  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.
