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.Cousin
- \(((3,2,2))_3\) Three-qutrit single-deletion code— The three-qutrit single-deletion code maps to the Wasilewski-Banaszek code via the simplex mapping [2].
Primary Hierarchy
Ouyang-Chao constant-excitation PI codeCE Amplitude-damping (AD) AQECC PI Cyclic quantum Hamiltonian-based QECC Quantum
Parents
The Wasilewski-Banaszek code is a simple example of an Ouyang-Chao PI code [3].
Wasilewski-Banaszek code
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]
- A. Aydin, V. V. Albert, and A. Barg, “Quantum Error Correction beyond <mml:math xmlns:mml=”http://www.w3.org/1998/Math/MathML” display=”inline”> <mml:mi>S</mml:mi> <mml:mi>U</mml:mi> <mml:mo stretchy=”false”>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy=”false”>)</mml:mo> </mml:math> : Spin, Bosonic, and Permutation-Invariant Codes from Convex Geometry”, PRX Quantum 7, (2026) arXiv:2509.20545 DOI
- [3]
- 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