XP stabilizer code[1] 

Description

The XP Stabilizer formalism is a generalization of the XS and Pauli stabilizer formalisms, with stabilizer generators taken from the group \( \{\omega I, X, P\}^{\otimes n} \). Here, \( \omega \) is a \( 2N \) root of unity, and \( P = \text{diag} ( 1, \omega^2) \). The codespace is a \(+1\) eigenspace of a set of XP stabilizer generators, which need not commute to define a valid codespace.

XP stabilizer codes are classified into XP-regular and XP-non-regular, where the former can be mapped to a CSS code with similar logical operator structure.

Parent

Children

Cousins

  • Qubit CSS code — Each XP-regular code can be mapped to a CSS code with a similar logical operator structure [1].
  • Codeword stabilized (CWS) code — The orbit representatives of XP codes play a similar role to the word operators of CWS codes.

References

[1]
M. A. Webster, B. J. Brown, and S. D. Bartlett, “The XP Stabiliser Formalism: a Generalisation of the Pauli Stabiliser Formalism with Arbitrary Phases”, Quantum 6, 815 (2022) arXiv:2203.00103 DOI
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Zoo Code ID: xp_stabilizer

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

“XP stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/xp_stabilizer

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qubits/nonstabilizer/xp_stabilizer.yml.