Revisiting a limit on efficient quantum computation

In this paper, we offer an exposition of a theorem originally due to Adleman, Demarrais and Huang that shows that the quantum complexity class BQP (Bounded-error Quantum Polynomial time) is contained in the classical counting class PP (Probabilistic Polynomial time). Our proof follows the one given by Fortnow and Rogers that relates quantum computing to counting complexity classes by way of GapP functions. The contribution of this paper is an exposition of an important result that assumes a minimal background in computational complexity theory and no knowledge of quantum mechanics.