Solving mathematical problems with quantum search algorithm

TL;DR

This paper presents quantum algorithms utilizing Grover's search and a quantum bit string comparator to efficiently solve mathematical problems such as finding zeros, extrema, and primality, advancing quantum computational methods.

Contribution

It introduces a quantum bit string comparator as an oracle for solving mathematical problems and demonstrates its use in implementing conditional statements in quantum algorithms.

Findings

Quantum algorithms for mathematical problems are feasible with the proposed comparator.

The quantum bit string comparator enables conditional logic in quantum algorithms.

The approach enhances the capabilities of quantum search algorithms for mathematical problem-solving.

Abstract

Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical algorithm. It is possible to use Grover algorithm, taking profit of its ability to find a specific value in a unordered database, to find, for example, the zero of a logical function; the minimal or maximal value in a database or to recognize if an odd number is prime or not. Here we show quantum algorithms to solve those cited mathematical problems. The solution requires the use of a quantum bit string comparator being used as oracle. This quantum circuit compares two quantum states and identifies if they are equal or, otherwise, which of them is the largest. Moreover, we also show the quantum bit string comparator allow us to implement conditional statements in quantum computation, a fundamental structure for designing of algorithms.