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.

翻译：变分量子算法利用叠加与纠缠特性，通过操控量子态高效优化代价函数，适用于近期全球研究界可访问的含噪中等规模量子（NISQ）计算机。本文在IBM Qiskit Runtime平台的5量子比特与7量子比特量子处理器上实现并演示了数值计算过程。我们将商用有限元法（FEM）软件ABAQUS与变分量子本征求解器（VQE）相结合，构建了集成化流水线。通过六边形桁架、铁木辛柯梁和平面应变连续体三个算例研究其性能，并利用这种混合量子-经典方法开展基频收敛性参数化分析。当未来具备数百量子比特的量子计算机问世时，本研究结论可推广至自由度更多的问题。