  We report on salient features of a mixed lattice QCD action using valence
M\"{o}bius domain-wall fermions solved on the dynamical $N_f=2+1+1$ HISQ
ensembles generated by the MILC Collaboration. The approximate chiral symmetry
properties of the valence fermions are shown to be significantly improved by
utilizing the gradient-flow scheme to first smear the HISQ configurations. The
greater numerical cost of the M\"{o}bius domain-wall inversions is mitigated by
the highly efficient QUDA library optimized for NVIDIA GPU accelerated compute
nodes. We have created an interface to this optimized QUDA solver in Chroma. We
provide tuned parameters of the action and performance of QUDA using ensembles
with the lattice spacings $a \simeq \{0.15, 0.12, 0.09\}$ fm and pion masses
$m_\pi \simeq \{310, 220,130\}$ MeV. We have additionally generated two new
ensembles with $a\sim0.12$ fm and $m_\pi\sim\{400, 350\}$ MeV. With a fixed
flow-time of $t_{gf}=1$ in lattice units, the residual chiral symmetry breaking
of the valence fermions is kept below 10\% of the light quark mass on all
ensembles, $m_{res} \lesssim 0.1\times m_l$, with moderate values of the fifth
dimension $L_5$ and a domain-wall height $M_5 \leq 1.3$. As a benchmark
calculation, we perform a continuum, infinite volume, physical pion and kaon
mass extrapolation of $F_{K^\pm}/F_{\pi^\pm}$ and demonstrate our results are
independent of flow-time, and consistent with the FLAG determination of this
quantity at the level of less than one standard deviation.
