Quantum Synchronizable Codes From Cyclotomic Classes of Order Two over $\mathbb{Z}_{2q}$
This work addresses synchronization issues in quantum error correction for quantum computing, but it appears incremental as it builds on existing methods with specific mathematical structures.
The paper tackled constructing quantum synchronizable codes to correct quantum noise and block misalignment, achieving synchronization capabilities that reach the upper bound under certain conditions and providing good error-correcting capability for bit and phase errors.
Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. This paper contributes to constructing two classes of quantum synchronizable codes by the cyclotomic classes of order two over $\mathbb{Z}_{2q}$, whose synchronization capabilities can reach the upper bound under certain conditions. Moreover, the quantum synchronizable codes possess good error-correcting capability towards bit errors and phase errors.