This work presents numerical experiments aimed at verifying solutions of Poisson’s equation using two existing methodologies. First, block-diagonalization is employed to block-encode the matrix derived from Poisson’s equation through the finite difference method (FDM), significantly improving computational complexity from N to \(\log (N)\) , where N is the matrix size. Second, the Quantum Singular Value Transformation (QSVT) algorithm is applied to invert the matrix. However, while block-diagonalization improves the complexity in N, QSVT introduces a bottleneck due to its linear dependency on the condition number \(\kappa \) , which grows exponentially with N, posing challenges for large-scale problems. As far as we know, this is the first numerical experiments solving problems with matrix size \(N=1024\) and condition number \(\kappa =500000\) ; the largest matrix size and condition number from existing works are 16 and \(<100\) , respectively.