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Quantum algorithm for preparing the ground state of a physical system through multi-step quantum resonant transitions

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Abstract

We present a quantum algorithm for preparing the ground state of a physical system by using a multi-step quantum resonant transition (QRT) method. We construct a sequence of intermediate Hamiltonians to reach the system Hamiltonian, and then, starting from the ground state of an initial Hamiltonian, the system is sequentially evolved to the ground states of the intermediate Hamiltonians step by step using the QRT method, finally reaching the ground state of the system Hamiltonian. The algorithm can be run efficiently if the overlap between the ground states of any two adjacent Hamiltonians and the energy gap between the ground state and the first excited state of each Hamiltonian are not exponentially small. By using this algorithm, preparing the ground state of a system is transformed to simulating the time evolution of a sequence of time-independent Hamiltonians. This algorithm can also be used for calculating energy eigenvalues of a physical system.

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Acknowledgements

We thank S. Ashhab, H. Xiang and S. C. Li for helpful discussions. This work was supported by the National Natural Science Foundation of China (Grant No. 11275145) and the Natural Science Fundamental Research Program of Shaanxi Province of China under Grants 2018JM1015.

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Authors and Affiliations

  1. MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Xi’an Jiaotong University, Xi’an, 710049, China

    Hefeng Wang

  2. School of Physics, Xi’an Jiaotong University and Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, Xi’an, 710049, China

    Hefeng Wang

  3. Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China

    Sixia Yu

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  1. Hefeng Wang
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  2. Sixia Yu
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Correspondence to Hefeng Wang.

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H. Wang is supported by the National Natural Science Foundation of China under Grants 11275145 and the Natural Science Fundamental Research Program of Shaanxi Province of China under Grants 2018JM1015.

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Wang, H., Yu, S. Quantum algorithm for preparing the ground state of a physical system through multi-step quantum resonant transitions. Quantum Inf Process 20, 40 (2021). https://doi.org/10.1007/s11128-020-02984-z

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