\([[7,2,2]]\) QETC[1]
Description
Seven-qubit pure QETC that transmutes all single-qubit Pauli errors to logical phase errors.
A stabilizer tableau for the code is given by [1; Table 1] \begin{align} \begin{array}{ccccccc} X & X & Y & Y & Z & I & Z \\ I & Z & X & Y & Y & X & Y \\ I & I & I & I & I & Z & Z \\ Z & Z & I & I & Z & I & Z \\ Z & Z & Z & Z & I & I & I \end{array}~. \tag*{(1)}\end{align} The above stabilizer tableau is equivalent to [2; ID 646] by applying \(H\) to qubits 1 and 2 and \(SH\) (with \(H\) applied first) to qubits 3 and 4, followed by the qubit relabeling \((1,2,3,4,5,6,7)\to(5,6,1,3,7,2,4)\).
Cousin
- \([[7,1,3]]\) bare code— The stabilizer group of the \([[7,2,2]]\) QETC, together with the logical-\(Z\) operator on the first logical qubit, generates the stabilizer group of a \([[7,1,3]]\) code [1] equivalent to the bare \([[7,1,3]]\) code [3].
Primary Hierarchy
Parents
\([[7,2,2]]\) QETC
References
- [1]
- D. Zhang and T. Cubitt, “Quantum Error Transmutation”, (2023) arXiv:2310.10278
- [2]
- Qiskit Community, “Qiskit QEC framework”, URL
- [3]
- V. V. Albert, private communication, 2026
Page edit log
- Victor V. Albert (2024-03-20) — most recent
Cite as:
“\([[7,2,2]]\) QETC”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/qetc_7_2