NLO QCD corrections to the processes pp $\to$ ZZ with 0, 1 and 2 jets at the LHC

We propose an implementation of ZZ, ZZj and ZZjj productions in MadGraph5_aMC@NLO framework at $\sqrt{s}$ = 14 TeV. We calculate these processes at leading order and next-to-leading order with QCD corrections and we present a theoretical prediction of their total cross sections with different cuts in transverse momentum of jets, including gluon fusion contributions. In the same time we estimate their theoretical uncertainty. We discuss the various kinematical distributions spectrums at partonic level and hadronic level applying the showering and hadronization using Pythia8. In order to reconstruct the events similar to that found at LHC, we use the ATLAS cards and the fast detector simulation Delphes.