QCD instantons are non-perturbative phenomena predicted to arise from the strong force, but which have not been directly observed. However, they may appear as a large number of soft jets in LHC collisions. In this paper the authors provide a state-of-the-art calculation of the event rate for these signals by making use of the optical theorem and higher-order contributions. Despite estimating a large cross-section, they find such searches will be difficult due to trigger thresholds and suggest to look for them in data from low-luminosity runs.