First-quantized adiabatic time evolution for the ground state of a many-electron system and the optimal nuclear configuration

7 Sep 2023  ·  Yusuke Nishiya, Hirofumi Nishi, Yannick Couzinié, Taichi Kosugi, Yu-ichiro Matsushita ·

We propose an adiabatic time evolution (ATE) method for obtaining the ground state of a quantum many-electron system on a quantum circuit based on first quantization for the first time. As a striking feature of the ATE method, it consists of only unitary operations, which means that it does not require any ancillary qubits, nor controlled real-time evolution operators. We also provide a way to prepare an antisymmetrized and non-degenerate initial ground state that is suitable as an input to an ATE circuit, which allows our ATE method to be applied to systems with any number of electrons. In addition, by considering a first-quantized Hamiltonian for quantum-mechanical electron system and classical nuclear system, we design a quantum circuit for optimal structure search based on ATE. Numerical simulations are demonstrated for simple systems, and it is confirmed that the ground state of the electronic system and optimal structure can be obtained by our method.

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Quantum Physics