  We compute the leading, strong-interaction contribution to the anomalous
magnetic moment of the electron, muon and tau using lattice quantum
chromodynamics (QCD) simulations. Calculations include the effects of $u$, $d$,
$s$ and $c$ quarks and are performed directly at the physical values of the
quark masses and in volumes of linear extent larger than $6\,\mathrm{fm}$. All
connected and disconnected Wick contractions are calculated. Continuum limits
are carried out using six lattice spacings. We obtain
$a_e^\mathrm{LO-HVP}=189.3(2.6)(5.6)\times 10^{-14}$,
$a_\mu^\mathrm{LO-HVP}=711.1(7.5)(17.4)\times 10^{-10}$ and
$a_\tau^\mathrm{LO-HVP}=341.0(0.8)(3.2)\times 10^{-8}$, where the first error
is statistical and the second is systematic.
