Converting leakage errors to erasure errors and cooling atoms while preserving coherence in neutral atoms for fault-tolerant quantum computation

Neutral atoms quantum information processing is growing in prominence with the recent demonstration of high-fidelity entangling gates and architectures that can be scaled to large numbers of qubits. One particular error channel that must be addressed is the loss of atoms that are weakly bound in optical traps. This leads to leakage errors that are detrimental to fault-tolerant quantum computation as they are not Pauli errors and need separate error correction protocols. In this work, we develop schemes for converting these leakage errors to erasure errors, which can be efficiently corrected by standard error correction protocols. Another critical roadblock for quantum computation with neutral atoms is the lack of schemes for cooling atomic motion while preserving the qubit coherence, which prevents us from doing arbitrarily long quantum computation. In this work, we extend the scheme for detecting leakage to cool atoms based on the work originally studied and recently revisited recently based on alkaline earth atoms with quantum information stored in the nuclear spin. For these atoms, one can use metastable states with narrow linewidth to employ the techniques of resolved sideband cooling. To avoid mixing electronic and nuclear degrees of freedom in the excited state, which we need for cooling, we consider moderate AC Stark shifts. This decouples the electronic and nuclear degrees of freedom and avoids the ``which way information’’ about the nuclear spin state and one can cool while preserving coherence.