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

Authors

Ilya Dumer, University of California, RiversideFollow
Alexey Kovalev, University of Nebraska - LncolnFollow
Leonid P. Pryadko, University of California at RiversideFollow

Document Type

Article

Date of this Version

2015

Citation

Phys. Rev. Lett. 115, 050502 (2015)

DOI: 10.1103/PhysRevLett.115.050502

Comments

© 2015 American Physical Society. Used by permission.

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.