Approaching unstructured search from function bilateral symmetry detection - A quantum algorithm

TL;DR

This paper introduces a quantum algorithm that reduces unstructured search problems to function bilateral symmetry detection, offering a novel approach to solving NP-complete problems with polynomial overhead.

Contribution

It presents a new quantum algorithm that transforms unstructured search into symmetry detection, expanding quantum problem-solving techniques.

Findings

Reduces unstructured search to symmetry detection with polynomial overhead

Demonstrates potential for quantum algorithms to solve NP-complete problems

Provides a framework for applying symmetry detection in quantum computing

Abstract

Detection of symmetry is vital to problem solving. Most of the problems of computer vision and computer graphics and machine intelligence in general, can be reduced to symmetry detection problem. Unstructured search problem can also be looked upon from symmetry detection point of view. Unstructured search can be thought as searching a binary string satisfying some search condition in an unsorted list of binary strings. In this paper unstructured search problem is reduced to function bilateral symmetry detection problem with polynomial overhead in terms of the size of the input. Keywords: Unstructured Search, Quantum algorithm, Function bilateral symmetry detection, Decision Problem, Quantum Black Box, Solving NP complete problems.