  We study the lattice spacing dependence, or scaling, of physical quantities
using the highly improved staggered quark (HISQ) action introduced by the
HPQCD/UKQCD collaboration, comparing our results to similar simulations with
the asqtad fermion action. Results are based on calculations with lattice
spacings approximately 0.15, 0.12 and 0.09 fm, using four flavors of dynamical
HISQ quarks. The strange and charm quark masses are near their physical values,
and the light-quark mass is set to 0.2 times the strange-quark mass. We look at
the lattice spacing dependence of hadron masses, pseudoscalar meson decay
constants, and the topological susceptibility. In addition to the commonly used
determination of the lattice spacing through the static quark potential, we
examine a determination proposed by the HPQCD collaboration that uses the decay
constant of a fictitious "unmixed s bar s" pseudoscalar meson. We find that the
lattice artifacts in the HISQ simulations are much smaller than those in the
asqtad simulations at the same lattice spacings and quark masses.
