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.

翻译：量子同步代码是量子错误校正代码的种类,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。本文有助于通过二次环形序列2+$\mathbb ⁇ 2q}来构建两类量子同步代码,其同步能力在某些条件下可以达到上限。此外,量子同步代码具有纠正误差的能力,以弥补小错误和相位错误。