Put flour and yeast and sugar and salt in a stand mixer and mix.
Then add olive oil and water. Mix until the dough is formed. It can be a little sticky. Add a little flour if needed.
Cover and rest for 1 hour so the dough is doubled in size. Do not punch the dough down.
Preheat the oven and a pizza stone to 500F.
Divide the dough into eight pieces and cover for 15 minutes to rise.
Take one dough ball and keep the rest covered.
Use your fingers to shape the dough into a disk and don't let the air out. Gently roll out the dough using a rolling pin. The disk shouldn't be thicker than ¼ inch.
Place the rolled disk on the hot pizza stone (or baking sheet) and close the oven door. Let it bake for two minutes, it will puff.
Flip the bread and bake for another two minutes.
Place the baked pita bread on a plate and cover with a towel.
Continue baking the remaining pita breads.
Store tightly in a plastic bag.