Symmetry enhanced variational quantum spin eigensolver

Lyu, Chufan1; Xu, Xusheng2; Yung, Man -Hong2,3,4; Bayat, Abolfazl1

2023-01-19

Quantum   Impact Factor & Quartile

2521-327X

The variational quantum-classical algo-rithms are the most promising approach for achieving quantum advantage on near-term quantum simulators. Among these methods, the variational quantum eigensolver has at-tracted a lot of attention in recent years. While it is very effective for simulating the ground state of many-body systems, its gen-eralization to excited states becomes very re-source demanding. Here, we show that this issue can significantly be improved by exploit-ing the symmetries of the Hamiltonian. The improvement is even more effective for higher energy eigenstates. We introduce two methods for incorporating the symmetries. In the first approach, called hardware symmetry preserv-ing, all the symmetries are included in the de-sign of the circuit. In the second approach, the cost function is updated to include the sym-metries. The hardware symmetry preserving approach indeed outperforms the second ap-proach. However, integrating all symmetries in the design of the circuit could be extremely challenging. Therefore, we introduce hybrid symmetry preserving method in which symme-tries are divided between the circuit and the classical cost function. This allows to harness the advantage of symmetries while preventing sophisticated circuit design.

SCI

English

Others

Na-tional Key R&D Program of China[2018YFA0306703] ; National Science Foun-dation of China["12050410253","92065115","12274059"] ; Ministry of Science and Technology of China[QNJ2021167001L]

Physics

Quantum Science & Technology ; Physics, Multidisciplinary

WOS:000926641500001

VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF

Web of Science

1.Univ Elect Sci & Technol China, Inst Fundamental & Frontier Sci, Chengdu 610051, Peoples R China
2.Huawei Technol, Cent Res Inst, Labs 2012, Hong Kong, Peoples R China
3.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China
4.Southern Univ Sci & Technol, Shenzhen Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China

Lyu, Chufan,Xu, Xusheng,Yung, Man -Hong,et al. Symmetry enhanced variational quantum spin eigensolver[J]. Quantum,2023,7.

Lyu, Chufan,Xu, Xusheng,Yung, Man -Hong,&Bayat, Abolfazl.(2023).Symmetry enhanced variational quantum spin eigensolver.Quantum,7.

Lyu, Chufan,et al."Symmetry enhanced variational quantum spin eigensolver".Quantum 7(2023).