An architecture for two-qubit encoding in neutral ytterbium-171 atoms

We present an architecture for encoding two qubits within the optical "clock" transition and nuclear spin-1/2 degree of freedom of neutral ytterbium-171 atoms. Inspired by recent high-fidelity control of all pairs of states within this four-dimensional ququart space, we present a toolbox for intra-ququart (single atom) one- and two-qubit gates, inter-ququart (two atom) Rydberg-based two- and four-qubit gates, and quantum nondemolition (QND) readout. We then use this toolbox to demonstrate the advantages of the ququart encoding for entanglement distillation and quantum error correction which exhibit superior hardware efficiency and better performance in some cases since fewer two-atom (Rydberg-based) operations are required. Finally, leveraging single-state QND readout in our ququart encoding, we present a unique approach to studying interactive circuits as well as to realizing a symmetry protected topological phase of a spin-1 chain with a shallow, constant-depth circuit. These applications are all within reach of recent experiments with neutral ytterbium-171 atom arrays or with several trapped ion species.