It depends on your situation. The general rule of thumb is that the thicker the quartz countertop, the less need there is for plywood. Plywood is used to provide added support to the stone that will prevent cracking by absorbing pressure. Many contractors will install it regardless if they know stone countertops are going to be installed. Yet, most manufacturers will say that it’s not always necessary.
The biggest consideration is how thick the quartz countertop you selected is. If you have 3cm quartz countertops, there’s no need for plywood. They are thick enough to absorb and distribute any pressure across the integrity of the slab. If you selected a 2cm slab, you typically don’t need to install plywood either. Unless you have an overhang of 8 inches or greater, in which case you should use plywood. Anything under 2cm should have plywood installed for it (unless you’re using it in a backsplash).