In this paper, we present a quantum property testing algorithm for recognizing a context-free language that is a concatenation of two palindromes $L_{REV}$. The query complexity of our algorithm is $O(\frac{1}{\varepsilon}n^{1/3}\log n)$, where $n$ is the length of an input. It is better than the classical complexity that is $\Theta^*(\sqrt{n})$. At the same time, in the general setting, the picture is different a little. Classical query complexity is $\Theta(n)$, and quantum query complexity is $\Theta^*(\sqrt{n})$. So, we obtain polynomial speed-up for both cases (general and property testing).

翻译：本文提出了一种用于识别上下文无关语言（即两个回文串连接语言$L_{REV}$）的量子属性测试算法。该算法的查询复杂度为$O(\frac{1}{\varepsilon}n^{1/3}\log n)$，其中$n$为输入长度。这一结果优于经典复杂度$\Theta^*(\sqrt{n})$。同时，在一般性设定下情况略有不同：经典查询复杂度为$\Theta(n)$，而量子查询复杂度为$\Theta^*(\sqrt{n})$。因此，我们在两种情形（一般性测试与属性测试）下均获得了多项式级别的加速。