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We proposed a general quantum-computing-based algorithm that harnesses theexponential power of noisy intermediate-scale quantum (NISQ) devices in solvingpartial differential equations (PDE). This variational quantum eigensolver(VQE)-inspired approach transcends previous idealized model demonstrationsconstrained by strict and simplistic boundary conditions. It enables theimposition of arbitrary boundary conditions, significantly expanding itspotential and adaptability for real-world applications, achieving this "fromad-hoc to systematic" concept. We have implemented this method using thefourth-order PDE (the Euler-Bernoulli beam) as example and showcased itseffectiveness with four different boundary conditions. This framework enablesexpectation evaluations independent of problem size, harnessing theexponentially growing state space inherent in quantum computing, resulting inexceptional scalability. This method paves the way for applying quantumcomputing to practical engineering applications.

From Ad-Hoc to Systematic: A Strategy for Imposing General Boundary Conditions in Discretized PDEs in variational quantum algorithm