PIRSA:17040076

Percolation transition vs. erasure thresholds for surface codes on graphs

Pryadko, L. (2017). Percolation transition vs. erasure thresholds for surface codes on graphs. Perimeter Institute. https://pirsa.org/17040076

Pryadko, Leonid. Percolation transition vs. erasure thresholds for surface codes on graphs. Perimeter Institute, Apr. 26, 2017, https://pirsa.org/17040076 

          @misc{ pirsa_PIRSA:17040076,
            doi = {10.48660/17040076},
            url = {https://pirsa.org/17040076},
            author = {Pryadko, Leonid},
            keywords = {Other},
            language = {en},
            title = {Percolation transition vs. erasure thresholds for surface codes on graphs},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {apr},
            note = {PIRSA:17040076 see, \url{https://pirsa.org}}
          }

Leonid Pryadko University of California, Riverside

DOI 10.48660/17040076
Collection
Talk Type Scientific Series
Subject

Abstract

For a family of finite rate stabilizer codes, one can define two distinct error correction thresholds: the usual "block" threshold for the entire code, and the single-qubit threshold, where we only care about the stability of a single encoded qubit corresponding to a randomly chosen conjugate pair of logical X and Z operators.  Our main result is that in the case of erasures, for hyperbolic surface codes related to a {p,q} tiling of the hyperbolic plane, it is the latter threshold that coincides exactly with the infinite-graph edge percolation transition.  I will also discuss likely generalizations to more general codes and other error models. This is joint work with Nicolas Delfosse.