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Finite density quantum field theories have evaded first principle Monte-Carlosimulations due to the notorious sign-problem. The partition function of suchtheories appears as the Fourier transform of the generalised density-of-states,which is the probability distribution of the imaginary part of the action. Withthe advent of Wang-Landau type simulation techniques and recent advances, thedensity-of-states can be calculated over many hundreds of orders of magnitude.Current research addresses the question whether the achieved precision is highenough to reliably extract the finite density partition function, which isexponentially suppressed with the volume. In my talk, I review thestate-of-play for the high precision calculations of the density-of-states aswell as the recent progress for obtaining reliable results from highlyoscillating integrals. I will review recent progress for the $Z_3$ quantumfield theory for which results can be obtained from the simulation of the dualtheory, which appears to free of a sign problem.

The density of states approach for the simulation of finite density quantum field theories