Renormalization Group Decoder for a Four-Dimensional Toric Code

N.P. Breuckmann, B. M. Terhal, K. Duivenvoorden

Research output: Contribution to journalArticleScientificpeer-review

18 Citations (Scopus)
293 Downloads (Pure)


We describe a computationally efficient heuristic algorithm based on a renormalization-group procedure which aims at solving the problem of finding a minimal surface given its boundary (curve) in any hypercubic lattice of dimension D > 2. We use this algorithm to correct errors occurring in a four-dimensional variant of the toric code, having open as opposed to periodic boundaries. For a phenomenological error model which includes measurement errors we use a five-dimensional version of our algorithm, achieving a threshold of 4.35±0.1%. For this error model, this is the highest known threshold of any topological code. Without measurement errors, a four-dimensional version of our algorithm can be used and we find a threshold of 7.3±0.1%. For the gate-based depolarizing error model we find a threshold of 0.31±0.01% which is below the threshold found for the twodimensional toric code.

Original languageEnglish
Article number8528891
Pages (from-to)2545-2562
Number of pages18
JournalIEEE Transactions on Information Theory
Issue number4
Publication statusPublished - 2019

Bibliographical note

Accepted author manuscript


  • quantum computing
  • error correcting codes
  • smoothing method


Dive into the research topics of 'Renormalization Group Decoder for a Four-Dimensional Toric Code'. Together they form a unique fingerprint.

Cite this