Quantum Property Testing Algorithm for the Concatenation of Two Palindromes Language

TL;DR

This paper introduces a quantum property testing algorithm for recognizing a language formed by concatenating two palindromes, achieving a polynomial speed-up over classical methods in terms of query complexity.

Contribution

The paper presents a novel quantum algorithm for property testing of a specific context-free language, improving query complexity compared to classical approaches.

Findings

Quantum algorithm has query complexity $O(rac{1}{\varepsilon}n^{1/3}\log n)$

Classical query complexity is $ heta^*(\sqrt{n})$ for property testing

Polynomial speed-up achieved in both general and property testing settings

Abstract

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).