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. In this paper, we construct two classes of quantum synchronizable codes which obtained by the cyclotomic classes of order two over $\mathbb{Z}_{2q}$. And the synchronization capabilities reach the upper bound under certain constrains. Moreover, the quantum synchronizable code posses good error-correcting capability towards bit error and phase error, since cyclic codes we employed to construct quantum synchronizable codes are optimal or almost optimal.

翻译：量子同步代码是量子误差校正代码的种类,它们不仅能够纠正量子噪音对qubits的影响,而且能够纠正区块同步的不匹配性。在本文中,我们构建了两类量子同步代码,由环球级序列获得,2美元以上,2美元以上,2美元以上。同步能力在某些限制下达到了上限。此外,量子同步代码可以对位错误和相位错误进行良好的误差校正能力,因为我们用来构建量子同步代码的周期代码是最佳的或几乎是最佳的。