A major breakthrough in the study of the strong interaction at low energies was achieved in 1974, when the foundations of lattice formalism were laid. This led to a very efficient, systematically correct and, most importantly, non-perturbative method. With the help of appropriate mathematical tools, the original theory can be reduced to a finite dimensional, finite volume statistical physical system in which the desired observables can be computed via Monte Carlo simulations. The limitations are typically the numerical difficulties, for which the obvious antidote would be to infinitely increase the computation time. This means that the algorithms should in principle be able to produce the exact results, but with finite machine time, very severe obstacles can arise, e.g. the notorious overlap and sign problem [1-3]. In my presentation I give a detailed insight into these numerical difficulties and show how they can be alleviated.
 M. Giordano, K. Kapás, S. D. Katz, D. Nógrádi and A. Pásztor. “Effect of stout smearing on the phase diagram from multiparameter reweighting in lattice QCD”. Physical Review D 102.3 (2020).
 M. Giordano, K. Kapás, S. D. Katz, D. Nógrádi és A. Pásztor. “New approach to lattice QCD at finite density; results for the critical end point on coarse lattices”. JHEP 05 (2020)
 M. Giordano, K. Kapás, S. D. Katz, A. Pásztor és Z. Tulipánt. “Exponential reduction of the sign problem at finite density in the 2+1D XY model via contour deformations”. Phys. Rev. D 106 (2022)