Quantum synchronizable code[1]
Description
A qubit stabilizer code designed to protect against synchronization errors (a.k.a. misalignment), which are errors that misalign the code block in a larger block by one or more locations.
In such a setting, the qubits are arranged in a line and embedded into a larger block that represents a stream of information coming into the receiver. The receiver may not properly identify the first qubit in the desired code block, leading to a misalignment of the block. A quantum synchronizable code is denoted by \((a_l,a_r)-[[n+a_l+a_r,k,d]]\), correcting misalignment by up to \(a_l\) (\(a_r\)) qubits to the left (right).
The initial construction of quantum synchronizable codes was based on the CSS construction [1], but later work extended it to non-CSS stabilizer codes [2].
Parent
Cousins
- Binary BCH code — BCH codes can be used to construct quantum synchronizable codes via the CSS construction [1].
- Binary quadratic-residue (QR) code — Binary QR codes can be used to construct quantum synchronizable codes via the CSS construction [3].
- Operator-algebra (OA) qubit stabilizer code — Quantum synchronizable versions of qubit subsystem codes, hybrid codes, and OA qubit stabilizer codes have been constructed [2].
References
- [1]
- Y. Fujiwara, “Block synchronization for quantum information”, Physical Review A 87, (2013) arXiv:1206.0260 DOI
- [2]
- T. Tansuwannont and A. Nemec, “Synchronizable hybrid subsystem codes”, (2024) arXiv:2409.11312
- [3]
- Y. Xie, J. Yuan, and Y. Fujiwara, “Quantum Synchronizable Codes From Quadratic Residue Codes and Their Supercodes”, (2014) arXiv:1403.6192
Page edit log
- Victor V. Albert (2024-09-20) — most recent
Cite as:
“Quantum synchronizable code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/quantum_synchronizable