Abstract
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 language | English |
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Pages (from-to) | 5955 - 5974 |
Number of pages | 20 |
Journal | IEEE Transactions on Information Theory |
Volume | 68 |
Issue number | 9 |
DOIs | |
Publication status | Published - 26 Apr 2022 |
Bibliographical note
Publisher Copyright:© 1963-2012 IEEE.
Keywords
- Calderbank-Shor-Steane codes (CSS codes)
- quantum codes
- quantum error correction
- quantum fault-tolerant computation
- transversal gates