Variational quantum simulation of the imaginary-time Lyapunov control for accelerating the ground-state preparation

Abstract

Quantum computers have been widely speculated to offer significant advantages in obtaining the ground state of difficult Hamiltonian in chemistry and physics. In this work, we first propose a Lyapunov control-inspired strategy to accelerate the well-established imaginary-time method for ground-state preparation. We also dig for the source of acceleration of the imaginary-time process under Lyapunov control with theoretical understanding and dynamic process visualization. To make the method accessible in the noisy intermediate-scale quantum era, we further propose a variational form of the algorithm that could work with shallow quantum circuits. Through numerical experiments on a broad spectrum of realistic models, including molecular systems, 2D Heisenberg models, and Sherrington-Kirkpatrick models, we show that imaginary-time control may substantially accelerate the imaginary time evolution for all systems and even generate orders of magnitude acceleration (suggesting exponential-like acceleration) for challenging molecular Hamiltonians involving small energy gaps as impressive special cases. Finally, with a proper selection of the control Hamiltonian, the new variational quantum algorithm does not incur additional measurement costs compared to the original variational quantum imaginary-time algorithm.