Quantum Pin Codes

Christophe Vuillot*, Nikolas P. Breuckmann

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)
10 Downloads (Pure)


We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a generalization of quantum color codes and Reed-Muller codes and share a lot of their structure and properties. Pin codes have gauge operators, an unfolding procedure and their stabilizers form so-called $\ell$-orthogonal spaces meaning that the joint overlap between any $\ell$ stabilizer elements is always even. This last feature makes them interesting for devising magic-state distillation protocols, for instance by using puncturing techniques. We study examples of these codes and their properties.
Original languageEnglish
Pages (from-to)5955 - 5974
Number of pages20
JournalIEEE Transactions on Information Theory
Issue number9
Publication statusPublished - 26 Apr 2022

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.


  • Calderbank-Shor-Steane codes (CSS codes)
  • quantum codes
  • quantum error correction
  • quantum fault-tolerant computation
  • transversal gates


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