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The WHOT-QCD Collaboration is pushing forward a series of lattice studies ofQCD at finite temperatures and densities using improved Wilson quarks. BecauseWilson-type quarks require more computational resources than the more widelyadopted staggered-type quarks, various theoretical and computational techniqueshave to be developed and applied. In this paper, we introduce the fixed-scaleapproach armed with the T-integration method, the Gaussian method based on thecumulant expansion, and the histogram method combined with the reweightingtechnique. Adopting these methods, we have carried out the first study offinite-density QCD with Wilson-type quarks and the first calculation of theequation of state with 2+1 flavors of Wilson-type quarks. We present results ofthese studies and discuss perspectives towards a clarification of theproperties of 2+1 flavor QCD at the physical point, at finite temperatures anddensities.

Ab initio study of QCD thermodynamics on the lattice at zero and finite densities