The quark-connected part of the hadronic light-by-light scattering contribution to the muons anomalous magnetic moment is computed using lattice QCD with chiral fermions. We report several significant algorithmic improvements and demonstrate their effectiveness through specific calculations which show a reduction in statistical errors by more than an order of magnitude. The most realistic of these calculations is performed with a near-physical, $171$ MeV pion mass on a $(4.6;mathrm{fm})^3$ spatial volume using the $32^3times 64$ Iwasaki+DSDR gauge ensemble of the RBC/UKQCD Collaboration.
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