Hardware-Efficient, Fault-Tolerant Quantum Computation with Rydberg Atoms

While neutral atom setups have emerged both theoretically and experimentally as attractive systems for quantum information processing, one important remaining roadblock for achieving large-scale quantum computation with these platforms is the decay of the finite-lifetime Rydberg states during entangling operations. Because such Rydberg state decay errors can result in many possible channels of leakage out of the computational subspace or correlated errors from unwanted blockade effects, they cannot be addressed directly through traditional proposals for fault-tolerant quantum computation. Here, we present a complete analysis of the effects of these intrinsic sources of errors on a neutral-atom quantum computer and propose fault-tolerant quantum computation schemes that address these errors. By making use of the specific structure of the error model, the multi-level nature of atoms, and dipole selection rules, we find that the resource cost for fault-tolerant quantum computation can be significantly reduced compared to existing, general-purpose schemes, even when additional types of errors must be considered. We illustrate the experimental feasibility of our protocols through concrete examples with qubits encoded in ⁸⁷Rb or ⁸⁵Rb atoms, and we discuss important considerations for near-term and scalable implementation.