  We determine the contribution to the anomalous magnetic moment of the muon
from the $\alpha^2_{\mathrm{QED}}$ hadronic vacuum polarization diagram using
full lattice QCD and including $u/d$ quarks with physical masses for the first
time. We use gluon field configurations that include $u$, $d$, $s$ and $c$
quarks in the sea at multiple values of the lattice spacing, multiple $u/d$
masses and multiple volumes that allow us to include an analysis of
finite-volume effects. We obtain a result for $a_{\mu}^{\mathrm{HVP,LO}}$ of
$667(6)(12)$, where the first error is from the lattice calculation and the
second includes systematic errors from missing QED and isospin-breaking effects
and from quark-line disconnected diagrams. Our result implies a discrepancy
between the experimental determination of $a_{\mu}$ and the Standard Model of
3$\sigma$.
