\([[7,1,3]]\) bare code

\([[7,1,3]]\) bare code[1]

Description

A \([[7,1,3]]\) code that admits fault-tolerant syndrome extraction using only one ancilla per stabilizer generator measurement.

A stabilizer tableau for the code is given by [2; ID 108] \begin{align} \begin{array}{ccccccc} X & I & I & I & Z & I & I \\ I & X & I & I & Z & I & I \\ I & I & X & I & I & Z & I \\ I & I & I & X & I & I & Z \\ I & I & Z & Z & I & Y & Y \\ Z & Z & Z & I & X & X & Z \end{array}~. \tag*{(1)}\end{align} It is one of sixteen distinct \([[7,1,3]]\) codes [3].

Decoding

Fault-tolerant syndrome extraction using a single ancilla [1].

Member of code lists

Primary Hierarchy

Quantum Domain

Qubit Kingdom

Qubit codeQECC Quantum

Union stabilizer (USt) codeQECC Quantum

Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum

Small-distance qubit stabilizer codeSmall-distance block quantum QECC Quantum

Parents

Small-distance qubit stabilizer code

\([[7,1,3]]\) bare code

References

[1]: M. Li, M. Gutiérrez, S. E. David, A. Hernandez, and K. R. Brown, “Fault tolerance with bare ancillary qubits for a [[7,1,3]] code”, Physical Review A 96, (2017) arXiv:1702.01155 DOI
[2]: Qiskit Community. Qiskit QEC framework. https://github.com/qiskit-community/qiskit-qec
[3]: S. Yu, Q. Chen, and C. H. Oh, “Graphical Quantum Error-Correcting Codes”, (2007) arXiv:0709.1780

Page edit log

Victor V. Albert (2024-09-25) — most recent

Cite as:

“\([[7,1,3]]\) bare code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/bare_7_1_3

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/small/7/bare_7_1_3.yml.