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We present advances in the development of the numerical unitarity method forthe computation of multi-loop amplitudes in QCD. As an application, we showresults for all the leading-color two-loop five-gluon helicity amplitudes. Theamplitudes are reduced to a linear combination of master integrals by employingunitarity-compatible integration-by-parts identities, and the correspondingintegral coefficients are computed in an exact manner on rational phase-spacepoints through finite fields arithmetics.

Five-Point Two-Loop Amplitudes from Numerical Unitarity