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

Scaling the neutral atom Rydberg gate quantum computer by collective encoding in Holmium atoms