Noisy Tree Data Structures and Quantum Applications

TL;DR

This paper introduces noisy walking tree data structures, demonstrates their asymptotic efficiency in classical operations, and applies them to quantum algorithms, including a new quantum string sorting method with tight bounds.

Contribution

It develops noisy data structures like walking trees, applies them to quantum algorithms, and proposes a quantum string sorting solution with matching bounds.

Findings

Noisy walking trees achieve classical operation complexity asymptotically.

Applications to quantum algorithms demonstrate improved efficiency.

New quantum string sorting algorithm with tight upper and lower bounds.

Abstract

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.