Squeezed fock-state code[1] 

Description

Approximate boosnic code that encodes a qubit into the same Fock state, but one which is squeezed in opposite directions.

Taking the Fock state \(|1\rangle\), the codewords are \begin{align} \begin{split} |\overline{0}\rangle&=S(r)|1\ket\\|\overline{1}\rangle&=S(-r)|1\ket~, \end{split} \tag*{(1)}\end{align} where \(S(\pm r)\) is the squeezing operator with squeezing parameter \(\pmr\).

Protection

The code approximately protects against loss and dephasing errors, becoming exact in the \(r\to\infty\) limit.

Parents

References

[1]
S. B. Korolev, E. N. Bashmakova, and T. Yu. Golubeva, “Error Correction Using Squeezed Fock States”, (2023) arXiv:2312.16000
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Zoo Code ID: squeezed_fock_state

Cite as:
“Squeezed fock-state code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/squeezed_fock_state
BibTeX:
@incollection{eczoo_squeezed_fock_state, title={Squeezed fock-state code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/squeezed_fock_state} }
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Cite as:

“Squeezed fock-state code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/squeezed_fock_state

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