  Background: Solving nuclear many-body problems with an ab initio approach is
widely recognized as a computationally challenging problem. Quantum computers
offer a promising path to address this challenge. There are urgent needs to
develop quantum algorithms for this purpose.
  Objective: In this work, we explore the application of the quantum algorithm
of adiabatic state preparation with quantum phase estimation in ab initio
nuclear structure theory. We focus on solving the low-lying spectra (including
both the ground and excited states) of simple nuclear systems.
  Ideas: The efficiency of this algorithm is hindered by the emergence of small
energy gaps (level crossings) during the adiabatic evolution. In order to
improve the efficiency, we introduce techniques to avoid level crossings: 1) by
suitable design of the reference Hamiltonian; 2) by insertions of perturbation
terms to modify the adiabatic path.
  Results: We illustrate this algorithm by solving the deuteron ground state
energy and the spectrum of the deuteron bounded in a harmonic oscillator trap
implementing the IBM Qiskit quantum simulator. The quantum results agree well
the classical results obtained by matrix diagonalization.
  Outlook: With our improvements to the efficiency, this algorithm provides a
promising tool for investigating the low-lying spectra of complex nuclei on
future quantum computers.
