Hybrid cat code[1,2] 

Description

A hybrid qubit-oscillator code admitting codewords that are tensor products of a single-qubit (e.g., photon polarization) state with either a cat state or a coherent state.

Codewords of the coherent-state version [1] are \(|\alpha\rangle|+\rangle\) and \(|-\alpha\rangle|-\rangle\), i.e., hyper-entangled states of the occupation-number and polarization degrees of freedom of a photon. Codewords of the cat-state version [2,3] are proportional to \((\left|\alpha\right\rangle +\left|-\alpha\right\rangle )|+\rangle\) and \((\left|i\alpha\right\rangle -\left|-i\alpha\right\rangle )|-\rangle\)

Fault Tolerance

Photonic architecture based on concatenation with RBH codes [2].

Notes

See reviews [4,5] for introductions to hybrid qudit-oscillator platforms.

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]
J. Lee et al., “Fault-tolerant quantum computation by hybrid qubits with bosonic cat-code and single photons”, (2023) arXiv:2401.00450
[3]
D. V. Sychev et al., “Entanglement and teleportation between polarization and wave-like encodings of an optical qubit”, Nature Communications 9, (2018) arXiv:1712.10206 DOI
[4]
U. L. Andersen et al., “Hybrid discrete- and continuous-variable quantum information”, Nature Physics 11, 713 (2015) arXiv:1409.3719 DOI
[5]
Y. Liu et al., “Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications”, (2024) arXiv:2407.10381
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Zoo Code ID: hybrid_cat

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

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

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