Thresholds for Correcting Errors, Erasures, and Faulty Syndrome Measurements in Degenerate Quantum Codes

Ilya Dumer, Alexey A. Kovalev, Leonid P. Pryadko

Type: Article

Publication Date: 2015-07-31

Citations: 29

DOI: https://doi.org/10.1103/physrevlett.115.050502

Abstract

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.

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Physical Review Letters - View - PDF
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