  Rydberg atom array with optical tweezers is a promising candidate for a
fault-tolerant quantum computer, thanks to its good properties such as
scalability, long coherence time and optical accessibility for communication. A
big barrier to overcome is non-Pauli errors, erasure errors and leakage errors.
Conventional work has revealed that leakage error is convertible to erasure
error. A remaining problem is that such (converted) erasure errors continuously
happen and accumulate. The previous proposal involved transporting atoms
directly from the reservoir area, where atoms are stored for spare, to the
computational area, where the computation and the error correction are
processed, to correct atom loss. However, transporting atoms takes a long time
and has side effects on surrounding qubits in practice. In this study, we
evaluate the effects on planar code by circuit-based Monte Carlo simulation
which has depolarizing errors and erasure errors, and propose a new scheme to
tolerate that problem, namely, k-shift erasure recovery scheme. Our scheme uses
online code deformation to tolerate erasures and repeatedly transfers the
logical qubit from an imperfect array in which erasure errors accumulated to
another perfect array in which erasure errors have been fixed by offline
optical tweezers, to tolerate a large (accumulated) number of erasures.
Furthermore, our scheme corrects erasure errors of atom arrays while logical
qubits are evacuated from that area to correct; therefore, manipulating optical
tweezers for erasure correction does not disturb qubits that compose logical
data. We believe that our scheme provides practical directions for Rydberg atom
quantum computers to realize feasible fault-tolerance.
