We present results for the strong coupling constant ($alpha_s$) and the charm quark mass ($m_c$) obtained from the moments of pseudoscalar current-current correlators. Our calculation employs the four flavor (2+1+1) HISQ ensembles generated by the MILC collaboration with six lattice spacings, including five with physical light-quark masses. We improve upon earlier calculations by including in our analysis two finer lattice spacings with a~0.042 fm and 0.03 fm along with a physical-mass ensemble with lattice spacing a~0.06 fm. Finally, we discuss plans for extending the current analysis to compute the mass of the bottom quark ($m_b$). The strong coupling and heavy-quark masses are important parametric inputs to Standard-Model and new-physics theory predictions, including for Higgs couplings.