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We propose a novel adiabatic time evolution (ATE) method for obtaining theground state of a quantum many-electron system on a quantum circuit based onfirst quantization. As a striking feature of the ATE method, it consists ofonly unitary operations representing real-time evolution, which means that itdoes not require any ancillary qubits, nor controlled real-time evolutionoperators. Especially, we explored the first-quantized formalism of ATE methodin this study, since the implementation of first-quantized real-time evolutionon quantum circuits is known to be efficient. However, when realizing the ATEquantum circuit in first-quantization formalism, obstacles are how to set theadiabatic Hamiltonian and how to prepare the corresponding initial groundstate. We provide a way to prepare an antisymmetrized and non-degenerateinitial ground state that is suitable as an input to an ATE circuit, whichallows our ATE method to be applied to systems with any number of electrons. Inaddition, by considering a first-quantized Hamiltonian for quantum-mechanicalelectron system and classical nuclear system, we design a quantum circuit foroptimal structure search based on ATE. Numerical simulations are demonstratedfor simple systems, and it is confirmed that the ground state of the electronicsystem and optimal structure can be obtained by our method.

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