Adapting Surface Codes to Defective Components

The presence of time-correlated errors, such as fabrication imperfections and two-level systems in solid-state processors, can render certain qubits or gates inoperable or much noisier than desired. We develop a suite of methods for adapting surface code patches in the presence of non-operational qubits and gates, such that the quantum error correction protocol based on the surface code can still be implemented. We demonstrate significant improvement in code distance and the logical performance of our adapted code patches over the previous approaches [1]. Our methods yield several valid strategies for a given configuration of defective components; we explain how our algorithm tests and compares different strategies in order to choose the optimal one for each configuration. The algorithm provides the global optimum or approximates the optimum using heuristics to improve runtime and minimize computer resources. In addition to logical memory we also show how to apply our methods to lattice surgery examples.

[1] Auger, J., Anwar, H., Gimeno-Segovia, M., Stace, T., & Browne, D. (2017). Fault-tolerance thresholds for the surface code with fabrication errors. Phys. Rev. A, 96, 042316.