In 2019, Google announced that they had achieved quantum supremacy: they performed a task on their newly constructed quantum device that could not be accomplished using classical computers in a reasonable amount of time. In this talk, we present the mathematics and statistics involved in the set-up and analysis of the experiment, sampling from random quantum circuits. We start with the theory of random matrices and explain how to produce a sequence of (pseudo) random unitary matrices using quantum circuits. We then discuss how the Google team compares quantum and classical approaches using cross entropy and the Porter-Thomas distribution. Along the way, we present other problems with potential quantum advantage and some of the latest results related to noisy near-term quantum computers.
