By Wen-Xiang Chen

I propose a restricted path integration method to efficiently simulate a class of quantum systems and Hamiltonians classically and computationally without boundary condition problems. Then the algorithm for the path integral of any bounded error quantum polynomial is mapped to the ground state of the Hamiltonian and made efficient to simulate. This approach is an Abelian U(1) local gauge theory for curved vacuum spacetimes. Using the zero geodesics of the Schwarzschild metric, the space-subequation of the (1+1)-dimensional vacuum center-symmetric curved space-time is established, and the mass-U(1) gauge potential relationship is obtained.