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

• URL: http://arxiv.org/abs/2310.11764v2
• Date: Fri, 3 Nov 2023 06:46:04 GMT
• Title: From Ad-Hoc to Systematic: A Strategy for Imposing General Boundary Conditions in Discretized PDEs in variational quantum algorithm
• Authors: Dingjie Lu (1), Zhao Wang (1), Jun Liu (1), Yangfan Li (1), Wei-Bin Ewe (1), Zhuangjian Liu (1) ((1) Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR), Singapore)
• Abstract summary: We propose a general quantum-computing-based algorithm that harnesses the exponential power of noisy quantum devices in solving PDEs. This variational quantum eigensolver (VQE)-inspired approach transcends previous idealized model demonstrations constrained by strict and simplistic boundary conditions. We have implemented this method using the fourth-order PDE (the Euler-Bernoulli beam) as example and showcased its effectiveness with four different boundary conditions.
• Score: 0.6134016746457569
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We proposed a general quantum-computing-based algorithm that harnesses the exponential power of noisy intermediate-scale quantum (NISQ) devices in solving partial differential equations (PDE). This variational quantum eigensolver (VQE)-inspired approach transcends previous idealized model demonstrations constrained by strict and simplistic boundary conditions. It enables the imposition of arbitrary boundary conditions, significantly expanding its potential and adaptability for real-world applications, achieving this "from ad-hoc to systematic" concept. We have implemented this method using the fourth-order PDE (the Euler-Bernoulli beam) as example and showcased its effectiveness with four different boundary conditions. This framework enables expectation evaluations independent of problem size, harnessing the exponentially growing state space inherent in quantum computing, resulting in exceptional scalability. This method paves the way for applying quantum computing to practical engineering applications.

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