  We show that the coherent interaction between free electrons and photons can
be used for universal control of continuous-variable photonic quantum states in
the form of Gottesman-Kitaev-Preskill (GKP) qubits. Specifically, we find that
electron energy combs enable non-destructive measurements of the photonic state
and can induce arbitrary gates. Moreover, a single electron interacting with
multiple photonic modes can create highly entangled states such as
Greenberger-Horne-Zeilinger states and cluster states of GKPs.
