# Quantum Computing for Solid Mechanics and Structural Engineering -- a Demonstration with Variational Quantum Eigensolver

arXiv: https://arxiv.org/abs/2308.14745 · HTML: https://mlsanity.com/paper/2308.14745/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Aug 2023.

## Built on by (most cited first, 1 of 1)

- [Hybrid Quantum Classical Surrogate for Real Time Inverse Finite Element Modeling in Digital Twins](https://mlsanity.com/paper/2508.00029/) (2025)

## Abstract (arXiv)

Variational quantum algorithms exploit the features of superposition and entanglement to optimize a cost function efficiently by manipulating the quantum states. They are suitable for noisy intermediate-scale quantum (NISQ) computers that recently became accessible to the worldwide research community. Here, we implement and demonstrate the numerical processes on the 5-qubit and 7-qubit quantum processors on the IBM Qiskit Runtime platform. We combine the commercial finite-element-method (FEM) software ABAQUS with the implementation of Variational Quantum Eigensolver (VQE) to establish an integrated pipeline. Three examples are used to investigate the performance: a hexagonal truss, a Timoshenko beam, and a plane-strain continuum. We conduct parametric studies on the convergence of fundamental natural frequency estimation using this hybrid quantum-classical approach. Our findings can be extended to problems with many more degrees of freedom when quantum computers with hundreds of qubits become available in the near future.