Quantum Computing for Solving Cubic Schrodinger Equation

Abstract

This thesis explores the numerical approximation of special case of Non linear Schr¨odinger Equation(NLSE) using quantum computing techniques. A Variational Quantum Linear Solver(VQLS) is utilized to address the challenges of solving complex-valued linear systems derived from the discretised form of the CSE. The original complex-valued problem is converted into a real-valued system to perform the approximations. The performance of the quantum simulation of VQLS algorithm is compared with the classical methods of approximation through numerical experiments on 4 × 4,8 × 8,16 × 16 systems via quantum simulations. While classical methods prove to be faster and more accurate for the given systems, the future of the hybrid quantum-classical algorithms are promising. Accuracy and runtime analyses showed the exponential scaling behaviour of the quantum approach as the system became larger. The results suggest that although quantum methods are currently constrained by hardware and algorithmic limitations, they offer a promising foundation for future research on computational sciences.