In this talk, we mainly introduce a ultra low-regularity integrator (ULI) for solving the nonlinear Dirac equation with rough initial data. A classical numerical method usually requires certain regularity of the solution. Once the regularity requirement is not satisfied, the numerical method will lose its accuracy. While our ULI enables optimal first-order convergence (in time) without requiring any additional regularities on the solution. In contrast to classical methods, the ULI overcomes the numerical loss of derivatives and is therefore more efficient and accurate for approximating low regular solutions.