Poster: Probing the limits of variational quantum algorithms for nonlinear ground states on Superconducting NISQ Processors: The effects of noise

A recently proposed variational quantum algorithm (VQA) has expanded the horizon of variational quantum computing to nonlinear physics and fluid dynamics. In this study, we leverage a variational algorithm, originally conceived within the framework of computational fluid dynamics, to determine the ground state of the nonlinear Schrödinger equation on superconducting quantum processors. We evaluate the expressivity of a real-amplitude ansatz in capturing the system's physics across a spectrum of interaction regimes. Our findings indicate that, despite the detrimental effects of quantum noise on the evaluation of the energy cost function, small-scale problem instances consistently converge to the correct ground state. Extensive simulations were conducted on IBM Q devices, wherein the impact of hardware noise on the quality of solutions was rigorously analyzed. Discrepancies in the energy and state fidelity was examined from experimental data, demonstrating a strong correlation with noiseless simulations for these problem instances. This comprehensive analysis offers crucial insights into the practical implementation and progression of variational algorithms for nonlinear quantum dynamics on Noisy Intermediate-Scale Quantum (NISQ) devices.