Thresholds for Correcting Errors, Erasures, and Faulty Syndrome Measurements in Degenerate Quantum Codes.
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 low-density parity-check codes with logarithmic or larger distances. These threshold estimates are parametrically better than the existing analytical bound based on percolation.
Department of Electrical Engineering, University of California, Riverside, California 92521, USA.
Ilya
I
Dumer
Department of Physics and Astronomy and Nebraska Center for Materials and Nanoscience, University of Nebraska, Lincoln, Nebraska 68588, USA.
Alexey A
AA
Kovalev
Department of Physics and Astronomy, University of California, Riverside, California 92521, USA.
Leonid P
LP
Pryadko