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

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 multiqubit ensembles with collective encoding results in a feasible design for a 1000-qubit fully connected quantum processor.

Figure 1

(Color online) Planar optical lattice defining an array of sites with spacing $D$, each one of which may be a single atom or a small ensemble containing $K$ atoms. Rydberg coupling enables gates within each ensemble and between ensembles.

Figure 2

(Color online) Qubit encoding in the symmetric states of an ensemble of $\left(2N+1\right)$-level systems. $|s⟩$ denotes the reservoir state. The figure depicts the state $|10\dots 01⟩$.

Figure 3

(Color online) Known [28] 111 levels of Ho below $25000{\text{cm}}^{-1}$ shown with odd-parity levels indicated by a dashed line. Transitions suitable for cooling and trapping (a)–(g), shelving to the $J=11/2$ metastable ground multiplet $\left(s_1,s_2\right)$, and readout by resonance fluorescence $\left(r_1,r_2,r_3\right)$, are indicated.

Figure 4

(Color online) Hyperfine structure of the Ho $4f^{11}6s^2\left({{}^{4}I}_{15/2}\right)$ ground state. Qubit assignments 1–60 are indicated together with hyperfine splittings and $g$ factors.

Figure 5

(Color online) Levels between 24 000 and $2600{\text{cm}}^{-1}$ that are connected by dipole-allowed transitions with the ground state are shown in solid blue, and dipole-forbidden levels are dashed. The dipole-allowed levels are labeled with their energy and lifetime. (b) shows trap depth (solid curve) and scattering rate (dashed curve) for light of the indicated energy.

Figure 6

(Color online) Protocol for loading small ensembles into a patterned lattice region. The small open circles are the repulsive lattice sites, and the large green circle is the outline of the bottle beam trap. The lattice is not drawn to scale for clarity. See text for details.