Abstract
We present the computation of Higgs boson production in association with a jet at the LHCincluding QCD corrections up to NNLO. The calculation includes the subsequent decay of theHiggs boson into four leptons, allowing for the full reconstruction of the final-state kinematics.In anticipation of improved LHC measurements based on the full Run II dataset, we present astudy for single- and double-differential cross sections within the fiducial volume as defined inprior ATLAS analyses. Higher-order corrections are found to have a sizeable impact on bothnormalisation and shape of differential cross sections