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Variational quantum eigensolvers by variance minimization |
| Dan-Bo Zhang(张旦波)1,2,†, Bin-Lin Chen(陈彬琳)2, Zhan-Hao Yuan(原展豪)3, and Tao Yin(殷涛)4,‡ |
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 |
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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.
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Received: 23 May 2022
Revised: 16 August 2022
Accepted manuscript online: 18 August 2022
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PACS:
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03.67.Ac
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(Quantum algorithms, protocols, and simulations)
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| Fund: This work was supported by the National Natural Science Foundation of China (Grant No. 12005065) and the Guangdong Basic and Applied Basic Research Fund (Grant No. 2021A1515010317). |
Corresponding Authors:
Dan-Bo Zhang, Tao Yin
E-mail: dbzhang@m.scnu.edu.cn;tao.yin@artiste-qb.net
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Cite this article:
Dan-Bo Zhang(张旦波), Bin-Lin Chen(陈彬琳), Zhan-Hao Yuan(原展豪), and Tao Yin(殷涛) Variational quantum eigensolvers by variance minimization 2022 Chin. Phys. B 31 120301
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