Probing the limits of variational quantum algorithms for nonlinear ground states on real quantum hardware: The effects of noise

A recently proposed variational quantum algorithm has expanded the horizon of variational quantum computing to nonlinear physics and fluid dynamics. In this work, we probe the ability of such approach to capture the ground state of the nonlinear Schr"odinger equation for a range of parameters on real superconducting quantum processors. Specifically, we study the expressivity of real-amplitude, hardware-efficient Ansatz to capture the ground state of this nonlinear system across various interaction regimes and implement different noise scenarios in both simulators and cloud processors. Our investigation reveals that although quantum hardware noise impairs the evaluation of the energy cost function, certain small instances of the problem consistently converge to the ground state. We test and demonstrate a variety of cases on IBM Q superconducting devices and analyze the discrepancies in the energy cost function evaluation due to quantum hardware noise. These discrepancies are absent in the state fidelity estimation because of the shallow state preparation circuit. Our comprehensive analysis offers valuable insights into the practical implementation and advancement of the variational algorithms for nonlinear problems.