首页|Variational quantum algorithms for scanning the complex spectrum of non-Hermitian systems
Variational quantum algorithms for scanning the complex spectrum of non-Hermitian systems
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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 eigen-values 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 prepar-ing the left and right eigenstates,verifying the biorthogonal relations,as well as evaluating the observables.We also investigate the impact of quan-tum 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.
quantum algorithmnon-Hermitian physicsquantum many-body systems
Xu-Dan Xie、Zheng-Yuan Xue、Dan-Bo Zhang
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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
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
National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaGuangdong Basic and Applied Basic Research FundGuangdong Provincial Key Laboratory
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