Single-spin code

Description

Permutation invariant qubit code encoding a \(K\)-dimensional Hilbert space into the maximally symmetric subspace or collective spin of \(2\ell\) spin-half systems. This \(2\ell+1\)-dimensional Hilbert space can be thought of as a spin-\(\ell\) quantum system.

Protection

Noise models can be categorized as those that cause the state to leave the maximally symmetric subspace and those that do not. The former include single-spin errors akin to qubit Pauli noise. The latter include collective rotations or decays.

Transversal Gates

When the physical Hilbert space is thought of a collective spin, logical gates for spin codes have the form \(U^{\otimes N}\), where \(U\) is a local rotation on the physical system.

Parents

Children

Cousin

  • Quantum spherical code (QSC) — Single-spin codes whose codewords are expressed in terms of discrete sets of spin-coherent states may also be interpreted as QSCs.
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Zoo Code ID: single_spin

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

Cite as:

“Single-spin code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/single_spin

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/spins/single_spin.yml.