Dark-cat encoding in atomic levels - Part II

Neutral atoms become one of the most promising platforms for quantum information and simulation purposes. Finding hardware-efficient way to encode quantum information and performing error correction is still an important problem for this system. In our work, we show how decoherence-free qubits can be efficiently encoded in the large spin hyperfine ground state of lanthanide atoms. In particular, they are encoded in the dark states of a Raman-coupled hyperfine structure. This encoding resembles cat code structure in bosonic systems. For the encoded qubits, readily available laser coupling methods are used to construct bias-preserving single-qubit holonomic gates, while laser coupling to Rydberg states is employed to create bias-preserving entangling gates among qubits. The bias-preserving operation set is sufficient for universal quantum computing on the concatenated repetition code level. In the second part, we will focus on the detailed protocol on the single-qubit and entangling gate design and show how they can be constructed in a bias-preserving manner.