Variational quantum eigensolver for nonlinear dynamics

Abstract

The simulation of quantum systems constitutes today one of the most fruitful applications of quantum computing in the era of Noisy Intermediate-Scale Quantum (NISQ) computers. Nonetheless, other dynamical systems that are not necessarily governed by the laws of quantum mechanics remain a fundamental challenge. Several approaches have emerged regarding the integration of arbitrary Partial Differential Equations (PDEs) on quantum computers [1]. A method based on the Feynmann-Kitaev formalism of quantum dynamics, where the full evolution of the system can be retrieved after a single optimization routine of an appropriate cost function has been recently put forth [2]. This spacetime formulation alleviates the accumulation of errors, but its application is restricted to quantum systems only. In this work [3], we introduce an extension of the Feynman–Kitaev formalism that is tailored to the integration of arbitrary PDEs with non-linearities and provide proof-of-principle calculations that demonstrate that fundamental processes such as diffusion and turbulence can be well-reproduced on the IBM Q System One and Quantinuum’s H1 quantum computers. We find numerical evidence of a favorable scaling of the variational approach with the number of qubits and present several optimization strategies that avoid barren plateaus, providing a powerful toolbox for the scalable integration of large dynamical systems on NISQ hardware. [1] Lubasch, M., Joo, J., Moinier, P., Kiffner, M., & Jaksch, D., Variational quantum algorithms for nonlinear problems. Physical Review A, 101, 010301(R) (2020). [2] S. Barison, F. Vicentini, I. Cirac, and G. Carleo, “Variational dynamics as a ground-state problem on a quantum computer,” arXiv preprint arXiv:2204.03454, 2022. [3] A. Pool, A. Somoza, M. Lubasch, B. Horstmann, Proceedings - 2022 IEEE International Conference on Quantum Computing and Engineering, QCE 2022