Before revision:  Namely, we demonstrate that any T-query algorithm using S qubits of memory must satisfy a tradeoff of T^3 S \geq \Omega( N^4)for finding \Theta(N) collisions in a random function.
After revision:  Namely, we demonstrate that any algorithm using S qubits of memory must satisfy a tradeoff of T^3 S \geq \Omega( N^4)for finding \Theta(N) collisions in a random function.