I doubt there is a vegetarian/vegan diet out there that doesn't use synthetic vitamins or supplements. For one thing, I think there are certain nutrients that just aren't produced by plants, so they'd have to be added to the mix. If you don't add them as an element of meat, you'd have to add highly processed, if not synthetic, ingredients to supply them.
This is especially true if your pet is a cat, which would make it an obligate carnivore and unlikely to do well on a vegetarian diet. It might be possible for a dog, but you'd have to be very careful to get the balance of vitamins and minerals right--and likely, your only source for some of them might be highly processed or synthetic.
Why do you wish to put your pet on a vegetarian diet?