Abstract: In 2001, we had a breakthrough: Shors algorithm was used to factor 15 in polynomial time. We will begin with a brief rundown of the mathematics involvded in quantum computation, such as qubits and entanglement, and see why linear algebra lets us have our cake and eat it too. The talk will focus on the construction of several quantum logic gates, such as the Toffoli and Hadamard gates, which we will leverage to prove that quantum circuits are actually capable of faster computation than classical ones. If time permits, we willhopefully get to an overview of Shors algorithm.