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 \( \mathsf{BD}_{2N}^{\otimes n} = \{\omega I, X, P\}^{\otimes n} \), which is the tensor product of the binary dihedral group of order \(8N\). Here, \( \omega \) is a \( 2N \)th 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.

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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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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/edit/main/codes/quantum/qubits/nonstabilizer/xp_stabilizer.yml.