Towards practical classical processing for the surface code: Timing analysis

摘要

Topological quantum error-correction codes have high thresholds and are well suited to physical implementation.nThe minimum-weight perfect-matching algorithm can be used to efficiently handle errors in such codes.Wenperform a timing analysis of our current implementation of the minimum-weight perfect-matching algorithm.nOur implementation performs the classical processing associated with an n × n lattice of qubits realizing a squarensurface code storing a single logical qubit of information in a fault-tolerant manner. We empirically demonstratenthat our implementation requires onlyO(n2) average time per round of error correction for code distances rangingnfrom 4 to 512 and a range of depolarizing error rates. We also describe tests we have performed to verify that itnalways obtains a true minimum-weight perfect matching.