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The anomalous magnetic moment of the muon is one of the most precisely
measured quantities in particle physics and can therefore serve as a
high-precision test of the Standard Model. The largest uncertainty in
the Standard Model prediction comes from the hadronic sector, where
the leading contribution is given by the Hadronic Vacuum Polarisation
(HVP). A determination of the HVP from lattice QCD aiming at
sub-percent level precision requires to include isospin breaking
corrections in the computation. I will discuss how these corrections
can be included in a lattice calculation and present results for the
QED and strong isospin breaking corrections to the HVP at physical
quark masses.