Blockaded Rydberg atoms vs. Fibonacci anyon chains

Blockaded Rydberg atom chains are well- described by an Ising model in a constrained Hilbert space.  This constrained Hilbert space also describes 1-dimensional arrays of interacting non-abelian (Fibonacci) anyons, which potentially offer a route to universal topological quantum computation.  This raises the question of whether blockaded Rydberg chains may offer an advantage in simulating such chains, and hence potentially find applications in fault-tolerant quantum computation.  I will show that there are important differences between the two systems that lead to fundamentally different dynamics, such that the answer to this question is … no.