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

Abstract

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 approaches to capture the ground state of the nonlinear Schrödinger 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 for 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.

11 Pages, 9 Figures, added two figure and made other changes

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• Tensor-Programmable Quantum Circuits for Solving Differential Equations
• Simulating Quantum Turbulence with Matrix Product States
• Resource-Efficient Hadamard Test Tailored Variational Framework for Nonlinear Dynamics on Quantum Computers
• Efficient Estimation and Sequential Optimization of Cost Functions in Variational Quantum Algorithms
• Nonlinear path-following via the asymptotic numerical method on a quantum processor