One-hot quantum code[1] 

Description

Encoding of a \(q\)-dimensional qudit into the single-excitation subspace of \(q\) modes. The \(j\)th logical state is the multi-mode Fock state with one photon in mode \(j\) and zero photons in the other modes.

Protection

This is an error-detecting code against one photon loss event.

Gates

Non-deterministic gates using linear optics and photon-number resolving detectors [1].The group \(SU(q)\) can be realized via Gaussian rotations [2].

Parents

Child

Cousin

  • One-hot code — The one-hot quantum code is the quantum version of the one-hot code.

References

[1]
M. Karácsony, L. Oroszlány, and Z. Zimborás, “Efficient qudit based scheme for photonic quantum computing”, (2023) arXiv:2302.07357
[2]
A. Denys and A. Leverrier, “Multimode bosonic cat codes with an easily implementable universal gate set”, (2023) arXiv:2306.11621
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Zoo Code ID: one_hot_quantum

Cite as:
“One-hot quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/one_hot_quantum
BibTeX:
@incollection{eczoo_one_hot_quantum, title={One-hot quantum code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/one_hot_quantum} }
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Permanent link:
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Cite as:

“One-hot quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/one_hot_quantum

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/oscillators/fock_state/constant_excitation/one_hot_quantum.yml.