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Quantum error correction thresholds for non-Abelian Turaev-Viro codes

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Abstract
We consider a two-dimensional quantum memory of qubits on a torus which encode the extended Fibonacci string-net code and devise strategies for error correction when those qubits are subjected to depolarizing noise. Building on the concept of tube algebras, we construct a set of measurements and of quantum gates which map arbitrary qubit errors to the string-net subspace and allow for the characterization of the resulting error syndrome in terms of doubled Fibonacci anyons. Tensor network techniques then allow us to quantitatively study the action of Pauli noise on the string-net subspace. We perform Monte Carlo simulations of error correction in this Fibonacci code and compare the performance of several decoders. For the case of a fixed-rate sampling depolarizing noise model, we find an error correction threshold of 4.7% using a clustering decoder.
Keywords
General Physics and Astronomy, INVARIANTS, ANYONS

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MLA
Schotte, Alexis, et al. “Quantum Error Correction Thresholds for Non-Abelian Turaev-Viro Codes.” PHYSICAL REVIEW X, vol. 12, no. 2, 2022, doi:10.1103/physrevx.12.021012.
APA
Schotte, A., Zhu, G., Burgelman, L., & Verstraete, F. (2022). Quantum error correction thresholds for non-Abelian Turaev-Viro codes. PHYSICAL REVIEW X, 12(2). https://doi.org/10.1103/physrevx.12.021012
Chicago author-date
Schotte, Alexis, Guanyu Zhu, Lander Burgelman, and Frank Verstraete. 2022. “Quantum Error Correction Thresholds for Non-Abelian Turaev-Viro Codes.” PHYSICAL REVIEW X 12 (2). https://doi.org/10.1103/physrevx.12.021012.
Chicago author-date (all authors)
Schotte, Alexis, Guanyu Zhu, Lander Burgelman, and Frank Verstraete. 2022. “Quantum Error Correction Thresholds for Non-Abelian Turaev-Viro Codes.” PHYSICAL REVIEW X 12 (2). doi:10.1103/physrevx.12.021012.
Vancouver
1.
Schotte A, Zhu G, Burgelman L, Verstraete F. Quantum error correction thresholds for non-Abelian Turaev-Viro codes. PHYSICAL REVIEW X. 2022;12(2).
IEEE
[1]
A. Schotte, G. Zhu, L. Burgelman, and F. Verstraete, “Quantum error correction thresholds for non-Abelian Turaev-Viro codes,” PHYSICAL REVIEW X, vol. 12, no. 2, 2022.
@article{8750130,
  abstract     = {{We consider a two-dimensional quantum memory of qubits on a torus which encode the extended
Fibonacci string-net code and devise strategies for error correction when those qubits are subjected to
depolarizing noise. Building on the concept of tube algebras, we construct a set of measurements and of
quantum gates which map arbitrary qubit errors to the string-net subspace and allow for the characterization
of the resulting error syndrome in terms of doubled Fibonacci anyons. Tensor network techniques then
allow us to quantitatively study the action of Pauli noise on the string-net subspace. We perform
Monte Carlo simulations of error correction in this Fibonacci code and compare the performance of several
decoders. For the case of a fixed-rate sampling depolarizing noise model, we find an error correction
threshold of 4.7% using a clustering decoder.}},
  articleno    = {{021012}},
  author       = {{Schotte, Alexis and Zhu, Guanyu and Burgelman, Lander and Verstraete, Frank}},
  issn         = {{2160-3308}},
  journal      = {{PHYSICAL REVIEW X}},
  keywords     = {{General Physics and Astronomy,INVARIANTS,ANYONS}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{39}},
  title        = {{Quantum error correction thresholds for non-Abelian Turaev-Viro codes}},
  url          = {{http://doi.org/10.1103/physrevx.12.021012}},
  volume       = {{12}},
  year         = {{2022}},
}

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