Quantum Pin Codes

Christophe Vuillot; Nikolas P. Breuckmann

doi:10.1109/tit.2022.3170846

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arXiv · 1906.11394

Quantum Pin Codes

Christophe Vuillot·Nikolas P. Breuckmann

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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.

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Christophe Vuillot, Nikolas P. Breuckmann. 2019-06-27. Quantum Pin Codes. https://doi.org/10.1109/tit.2022.3170846

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