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, a new method for construct quantum synchronizable codes from negacyclic codes are proposed, where the length of these negacyclic codes are $p$ and $pq$. Through this method, the quantum synchronizable code possesses optimal or almost optimal error-correcting capability towards bits errors and phase errors, since the negacyclic codes we used are optimal or almost optimal. Moreover, this paper contributes to construct two classes quantum synchronizable codes, whose synchronization capabilities can reach the upper limit under certain conditions.

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中的误差。在本文中,提出了从中环代码构建量子同步代码的新方法,这些中环代码的长度为$p美元和$pq美元。通过这种方法,量子同步代码拥有对位子错误和相位错误的最佳或几乎是最佳的错误校正能力,因为我们使用的全环代码是最佳或几乎最佳的。此外,本文还有助于构建两个可同步的量子代码,这些代码的同步能力在某些条件下可以达到上限。