Variational quantum simulation of the imaginary-time Lyapunov control
for accelerating the ground-state preparation
- URL: http://arxiv.org/abs/2112.11782v2
- Date: Tue, 20 Dec 2022 04:44:29 GMT
- Title: Variational quantum simulation of the imaginary-time Lyapunov control
for accelerating the ground-state preparation
- Authors: Yu-Cheng Chen, Yu-Qin Chen, Alice Hu, Chang-Yu Hsieh, Shengyu Zhang
- Abstract summary: We first propose a Lyapunov control-inspired strategy to accelerate the well-established imaginary-time method for ground-state preparation.
To make the method accessible in the noisy intermediate-scale quantum era, we propose a variational form of the algorithm that could work with shallow quantum circuits.
- Score: 17.802280143175235
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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