Non-Abelian Anyon Statistics in Rydberg Atoms

We study the emergence of topological matter in two-dimensional systems of neutral Rydberg atoms in Ruby lattices. While abelian anyons have been predicted in such systems, non-abelian anyons, which would form a substrate for quantum computing, have not been generated. To generate anyons with non-abelian braiding statistics, we create punctures in the system with mixed e and m-condensed (smooth and rough) boundaries. 2-puncture states have a fourfold ground state degeneracy, based on the type of anyon enclosed; they can be trivial, e-enclosing, m-enclosing, or fermion-enclosing. We create superposition states of 2 punctures each containing e and m anyons, which can reproduce the Ising fusion matrix. Additionally, a 4-puncture state comprised of 2 superposition states allows braiding operations that implement the X gate. We confirm the presence of mixed boundary punctures as well as the emergence of these ground states numerically using the infinite DMRG technique.