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Pauli group-representation QSC[1]

Description

Non-uniform QSC whose projection is onto a copy of an irreducible representation of the single-qubit Pauli group, the symmetry group of the \(\{2,2,4\}\) tesselation of the sphere. Each codeword is a quantum superposition of vertices of a tetrahedron with \(\pm 1\) coefficients.

Gates

The single-qubit Pauli group can be realized via Gaussian rotations.

Cousin

  • Simplex spherical code— Each codeword of the Pauli group-representation QSC is a quantum superposition of vertices of a tetrahedron with \(\pm 1\) coefficients.

Member of code lists

Primary Hierarchy

Quantum Domain
Bosonic Kingdom
Bosonic codeQECC OAQECC AQECC Quantum
Coherent-state constellation code
Quantum spherical code (QSC)QECC OAQECC AQECC Quantum
Parents
Quantum spherical code (QSC)
The Pauli group-representation QSC has non-uniform coefficients.
Group-representation codeQECC OAQECC AQECC Quantum
The Pauli group-representation QSC is a group-representation code with \(G\) being the single-qubit Pauli group.
Pauli group-representation QSC

References

[1]
Y. Wang, Y. Xu, and Z.-W. Liu, “Encoded quantum gates by geometric rotation on tessellations”, (2024) arXiv:2410.18713
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Zoo Code ID: pauli_qsc

Cite as:
“Pauli group-representation QSC”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/pauli_qsc
BibTeX:
@incollection{eczoo_pauli_qsc, title={Pauli group-representation QSC}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/pauli_qsc} }
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Permanent link:
https://errorcorrectionzoo.org/c/pauli_qsc

Cite as:

“Pauli group-representation QSC”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/pauli_qsc

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/oscillators/qsc/pauli_qsc.yml.