  We bound the time necessary to implement the shift unitary on a
one-dimensional ring, both using local Hamiltonians and those with power-law
interactions. This time is constrained by the Frobenius light cone; hence we
prove that shift unitaries are parametrically harder to implement than
preparing long-range Bell pairs for sufficiently small power-law exponent. We
note an intriguing similarity between the proof of our results, and the
hardness of preparing symmetry-protected topological states with
symmetry-preserving Hamiltonians.
