I want to model a torus with grid, i.e torus code in topology quantum computation, just like followin, but I do not know how to draw grid.
Maybe using texture might be helpful, but are there any other ways?
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You can unwrap the UVs for the torus
Then use the UV mapping on a brick texture with no offset, and a frequency of 1. The fac output you can use to control a color mix used as color on the material.
Or you can Export the UV layout.
You'll get an image like this saved on a file, where each of the vertices on the mesh is represented by a line and the faces are the alpha channel:
Then use that image to control the mix of whatever colors you want.
(the color ramp is there to make the alpha channel more contrasted, only pure black and pure white)