  The notable claim of quantum supremacy presented by Google's team in 2019
consists of demonstrating the ability of a quantum circuit to generate, albeit
with considerable noise, bitstrings from a distribution that is considered hard
to simulate on classical computers. Verifying that the generated data is indeed
from the claimed distribution and assessing the circuit's noise level and its
fidelity is a purely statistical undertaking. The objective of this paper is to
explain the relations between quantum computing and some of the statistical
aspects involved in demonstrating quantum supremacy in terms that are
accessible to statisticians, computer scientists, and mathematicians. Starting
with the statistical analysis in Google's demonstration, which we explain, we
study various estimators of the fidelity, and different approaches to testing
the distributions generated by the quantum computer. We propose different noise
models, and discuss their implications. A preliminary study of the Google data,
focusing mostly on circuits of 12 and 14 qubits is discussed throughout the
paper.
