Erasure-tolerance scheme for the surface codes on neutral atom quantum computers

Neutral atom arrays manipulated with optical tweezers are promising candidates for fault-tolerant quantum computers due to their advantageous properties, such as scalability, long coherence times, and optical accessibility for communication. A significant challenge to overcome is the presence of non-Pauli errors, specifically erasure errors and leakage errors. Previous work has shown that leakage errors can be converted into erasure errors; however, these (converted) erasure errors continuously occur and accumulate over time. Prior proposals have involved transporting atoms directly from a reservoir area--where spare atoms are stored--to the computational area--where computation and error correction are performed--to correct atom loss. While coherent transport is promising, it may not address all challenges--particularly its effectiveness in dense arrays and alternative methods must help. In this study, we evaluate the effects of erasure errors on the surface code using circuit-based Monte Carlo simulations that incorporate depolarizing and accumulated erasure errors. We propose a new scheme to mitigate this problem: a k-shift erasure recovery scheme. Our scheme employs code deformation to repeatedly transfer the logical qubit from an imperfect array with accumulated erased qubits to a perfect array, thereby tolerating many accumulated erasures. Furthermore, our scheme corrects erasure errors in the atom arrays while the logical qubits are evacuated from the area being corrected; thus, manipulating optical tweezers for erasure correction does not disturb the qubits that constitute the logical data. Our scheme provides a practical pathway for neutral atom quantum computers to achieve feasible fault tolerance.