The detection of variations of fundamental constants of the Standard Model
would provide us with compelling evidence of new physics, and could lift the
veil on the nature of dark matter and dark energy. In this work, we discuss how
a network of atomic and molecular clocks can be used to look for such
variations with unprecedented sensitivity over a wide range of time scales.
This is precisely the goal of the recently launched QSNET project: A network of
clocks for measuring the stability of fundamental constants. QSNET will include
state-of-the-art atomic clocks, but will also develop next-generation molecular
and highly charged ion clocks with enhanced sensitivity to variations of
fundamental constants. We describe the technological and scientific aims of
QSNET and evaluate its expected performance. We show that in the range of
parameters probed by QSNET, either we will discover new physics, or we will
impose new constraints on violations of fundamental symmetries and a range of
theories beyond the Standard Model, including dark matter and dark energy
models.