WebGL 2.0 would correspond to OpenGL ES 3.0. OpenGL ES 3.0 does not have compute shaders, so I'm guessing that WebGL 2.0 would neither have them. OpenGL ES 3.1 does have compute shaders and the specification was released in March. However, there is no OpenGL ES extension for compute shaders.This probably means that compute shaders would arrive with WebGL 2.1 (that would correspond to OpenGL ES 3.1). WebGL 2.0 might arrive this year, which would mark it around 2.5 years after release of the OpenGL ES 3.0 specification. Assuming this interval stays around the same, I think you would be able to expect WebGL 2.1 in 2-3 years, around 2017.