Hadronic vacuum polarization contribution to the anomalous magnetic moments of leptons from first principles

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 $6\mathrm{f}\mathrm{m}$. All connected and disconnected Wick contractions are calculated. Continuum limits are carried out using six lattice spacings. We obtain $a_e^{\mathrm{L}\mathrm{O}-\mathrm{H}\mathrm{V}\mathrm{P}}=189.3(2.6)(5.6)\times {10}^{-14}$, $a_{\mu }^{\mathrm{L}\mathrm{O}-\mathrm{H}\mathrm{V}\mathrm{P}}=711.1(7.5)(17.4)\times {10}^{-10}$ and $a_{\tau }^{\mathrm{L}\mathrm{O}-\mathrm{H}\mathrm{V}\mathrm{P}}=341.0(0.8)(3.2)\times {10}^{-8}$, where the first error is statistical and the second is systematic.