Variational quantum algorithms for scanning the complex spectrum of non-Hermitian systems

doi:10.1007/s11467-023-1382-3

Frontiers of Physics

2024, Vol. 19

Issue (4): 41202 https://doi.org/10.1007/s11467-023-1382-3

本期目录

Variational quantum algorithms for scanning the complex spectrum of non-Hermitian systems

Xu-Dan Xie¹, Zheng-Yuan Xue^1,²(

), Dan-Bo Zhang^1,²(

)

¹. Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, and School of Physics, South China Normal University, Guangzhou 510006, China
². Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong−Hong Kong Joint Laboratory of Quantum Matter, and Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China

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Abstract：

Solving non-Hermitian quantum many-body systems on a quantum computer by minimizing the variational energy is challenging as the energy can be complex. Here, we propose a variational quantum algorithm for solving the non-Hermitian Hamiltonian by minimizing a type of energy variance, where zero variance can naturally determine the eigenvalues and the associated left and right eigenstates. Moreover, the energy is set as a parameter in the cost function and can be tuned to scan the whole spectrum efficiently by using a two-step optimization scheme. Through numerical simulations, we demonstrate the algorithm for preparing the left and right eigenstates, verifying the biorthogonal relations, as well as evaluating the observables. We also investigate the impact of quantum noise on our algorithm and show that its performance can be largely improved using error mitigation techniques. Therefore, our work suggests an avenue for solving non-Hermitian quantum many-body systems with variational quantum algorithms on near-term noisy quantum computers.

Key words： quantum algorithm non-Hermitian physics quantum many-body systems

收稿日期: 2023-11-02 出版日期: 2024-02-05

Corresponding Author(s): Zheng-Yuan Xue,Dan-Bo Zhang

引用本文:

. [J]. Frontiers of Physics, 2024, 19(4): 41202.
Xu-Dan Xie, Zheng-Yuan Xue, Dan-Bo Zhang. Variational quantum algorithms for scanning the complex spectrum of non-Hermitian systems. Front. Phys. , 2024, 19(4): 41202.

链接本文:

https://academic.hep.com.cn/fop/CN/10.1007/s11467-023-1382-3
https://academic.hep.com.cn/fop/CN/Y2024/V19/I4/41202

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

	$n = 0$	$n = 1$	$n = 2$	$n = 3$	$n = 4$	$n = 5$	$n = 6$	$n = 7$

VQA ( $κ = 0.4$ )	0.7988	0.7988	0.9165	0.7719	0.7719	0.9165	0.7978	0.7994
Exact	0.7988	0.7988	0.9165	0.7719	0.7719	0.9165	0.7979	0.7994
VQA ( $κ = 0.2$ )	0.1680	0.1680	0.9798	0.5822	0.5821	0.9798	0.9537	0.9541
Exact	0.1681	0.1681	0.9798	0.5821	0.5821	0.9798	0.9537	0.9541

Tab.1

Fig.6

Fig.7

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Fig.9

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