Variational quantum eigensolvers by variance minimization

• URL: http://arxiv.org/abs/2006.15781v1
• Date: Mon, 29 Jun 2020 02:44:37 GMT
• Title: Variational quantum eigensolvers by variance minimization
• Authors: Dan-Bo Zhang, Zhan-Hao Yuan, Tao Yin
• Abstract summary: Variational quantum eigensolver(VQE) typically minimizes energy with hybrid quantum-classical optimization. We propose a VQE by minimizing energy variance, which is called as variance-VQE(VVQE)
• Score: 0.3093890460224435
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Variational quantum eigensolver(VQE) typically minimizes energy with hybrid quantum-classical optimization, which aims to find the ground state. Here, we propose a VQE by minimizing energy variance, which is called as variance-VQE(VVQE). The VVQE can be viewed as an self-verifying eigensolver for arbitrary eigenstate by designing, since an eigenstate for a Hamiltonian should have zero energy variance. We demonstrate properties and advantages of VVQE for solving a set of excited states with 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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