Wasilewski-Banaszek code[1] 

Description

Three-oscillator Fock-state code encoding a single logical qubit using codewords \begin{align} \begin{split} |\overline{0}\rangle &= \frac{1}{\sqrt{3}}(|003\rangle+|030\rangle+|300\rangle)\\ |\overline{1}\rangle &= |111\rangle \end{split}. \tag*{(1)}\end{align}

Protection

Protects against single photon loss in any one mode.

Encoding

A qubit in the dual-rail code can be transferred to this code via a linear optical network using four ancillary modes, each with one photon input. Successful encoding is conditioned on measuring the state \(|110\rangle\) on the last three modes.

Gates

Single-qubit gates implemented using linear optical networks, sometimes with the addition of auxiliary modes with vacuum input and (conditional) output.

Decoding

Destructive measurement with photon number measurements on each mode.

Parent

References

[1]
W. Wasilewski and K. Banaszek, “Protecting an optical qubit against photon loss”, Physical Review A 75, (2007) arXiv:quant-ph/0702075 DOI
[2]
Y. Ouyang and R. Chao, “Permutation-Invariant Constant-Excitation Quantum Codes for Amplitude Damping”, IEEE Transactions on Information Theory 66, 2921 (2020) arXiv:1809.09801 DOI
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Zoo Code ID: wasilewski-banaszek

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

“Wasilewski-Banaszek code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/wasilewski-banaszek

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