Reducing T-Count in quantum string matching algorithm using relative-phase Fredkin gate

TL;DR

This paper presents a method using the relative-phase Fredkin gate to significantly reduce T-gate count and other circuit costs in quantum string matching algorithms, enhancing their practical fault-tolerant implementation.

Contribution

Introduction of the relative-phase Fredkin gate to lower T-count and circuit costs in quantum string matching algorithms, improving their efficiency and feasibility.

Findings

T-count reduced from 14N^{3/2} log_2 N to 8N^{3/2} log_2 N

Circuit depth and CNOT gate count are also decreased

Method enhances the practicality of fault-tolerant quantum string matching

Abstract

The string-matching problem, ubiquitous in computer science, can significantly benefit from quantum algorithms due to their potential for greater efficiency compared to classical approaches. The practical implementation of the quantum string matching (QSM) algorithm requires fault-tolerant quantum computation due to the fragility of quantum information. A major obstacle in implementing fault-tolerant quantum computation is the high cost associated with executing T gates. This paper introduces the relative-phase Fredkin gate as a strategy to notably reduce the number of T gates (T-count) necessary for the QSM algorithm. This reduces the T-count from 14N^(3/2) log_2 N-O(N^(3/2)) to 8N^(3/2) log_2 N-O(N^(3/2)), where N represents the size of the database to be searched. Additionally, we demonstrate that our method is advantageous in terms of other circuit costs, such as the depth of T gates and the number of CNOT gates. This advancement contributes to the ongoing development of the QSM algorithm, paving the way for more efficient solutions in the field of computer science.