Thresholds for correcting errors, erasures, and faulty syndrome measurements in degenerate quantum codes

Understand

We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold to scalable quantum computation applicable to degenerate quantum codes with sublinear distance scaling.

• We give explicit analytic expressions combining probabilities of erasures, depolarizing errors, and phenomenological syndrome measurement errors for quantum LDPC codes with logarithmic or larger distances.
• These threshold estimates are parametrically better than the existing analytical bound based on percolation.