  A recently proposed variational quantum algorithm has expanded the horizon of
variational quantum computing to nonlinear physics and fluid dynamics. In this
work, we employ this algorithm to find the ground state of the nonlinear
Schr\"{o}dinger equation with a quadratic potential and implement it on the
cloud superconducting quantum processors. We analyze the expressivity of
real-amplitude ansatz to capture the ground state of the nonlinear system
across various interaction regimes characterized by varying strengths of
nonlinearity. Our investigation reveals that although quantum hardware noise
impairs the evaluation of the energy cost function, small instances of the
problem consistently converge to the ground state. We implement a variety of
problem instances on IBM Q devices and report analogous discrepancies in the
energy cost function evaluation attributable to quantum hardware noise. The
latter are absent in the state fidelity estimation. Our comprehensive analysis
offers valuable insights into the practical implementation and advancement of
the variational algorithms for nonlinear quantum dynamics.
