How are quantum gates synthesized practically? Is like classical AND or NAND gates?
Synthesis, if I understand your question correctly, involves creating the physical machine from an abstract description.
There are many ways of implementing quantum gates. However, Google us good place to look for more information (seriously). One of their goals of their work in quantum computing is to have the physical machines built by outside vendors. Part of this means having a way to specify what they want.
If something like VHDL for quantum computers is somewhere in our future, I’d expect Google to be involved. I’d also expect the various fabricators to have explanations of how they translate the spec into physical hardware. At the moment, though, there’s not a lot of information available.