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In order to understand the role of QCD in the early universe, we performhybrid Monte-Carlo simulation of lattice QCD with $N_f=2+1+1$ optimaldomain-wall quarks at the physical point, on the $64^3 \times(6,8,10,12,16,20,64)$ lattices, each with three lattice spacings. The latticespacings and the bare quark masses are determined on the $64^4$ lattices. Theresulting gauge ensembles provide a basis for studying finite temperature QCDwith $N_f=2+1+1 $ domain-wall quarks at the physical point. In this Proceeding,we present our first result on the topological susceptibility of the QCDvacuum. The topological charge of each gauge configuration is measured by theclover charge in the Wilson flow at the same flow time in physical units, andthe topological susceptibility $ \chi_t(a,T) $ is determined for each ensemblewith lattice spacing $a$ and temperature $T$. Using the topologicalsusceptibility $\chi_t(a,T) $ of 15 gauge ensembles with three lattice spacingsand different temperatures in the range $T \sim 155-516 $~MeV, we extract thetopological susceptibility $\chi_t(T)$ in the continuum limit.

Finite temperature QCD with physical $(u/d, s, c)$ domain-wall quarks