Dissipative stabilization and bias-preserving operations for dark-cat operations in atomic structures

Neutral atoms become one of the most promising platforms for quantum information and simulation purposes. Finding hardware-efficient ways to encode quantum information and performing error correction is still an important problem for this system. Our work shows how decoherence-free qubits can be efficiently encoded in the large spin hyperfine ground or metastable states of 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 any single-qubit gates in holonomic manners including those that preserve error bias, 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. When encoded in metastable levels, certain errors during gates can be treated as erasure errors. Also, with continuous syndrome monitoring and fresh atom replacement these errors can be converted to biased type. Those features of errors will be beneficial for further quantum error correcting strategies with reduced resource overhead and improved threshold.