Exact Numerical 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}-dimension matrix is reduced to the polynomial problem of N-dimension matrix. It is essential to validate this method on a real quantum 
Feng Xu, An Min Wang, and Xiaodong Yang, Hao You, Xiaosan Ma