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Variational quantum eigensolvers by variance minimization
- Source :
- Chinese Physics B. 31:120301
- Publication Year :
- 2022
- Publisher :
- IOP Publishing, 2022.
-
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.
- Subjects :
- General Physics and Astronomy
Subjects
Details
- ISSN :
- 16741056
- Volume :
- 31
- Database :
- OpenAIRE
- Journal :
- Chinese Physics B
- Accession number :
- edsair.doi...........213246fc2c69b109249a00b8f713fdc9