  We discuss a method for scaling a neutral atom Rydberg gate quantum processor
to a large number of qubits. Limits are derived showing that the number of
qubits that can be directly connected by entangling gates with errors at the
$10^{-3}$ level using long range Rydberg interactions between sites in an
optical lattice, without mechanical motion or swap chains, is about 500 in two
dimensions and 7500 in three dimensions. A scaling factor of 60 at a smaller
number of sites can be obtained using collective register encoding in the
hyperfine ground states of the rare earth atom Holmium. We present a detailed
analysis of operation of the 60 qubit register in Holmium. Combining a lattice
of multi-qubit ensembles with collective encoding results in a feasible design
for a 1000 qubit fully connected quantum processor.
