A Voxel-Based Quantum Computing Method (VBQC) for Solid Mechanics Problem

2026-06-02

AI Summary

This work addresses the challenge of efficiently simulating solid mechanics problems on quantum computers, which typically require unstructured meshes due to Lagrangian descriptions and complex boundaries, leading to system matrices ill-suited for quantum simulation. To overcome this, the authors propose a Voxel-Based Quantum Computing (VBQC) method that discretizes the spatial domain using a regular voxel grid, yielding mass and stiffness matrices with a tridiagonal fractal structure. They introduce a KCQ decomposition to factorize these matrices into three fundamental types, enabling efficient Hamiltonian simulation via the quantum Fourier transform and quantum multiplexers. By integrating voxel discretization with KCQ decomposition for the first time, this approach circumvents the quantum encoding bottleneck imposed by irregular meshes and demonstrates correctness and feasibility on representative three-dimensional solid mechanics problems.

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.

Problem

• quantum computing
• solid mechanics
• irregular grids
• Hamiltonian simulation
• spatial discretization

Innovation

• Voxel-Based Quantum Computing
• KCQ Decomposition
• Hamiltonian Simulation
• Solid Mechanics
• Quantum Fourier Transform