  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
fault-tolerant quantum computing, have not been generated. To generate anyons
with non-Abelian braiding statistics, we consider systems with mixed-boundary
punctures. We obtain the topologically distinct ground states of the system
numerically using the iDMRG technique. We discuss how these topological states
can be created using ancilla atoms of a different type. We show that a system
with 2N+2 punctures and an equal number of ancilla atoms leads to N logical
qubits whose Hilbert space is determined by a set of stabilizing conditions on
the ancilla atoms. Quantum gates can be implemented using a set of gates acting
on the ancilla atoms that commute with the stabilizers and realize the braiding
group of non-Abelian Ising anyons.
