Open quantum maps are discrete toy models for open quantum chaotic systems. They are given by subunitary matrices quantizing open symplectic maps, popular in both theoretical and numerical studies for their simplicities. In this talk, we discuss the results of spectral gaps for open quantum baker's map using discrete fractal uncertainty principle. We will start by reviewing the results on one-dimensional models (joint work with Dyatlov) and higher-dimensional models (work of Cohen), then introduce our recent work on two dimensional anisotropic models (joint work with Zhang An and Zhang Hong).