Abstract
It has long been known that Clifford circuits can be efficiently simulated, even with relatively low-depth classical circuits. That said, a recent line of work shows that Clifford circuits still enjoy a provable advantage over their classical counterparts. For example, constant-depth Clifford circuits can solve problems that no constant-depth classical circuit can solve. I will talk about some of this history and give my perspective on the open problems that remain to be solved in this area.