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

TL;DR

This paper demonstrates the application of variational quantum eigensolver algorithms on small quantum processors to solve solid mechanics problems, integrating quantum computing with finite element software for potential future large-scale structural analysis.

Contribution

It introduces a hybrid quantum-classical pipeline combining VQE with FEM software and demonstrates its feasibility on current quantum hardware for structural mechanics problems.

Findings

Successful implementation on 5- and 7-qubit quantum processors

Effective estimation of natural frequencies in structural models

Potential scalability to larger problems with future quantum hardware

Abstract

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.