  Quantum chemistry is one of the important applications of quantum information
technology. Especially, an estimation of the energy gap between a ground state
and excited state of a target Hamiltonian corresponding to a molecule is
essential. In the previous approach, an energy of the ground state and that of
the excited state are estimated separately, and the energy gap can be
calculated from the subtraction between them. Here, we propose a direct
estimation of the energy gap between the ground state and excited state of the
target Hamiltonian with quantum annealing. The key idea is to combine a Ramsey
type measurement with the quantum annealing. This provides an oscillating
signal with a frequency of the energy gap, and a Fourier transform of the
signal let us know the energy gap. Based on typical parameters of
superconducting qubits, we numerically investigate the performance of our
scheme when we estimate an energy gap between the ground state and first
excited state of the Hamiltonian. We show robustness against non-adiabatic
transitions between the ground state and first-excited state. Our results pave
a new way to estimate the energy gap of the Hamiltonian for quantum chemistry.
