Resumen:
We have presented a method to detect degenerate errors in sparse quantum codes in a computationally efficient manner. We have also shown how this method is less complex than other existing strategies to compute the logical error rate of sparse CSS quantum codes. Making use of our scheme, we have shown how sparse quantum codes have a significant percentage of degenerate errors. This means that the discrepancy between the logical error rate and the physical error rate is exacerbated for sparse quantum codes. Our results show that, for specific families of QLDPC codes, performance may be up to 20% better than would be expected from previous results in the literature that are based on the physical error rate. In addition, these simulation outcomes serve to show how performance may be improved by constructing degenerate quantum codes, and they also speak toward the positive impact that modified decoding strategies can have on the performance of sparse quantum codes.
