  Quantum computers are capable of calculating the energy gap of two electronic
states by using the quantum phase difference estimation (QPDE) algorithm. The
Bayesian inference based implementations for the QPDE have been reported so
far, but this approach is not projective, and the quality of the calculated
energy gap depends on the input wave functions being used. Here, we report the
inverse quantum Fourier transformation based QPDE with $N_a$ of ancillary
qubits, which allows us to compute the difference of eigenenergies based on the
single-shot projective measurement. As a proof-of-concept demonstrations, we
report numerical experiments for the singlet--triplet energy gap of hydrogen
molecule and the vertical excitation energies of halogen-substituted methylenes
(CHF, CHCl, CF$_2$, CFCl and CCl$_2$) and formaldehyde (HCHO).
