PIRSA:14070003

Video URL

https://pirsa.org/14070003

Spin glass reflection of the decoding transition for space-time codes

Kovalev, A. (2014). Spin glass reflection of the decoding transition for space-time codes. Perimeter Institute for Theoretical Physics. https://pirsa.org/14070003

Kovalev, Alexey. Spin glass reflection of the decoding transition for space-time codes. Perimeter Institute for Theoretical Physics, Jul. 14, 2014, https://pirsa.org/14070003 

          @misc{ scivideos_PIRSA:14070003,
            doi = {10.48660/14070003},
            url = {https://pirsa.org/14070003},
            author = {Kovalev, Alexey},
            keywords = {},
            language = {en},
            title = {Spin glass reflection of the decoding transition for space-time codes},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2014},
            month = {jul},
            note = {PIRSA:14070003 see, \url{https://scivideos.org/index.php/pirsa/14070003}}
          }

Alexey Kovalev University of California, Riverside

Talk numberPIRSA:14070003
DOI10.48660/14070003
Source RepositoryPIRSA
Collection
Talk Type Conference

Abstract

We introduce space-time quantum code construction which is based on repeating the layers of an arbitrary quantum error correcting code. The error threshold of such space-time construction is shown to be related to the fault tolerant error threshold of the original quantum error correcting code in the presence of errors in syndrome measurements. The decoding transition for space-time codes can be further mapped to random-bond Wegner spin models.
Families of quantum low density parity-check (LDPC) codes with a finite decoding threshold lead to both known models (e.g., random bond Ising and random plaquette Z2 gauge models) as well as unexplored earlier and generally non-local disordered spin models with non-trivial phase diagrams that include the spin glass phase.
We apply this construction to the simplest examples of recently discovered hypergraph-product codes and numerically find the fault tolerant threshold in excess of 5% by employing Monte-Carlo simulations.