Proof the active dry yeast with the sugar and 1 1/2 cups of the water until the water looks a little foamy on top (about 5-10 minutes).
Add the white flour, wheat flour, salt, and olive oil to a bowl (or the bowl of a stand mixer, if you plan to knead by machine).
Stir in the water/yeast/sugar mixture until the dough starts to come together. If the dough looks a little dry, gradually add a little more water, about 1/2 tablespoon at a time. The dough ball should not be too soupy or dry (somewhere in between is best). It should look a lot like store-bought pizza dough, but just a little stickier. If the dough is too wet, add a little more flour to compensate (about 2 tablespoons at a time).
Knead until the dough ball passes the window pane test. It should come together into an elastic ball that has a smooth surface (see dough photo above). Kneading should take about 5-15 minutes by machine with a dough hook, or 10-20 minutes by hand. Pay more attention to the dough’s consistency than the time you’ve spent kneading.
Place the dough in a bowl, cover it, and let it rise at room temperature for about 1 hour and 15 minutes. It will rise noticeably. If it’s a little chilly in your kitchen (e.g., below 67° F), you might need to let it rise for about 15 minutes longer.
Place a pizza stone (or sheet pan) on the oven floor, move the oven racks up and out of the way, so you can very easily access the pizza stone, and pre-heat the oven to 500° F (or its hottest setting).
Lightly flour a clean, food-safe work surface, divide the dough into 8 equal pieces, and shape each chunk into a round ball with a smooth surface.
Roll out each dough ball into a circle, about 7 or 8 inches in diameter, dusting the surface with more flour as needed. They should be 1/8 inch thick, which is very thin, but not paper-thin (see above photos). By the time you are done rolling the last disc, the first one will be ready to bake. They can be held at room temperature for about 20 minutes.
The oven will be ready to bake once it has reached 500° F and stayed there for about 5 to 10 minutes. This gives the pizza stone a chance to get really hot.
Throw 2 to 3 of the rolled-out discs onto the baking stone. Make sure they lay flat and are not touching. Bake for about 4 minutes. They’ll puff up and slightly brown. Remove and cool (they’ll start to deflate at room temperature). Repeat until all pitas are cooked