Numerical Simulation Solution of the BCS Pairing Problem

We propose a new simulation computational method to solve the reduced BCS Hamiltonian based on spin analogy and submatrix diagonalization. Then we further apply this method to solve superconducting energy gap and the results are well consistent with those obtained by Bogoliubov transformation method. The exponential problem of 2^N-dimensional matrix is reduced to thepolynomial problem of N-dimensional matrix. It is essential to validate thismethod on a real quantum computer and is helpful to understanding the many-body quantum theory.