PIRSA:14070002

Video URL

https://pirsa.org/14070002

Maximum likelihood decoding threshold as a phase transition

Pryadko, L. (2014). Maximum likelihood decoding threshold as a phase transition. Perimeter Institute for Theoretical Physics. https://pirsa.org/14070002

Pryadko, Leonid. Maximum likelihood decoding threshold as a phase transition. Perimeter Institute for Theoretical Physics, Jul. 14, 2014, https://pirsa.org/14070002 

          @misc{ scivideos_PIRSA:14070002,
            doi = {10.48660/14070002},
            url = {https://pirsa.org/14070002},
            author = {Pryadko, Leonid},
            keywords = {},
            language = {en},
            title = {Maximum likelihood decoding threshold as a phase transition},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2014},
            month = {jul},
            note = {PIRSA:14070002 see, \url{https://scivideos.org/index.php/pirsa/14070002}}
          }

Leonid Pryadko University of California, Riverside

Talk numberPIRSA:14070002
DOI10.48660/14070002
Source RepositoryPIRSA
Collection
Talk Type Conference

Abstract

In maximum likelihood (ML) decoding, we are trying to find the most likely error given the measured syndrome. While this is hardly ever practical, such a decoder is expected to have the highest threshold.
I will discuss the mapping between the ML threshold for an infinite family of stabilizer codes and a phase transition in an associated family of Ising models with bond disorder [1]. This is a generalization of the map between the toric codes and the square lattice Ising model. Quantum LDPC codes produce generally non-local spin models with few-body interactions. A relatively simple Monte Carlo simulation of such a model can give an upper bound on the decoding threshold for the original code family. This can be used to compare code families irrespectively of decoders, and to establish an absolute measure of decoder performance.

[1] A. A. Kovalev and L. P. Pryadko, "Spin glass reflection of the decoding transition for quantum error correcting codes," unpublished,
arXiv:1311.7688 (2013).