Hybrid qudit-oscillator code 

Description

Encodes a \(K\)-dimensional logical Hilbert space into \(n_1\) modular qudits of dimension \(q\) and \(n_2 \neq 0\) oscillators, i.e., the Hilbert space of \(\ell^2\)-normalizable functions on \(\mathbb{Z}_q^{n_1} \times \mathbb{R}^{n_2}\).

Codewords of a simple hybrid code [1] are \(|\alpha\rangle|+\rangle\) and \(|-\alpha\rangle|V\rangle\), i.e., hyper-entangled states of the polarization \(|\pm\rangle\) and occupation-number degrees of freedom of a photon, with the latter being in a coherent state \(|\pm\alpha\rangle\).

Notes

See review [2] for an introduction to hybrid qudit-oscillator codes.

Parent

  • Bosonic code — The physical Hilbert space of a hybrid qubit-oscillator code contains at least one oscillator.

Cousins

References

[1]
S.-W. Lee and H. Jeong, “Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits”, Physical Review A 87, (2013) arXiv:1112.0825 DOI
[2]
U. L. Andersen et al., “Hybrid discrete- and continuous-variable quantum information”, Nature Physics 11, 713 (2015) arXiv:1409.3719 DOI
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Zoo Code ID: hybrid_qudit_oscillator

Cite as:
“Hybrid qudit-oscillator code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/hybrid_qudit_oscillator
BibTeX:
@incollection{eczoo_hybrid_qudit_oscillator, title={Hybrid qudit-oscillator code}, booktitle={The Error Correction Zoo}, year={2021}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/hybrid_qudit_oscillator} }
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Cite as:

“Hybrid qudit-oscillator code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/hybrid_qudit_oscillator

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