  Synthetic lattices in photonics enable the exploration of light states in new
dimensions, transcending phenomena common only to physical space. We propose
and demonstrate a Quantum Walk Laser in synthetic frequency space formed by
externally modulating a ring-shaped semiconductor laser with ultrafast recovery
times. In this device, the initially ballistic quantum walk does not dissipate
into low supermode states of the synthetic lattice; instead, thanks to the
fast-gain nonlinearity of our quantum cascade laser active material, the state
stabilizes in a broad frequency comb, unlocking the full potential of the
lattice. This device produces a low-noise, nearly-flat broadband comb (reaching
100 cm$^{-1}$ bandwidth), well predicted by our models. The proposed Quantum
Walk Laser offers a promising platform to generate broadband, tunable and
stable frequency combs.
