Variational quantum eigensolvers by variance minimization |
| |
| Affiliation: | 1.Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China;2.Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China;3.Guangzhou Educational Infrastructure and Equipment Center, Guangzhou 510006, China;4.Yuntao Quantum Technologies, Shenzhen 518000, China |
| |
| 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. |
| |
| Keywords: | quantum computing quantum algorithm quantum chemistry |
|
| 点击此处可从《中国物理 B》浏览原始摘要信息 |
|
点击此处可从《中国物理 B》下载免费的PDF全文 |
|
