  In the last few years, the Yang--Mills gradient flow was shown to be an
attractive tool for non-perturbative studies of non-Abelian gauge theories.
Here a simple extension of the flow to the quark fields in QCD is considered.
As in the case of the pure-gauge gradient flow, the renormalizability of
correlation functions involving local fields at positive flow times can be
established using a representation through a local field theory in 4+1
dimensions. Applications of the extended flow in lattice QCD include
non-perturbative renormalization and O(a) improvement as well as accurate
calculations of the chiral condensate and of the pseudo-scalar decay constant
in the chiral limit.
