  We report on recent progress in employing the Highly Improved Staggered Quark
(HISQ) action introduced by the HPQCD/UKQCD collaboration in simulations with
dynamical fermions. The HISQ action is an order $a^2$ Symanzik-improved action
with further suppressed taste symmetry violations. The improvement in taste
symmetry is achieved by introducing Fat7 smearing of the original gauge links
and reunitarization (projection to an element of U(3) or SU(3)) followed by
Asq-type smearing. Major challenges for calculating the fermion force are
related to the reunitarization step. We present a preliminary study of the HISQ
action on two 2+1+1 flavor ensembles with the lattice spacing roughly
equivalent to the MILC asqtad a=0.125 and 0.09 fm ensembles.
