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arXiv · 2006.15781

Variational quantum eigensolvers by variance minimization

Dan-Bo Zhang·Zhan-Hao Yuan·Tao Yin
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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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Dan-Bo Zhang, Zhan-Hao Yuan, Tao Yin. 2020-06-29. Variational quantum eigensolvers by variance minimization. https://arxiv.org/abs/2006.15781

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