The paper presents a technique for constructing noisy data structures called a walking tree. We apply it for a Red-Black tree (an implementation of a Self-Balanced Binary Search Tree) and a segment tree. We obtain the same complexity of the main operations for these data structures as in the case without noise (asymptotically). We present several applications of the data structures for quantum algorithms. Finally, we suggest new quantum solution for strings sorting problem and show the lower bound. The upper and lower bounds are the same up to a log factor. At the same time, it is more effective than classical counterparts.

翻译：本文提出了一种构建含噪数据结构的技术——行走树。我们将其应用于红黑树（自平衡二叉搜索树的一种实现）和线段树。对于这些数据结构，我们得到了与无噪声情况相同的主要操作复杂度（渐近意义下）。我们展示了这些数据结构在量子算法中的若干应用。最后，我们提出了字符串排序问题的量子新解法，并给出了下界。该上下界仅相差一个对数因子。同时，该方法比经典方法更高效。