  We develop a Floquet protocol for long-range entanglement generation in the
one-dimensional quantum Potts model, which generalizes the transverse-filed
Ising model by allowing each spin to have $n>2$ states. We focus on the case of
$n=3$, so that the model describes a chain of qutrits. The suggested protocol
creates qutrit Bell-like pairs with non-local long-range entanglement that
spans over the entire chain. We then conjecture that the proposed Floquet
protocol is integrable and explicitly construct a few first non-trivial
conserved quantities that commute with the stroboscopic evolution operator. Our
analysis of the Floquet integrability relies on the deep connection between the
quantum Potts model and a much broader class of models described by the
Temperley-Lieb algebra. We work at the purely algebraic level and our results
on Floquet integrability are valid for any representation of the Temperley-Lieb
algebra. We expect that our findings can be probed with present experimental
facilities using Rydberg programmable quantum simulators and can find various
applications in quantum technologies.
