  We demonstrate ballistic spin transport of an integrable unitary quantum
circuit, which can be understood either as a paradigm of an integrable
periodically driven (Floquet) spin chain, or as a Trotterized anisotropic
($XXZ$) Heisenberg spin-1/2 model. We construct an analytic family of
quasi-local conservation laws that break the spin-reversal symmetry and compute
a lower bound on the spin Drude weight which is found to be a fractal function
of the anisotropy parameter. Extensive numerical simulations of spin transport
suggest that this fractal lower bound is in fact tight.
