

pp. 232-247 · 10.2478/qic-2025-0012

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Abstract

Variational quantum algorithms (VQAs) have attracted attention as quantum algorithms employing on noisy intermediate-scale quantum devices. VQAs for solving the Poisson equation were recently proposed, as this method transforms the linear equation with a symmetric positive definite matrix obtained by discretizing the Poisson equation into a minimization problem. In this study, we propose a VQA for second-order linear differential equations including the Poisson equation on the basis of the referenced study, where the coefficient matrix obtained through discretization is a non-symmetric matrix. Furthermore, in our VQAs, we succeeded in decomposing the coefficient matrices arising from the periodic and the Dirichlet boundary condition into linear combinations of measurement operators and unitary matrices.
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Keywords

  • quantum computing
  • variational quantum algorithm
  • linear equations

Suggested citation

Ryo Sugaya, Tomohiro Sogabe, Tomoya Kemmochi, Shao-Liang Zhang (2025). Variational Quantum Algorithm for Solving Second-Order Linear Differential Equations. Quantum Information & Computation, 25(3), 232-247. https://doi.org/10.2478/qic-2025-0012

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