English

On maximum-likelihood decoding with circuit-level errors

Quantum Physics 2020-08-12 v4

Abstract

Error probability distribution associated with a given Clifford measurement circuit is described exactly in terms of the circuit error-equivalence group, or the circuit subsystem code previously introduced by Bacon, Flammia, Harrow, and Shi. This gives a prescription for maximum-likelihood decoding with a given measurement circuit. Marginal distributions for subsets of circuit errors are also analyzed; these generate a family of related asymmetric LDPC codes of varying degeneracy. More generally, such a family is associated with any quantum code. Implications for decoding highly-degenerate quantum codes are discussed.

Keywords

Cite

@article{arxiv.1909.06732,
  title  = {On maximum-likelihood decoding with circuit-level errors},
  author = {Leonid P. Pryadko},
  journal= {arXiv preprint arXiv:1909.06732},
  year   = {2020}
}

Comments

15 pages, 4 figures. In v2, added analysis of marginal distributions and discussion of decoding. In v3, some typos corrected and references added. In v4, only license has been updated