Wasilewski-Banaszek code[1]
Description
Three-oscillator constant-excitation Fock-state code encoding a single logical qubit.
A basis of codewords is \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
- Ouyang-Chao constant-excitation PI code — The Wasilewski-Banaszek code is a simple example of an Ouyang-Chao PI code [2].
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
Page edit log
- Victor V. Albert (2021-12-09) — most recent
- Jonathan Kunjummen (2021-12-07)
Cite as:
“Wasilewski-Banaszek code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/wasilewski-banaszek