Quantum low-weight check (QLWC) code[1] 

Description

Member of a family of \([[n,k,d]]\) modular-qudit or Galois-qudit stabilizer codes for which the number of sites participating in each stabilizer generator is bounded by a constant as \(n\to\infty\).

Parent

Child

Cousins

  • Unary code — A family of approximate non-stabilizer QLWC codes with linear distance and rate has been constructed [1] using unary codes that arise from the Feynman-Kitaev clock construction [2].
  • Approximate quantum error-correcting code (AQECC) — A family of approximate non-stabilizer QLWC codes with linear distance and rate has been constructed [1] using unary codes that arise from the Feynman-Kitaev clock construction [2].

References

[1]
C. Nirkhe, U. Vazirani, and H. Yuen, “Approximate Low-Weight Check Codes and Circuit Lower Bounds for Noisy Ground States”, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany (2018) arXiv:1802.07419 DOI
[2]
A. Kitaev, A. Shen, and M. Vyalyi, Classical and Quantum Computation (American Mathematical Society, 2002) DOI
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Zoo Code ID: qlwc

Cite as:
“Quantum low-weight check (QLWC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/qlwc
BibTeX:
@incollection{eczoo_qlwc, title={Quantum low-weight check (QLWC) code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/qlwc} }
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Permanent link:
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Cite as:

“Quantum low-weight check (QLWC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/qlwc

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/properties/stabilizer/qldpc/qlwc.yml.