中国物理B ›› 2022, Vol. 31 ›› Issue (12): 120301-120301.doi: 10.1088/1674-1056/ac8a8d
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
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
摘要： 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.
中图分类号: (Quantum algorithms, protocols, and simulations)
- 03.67.Ac