**Single-qubit gates by graph scattering**

Continuous-time quantum walkers with tightly peaked momenta can simulate quantum computations by scattering off finite graphs. We enumerate all single-qubit gates that can be enacted by scattering off a single graph on up to $n=9$ vertices at certain momentum values, and provide numerical evidence that the number of such gates grows exponentially with $n$. The single-qubit rotations are about axes distributed roughly uniformly on the Bloch sphere, and rotations by both rational and irrational multiples of $\pi$ are found.