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

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