Quantum Pin Codes

Christophe Vuillot; Nikolas P. Breuckmann

doi:10.1109/TIT.2022.3170846

Quantum Pin Codes

Christophe Vuillot^*, Nikolas P. Breuckmann

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

12 Citations (Scopus)

71 Downloads (Pure)

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
Pages (from-to)	5955 - 5974
Number of pages	20
Journal	IEEE Transactions on Information Theory
Volume	68
Issue number	9
DOIs	https://doi.org/10.1109/TIT.2022.3170846
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

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title = "Quantum Pin Codes",

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 \$\textbackslash{}ell\$-orthogonal spaces meaning that the joint overlap between any \$\textbackslash{}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.",

keywords = "Calderbank-Shor-Steane codes (CSS codes), quantum codes, quantum error correction, quantum fault-tolerant computation, transversal gates",

author = "Christophe Vuillot and Breuckmann, \{Nikolas P.\}",

note = "Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2022",

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day = "26",

doi = "10.1109/TIT.2022.3170846",

language = "English",

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T1 - Quantum Pin Codes

AU - Vuillot, Christophe

AU - Breuckmann, Nikolas P.

PY - 2022/4/26

Y1 - 2022/4/26

N2 - 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.

AB - 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.

KW - Calderbank-Shor-Steane codes (CSS codes)

KW - quantum codes

KW - quantum error correction

KW - quantum fault-tolerant computation

KW - transversal gates

UR - https://www.scopus.com/pages/publications/85129641178

U2 - 10.1109/TIT.2022.3170846

DO - 10.1109/TIT.2022.3170846

M3 - Article (Academic Journal)

SN - 0018-9448

VL - 68

SP - 5955

EP - 5974

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 9

ER -

Quantum Pin Codes

Abstract

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Keywords

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