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 \((a_l,a_r)-[[n+a_l+a_r,k]]\), 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].
Protection
In the original CSS construction based on cyclic codes \(C \subset D\) with parameters \([n,k_1,d_1]\) and \([n,k_2,d_2]\), one obtains an \((a_l,a_r)-[[n+a_l+a_r,2k_1-n]]\) code whenever \(a_l+a_r<k_2-k_1\), correcting at least \(\lfloor (d_1-1)/2\rfloor\) phase errors and \(\lfloor (d_2-1)/2\rfloor\) bit errors [1; Thm. 1].Cousins
- Cyclic linear binary code— The original construction of quantum synchronizable codes is based on pairs of binary cyclic codes satisfying \(C^\perp \subseteq C \subset D\) [1].
- 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].
Member of code lists
Primary Hierarchy
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”, IEEE Transactions on Quantum Engineering 7, 2100730 (2026) arXiv:2409.11312 DOI
- [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 (2026-06-08) — most recent
- Victor V. Albert (2024-09-20)
Cite as:
“Quantum synchronizable code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/quantum_synchronizable, arXiv:2606.11484