Quantum Computing for Solid Mechanics and Structural Engineering -- a
  Demonstration with Variational Quantum Eigensolver
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.
Yunya Liu Jiakun Liu Jordan R. Raney Pai Wang