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Clifford group-representation QSC[1]

Description

Non-uniform QSC whose projection is onto a copy of an irreducible representation of the single-qubit Clifford group, taken as the binary octahedral subgroup of the group \(SU(2)\) of Gaussian rotations. Its codewords consist of non-uniform superpositions of 48 coherent states.

Gates

The single-qubit Clifford group can be realized via Gaussian rotations. The \(T\) and \(CZ\) gates can be realized using quartic Kerr operations [1].

Primary Hierarchy

Parents
The Clifford group-representation QSC has non-uniform coefficients.
The Clifford group-representation QSC is a group-representation code with \(G\) being the binary octahedral subgroup of \(SU(2)\).
Clifford group-representation QSC

References

[1]
A. Denys and A. Leverrier, “Quantum Error-Correcting Codes with a Covariant Encoding”, Physical Review Letters 133, (2024) arXiv:2306.11621 DOI
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Cite as:

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

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