While I'm reading some literature about synthesizing quantum circuit, I couldn't understand what cascades of Toffoli gates means. How Toffoli cascade runs in quantum circuit?
I think a "cascade" of gates is just a fancy word for a sequence of gates that follow a certain pattern. A good example is offered in this answer that details implementing a multi-controlled-NOT gate using Toffoli gates. The pictures in that answer show Toffoli gates form two ladder-like patterns. I don't think the term "cascade" means anything more specific than that.