  We propose a novel adiabatic time evolution (ATE) method for obtaining the
ground state of a quantum many-electron system on a quantum circuit based on
first quantization. As a striking feature of the ATE method, it consists of
only unitary operations representing real-time evolution, which means that it
does not require any ancillary qubits, nor controlled real-time evolution
operators. Especially, we explored the first-quantized formalism of ATE method
in this study, since the implementation of first-quantized real-time evolution
on quantum circuits is known to be efficient. However, when realizing the ATE
quantum circuit in first-quantization formalism, obstacles are how to set the
adiabatic Hamiltonian and how to prepare the corresponding initial ground
state. We 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.
