Numerical Methods for Solving High-Order Mathematical Problems using Quantum Linear System Algorithm on IBM QISKit Platform

Researchers are currently working on computational solutions based on quantum systems to accelerate the speed of complex mathematical models. This work presented how to formulate complex computational problems as a quantum system of linear equations and find solutions using Quantum Linear System Algorithm (QLSA), also called Quantum Harrow-Hassidim-Lloyd (HHL) algorithm. This paper showed experimental evaluation of multiple problem statements (curve-fitting functions, interpolating polynomials) as a quantum system of linear equations that involve computation of Vandermonde matrices as co-efficient matrices on IBM Quantum Information Software Kit for Quantum Computation (QISKit) platform. Along with a few examples demonstrating its evaluation on diagonal, Hermitian, and Non-Hermitian matrices as co-efficient matrices. The fidelity is used as a measure of performance for comparing the accuracy of quantum results with respect to existing classical solutions on IBM QISKit and drawing conclusions from the experimental results. Experimental evaluation shows that the fidelity depends on the sparsity of the input matrices and therefore the results vary depending on those matrices.