I am having a difficulty in finding the full derivation for local search energy gap, as described in In the adiabatic version of Grover's algorithm, how is the Hamiltonian constructed?. I looked up the original source, but it simply brushes aside the derivation as "easy, simple and straightforward," but it does not seem to me very easy. Since initial and final matrices do not share eigenvectors, my initial thought is to calculate determinants and find out some energy gap, and I may be missing something, but they do not seem so straightforward.
Can anyone help me out here?
