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 the efficacy of alternative methods should be investigated. 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.