Quantum Error Correction resilient against Atom Loss

Abstract: We investigate quantum error correction protocols for neutral atoms quantum processors in the presence of atom loss. We complement the surface code with loss detection units (LDU) and analyze its performances by means of circuit-level simulations for two distinct protocols -- the standard LDU and a recently proposed teleportation-based LDU --, focussing on the impact of both atom loss and depolarizing noise on the logical error probability. We introduce and employ a new adaptive decoding procedure that leverages the knowledge of loss locations provided by the LDUs, improving logical error probabilities by nearly three orders of magnitude compared to a naive decoder. For the considered error models, our results demonstrate the existence of an error threshold line that depends linearly on the probabilities of atom loss and of depolarizing errors. For zero depolarizing noise, the atom loss threshold is about $2.6\%$.