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 the Variational Quantum Linear Solver (VQLS) algorithm seems like a promising near term solution. This algorithm evaluates a cost function on a quantum machine and uses a classical optimizer to minimize this cost function. The minimum of this cost function corresponds to the solution of the linear system. This work aims at finding what the practical limitations are when solving the Poisson equation by means of VQLS. Results showed that problems small in size can be solved, however for larger problems obtaining the solution becomes effectively impossible due to barren plateaus, which are flat spots in the cost function landscape. / Aerospace Engineering