Year: 2022
Type: article
Abstract: The original variational quantum eigensolver (VQE) typically minimizes energy with hybrid quantum-classical optimization that aims to find the ground state. Here, we propose a VQE based on minimizing energy variance and call it the variance-VQE, which treats the ground state and excited states on the same footing, since an arbitrary eigenstate for a Hamiltonian should have zero energy variance. We demonstrate the properties of the variance-VQE for solving a set of excited states in quantum chemistry problems. Remarkably, we show that optimization of a combination of energy and variance may be more efficient to find low-energy excited states than those of minimizing energy or variance alone. We further reveal that the optimization can be boosted with stochastic gradient descent by Hamiltonian sampling, which uses only a few terms of the Hamiltonian and thus significantly reduces the quantum resource for evaluating variance and its gradients.
Source: Chinese Physics B
Authors: Dan-Bo Zhang, Bin-Lin Chen, Zhan-Hao Yuan, Tao Yin
Institution: South China Normal University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
Award: G3819940738
OpenAlex ID: W3037047391