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

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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.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12375013 and 12275090), the Guangdong Basic and Applied Basic Research Fund (Grant No. 2023A1515011460), and the Guangdong Provincial Key Laboratory (Grant No. 2020B1212060066).

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Authors and Affiliations

  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

    Xu-Dan **e, Zheng-Yuan Xue & Dan-Bo Zhang

  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

    Zheng-Yuan Xue & Dan-Bo Zhang

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  1. Xu-Dan **e
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**e, XD., Xue, ZY. & Zhang, DB. Variational quantum algorithms for scanning the complex spectrum of non-Hermitian systems. Front. Phys. 19, 41202 (2024). https://doi.org/10.1007/s11467-023-1382-3

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