Analog surface code[1] 

Description

Also called a continuous-variable (CV) surface code. An analog CSS version of the Kitaev surface code.

Decoding

Shift-based decoder [2].

Notes

See [3; Sec. III.C2] for an exposition.

Parent

Cousins

  • Modular-qudit surface code — The analog surface code realizes a straightforward extension of the modular-qudit surface code to infinite local dimension, \(q\to\infty\). There are two types of anyons, \(e\) and \(m\), with each type being valued in \(U(1)\) as opposed to \(\mathbb{Z}_q\) for the qudit surface code.
  • Abelian topological code — The analog surface code realizes a straightforward extension of the modular-qudit surface code to infinite local dimension, \(q\to\infty\). There are two types of anyons, \(e\) and \(m\), with each type being valued in \(U(1)\) as opposed to \(\mathbb{Z}_q\) for the qudit surface code.

References

[1]
J. Zhang et al., “Anyon statistics with continuous variables”, Physical Review A 78, (2008) arXiv:0711.0820 DOI
[2]
C. Vuillot et al., “Quantum error correction with the toric Gottesman-Kitaev-Preskill code”, Physical Review A 99, (2019) arXiv:1810.00047 DOI
[3]
B. M. Terhal, “Quantum error correction for quantum memories”, Reviews of Modern Physics 87, 307 (2015) arXiv:1302.3428 DOI
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Zoo Code ID: analog_surface

Cite as:
“Analog surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/analog_surface
BibTeX:
@incollection{eczoo_analog_surface, title={Analog surface code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/analog_surface} }
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“Analog surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/analog_surface

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/oscillators/stabilizer/hyperplane/analog_surface.yml.