Adaptive surface code for quantum error correction in the presence of temporary or permanent defects

Whether it is at the fabrication stage or during course of quantum computation, e.g. because high-energy events like cosmic rays, qubits constituting an error correcting code may be rendered inoperable. Such defects correspond to individual clusters and could potentially disrupt sufficiently generate logical errors. In this paper, we explore a novel adaptive approach for surface correction on defective lattice. We show that combining appropriate defect detection algorithm quarantine identified zone allows one preserve advantage finite sizes, cost qubit overhead scales with size defect. Our numerics indicate code's threshold need not significantly affected; example, certain scenario where small repeatedly arise in each qubit, noise $2.7\%$ (versus defect-free case $2.9\%$). These results pave way experimental implementation large-scale computers will inevitable.