VQLS Read the Fine Print: Practical Challenges for Solving the Poisson Equation by Means of a Variational Quantum Linear Solver

The need of computational power for engineering applications has been ever increasing and with classical computers approaching their physical limits, new ways of improvement have to be investigated. One of the promising solutions is quantum computing. Most engineering problems require solving a system of linear equations of higher dimensions and...

Variational Quantum Linear Solver for Finite Element Problems: a Poisson equation test case

This research investigates the possibility of solving one dimensional Poisson's equation on quantum computers using the Variational Quantum Linear Solver (VQLS) as a simplified test case for fluid dynamics applications. In this work, Poisson's equation is discretized with the finite element method and the resulting matrix is decomposed as a...