Towards a Numerical Unitarity Approach for Two-loop Amplitudes in QCD

The numerical unitarity approach has been important for obtaining reliable QCD predictions for the LHC. Here I discuss the extension of the approach beyond the leading quantum corrections for computing multi-loop amplitudes. The numerical unitarity approach requires a suitable parametrisation of the loop integrands as a sum of terms that integrate to zero (surface terms) and master integrands. The construction and classification of suitable surface terms which match the propagators structures of Feynman amplitudes is the main technical advance discussed. A number of spin-offs for integral reduction and further formal questions are briefly reviewed.