A Voxel-Based Quantum Computing Method (VBQC) for Solid Mechanics Problem
2026-06-02 • Computational Engineering, Finance, and Science
Computational Engineering, Finance, and Science
AI summaryⓘ
The authors propose a new method called voxel-based quantum computing (VBQC) to help simulate solid mechanics problems using quantum computers. They use regular voxel grids to make complex solid structures easier to break down into simpler parts, called the KCQ decomposition. This helps represent the system matrix in a way that quantum algorithms can handle more efficiently. They tested their method on three different solid mechanics problems and showed it works correctly. Overall, the authors provide a way to make quantum simulations for solid mechanics more practical.
quantum computingsolid mechanicsvoxel gridHamiltonianKCQ decompositionquantum Fourier transformquantum multiplexersystem matrixspatial discretizationtridiagonal matrix
Authors
Feng Wu, Yuxiang Yang, Li Zhu, Chen Li, Yansong Guo, Xu Guo
Abstract
Quantum computing presents a promising method to overcome the efficiency and memory constraints in large-scale mechanical problems, with numerous successful applications demonstrated in fluid mechanics. However, solid mechanics problems usually require irregular grids for spatial discretization, due to the Lagrange formulations and complex boundaries, which makes the quantum simulation of the system matrix, e.g., the mass or stiffness matrix which is often referred to as the Hamiltonian in quantum computing, difficult to be effectively conducted. This study proposes a voxel-based quantum computing method (VBQC) for the quantum simulation of Hamiltonians in solid mechanics. VBQC applies voxel grids to discretize the spatial domain, thereby enabling the system matrix to exhibit the tridiagonal fractal property. Based on this property, the system matrix can be decomposed into three groups of fundamental matrices, $\mathbf{k}_{n}$, $\mathbf{c}_{n}$, and $\mathbf{q}_{n}$. This decomposition process is referred to as the KCQ decomposition. By integrating the KCQ decomposition with the quantum Fourier transform and the quantum multiplexer, VBQC enables efficient quantum simulation of Hamiltonians in solid mechanics. Three specific solid problems with different dimensions and numbers of variables are applied to preliminarily verify the correctness of the proposed VBQC for solid mechanics problems.