Solving Linear Systems of Equations by Using the Concept of Grover's Search Algorithm: An IBM Quantum Experience

TL;DR

This paper demonstrates a quantum approach using Grover's search algorithm to solve specific linear systems of equations, implementing and verifying the method on IBM's quantum simulator.

Contribution

It introduces a novel quantum circuit design for solving linear equations with Grover's algorithm and validates it on multiple equation sets using IBM quantum simulation.

Findings

Successful implementation of the quantum algorithm on IBM simulator

Verification of the solution accuracy for 48 different equation sets

Demonstration of exponential speedup potential over classical methods

Abstract

Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept of well-known Grover's quantum search algorithm. The algorithm finds the solution by rotating the initial state vector in the Hilbert space to get the target solution state. It mainly involves finding particular matrices that solve the set of equations and constructing corresponding quantum circuits using the basic quantum gates. We explicitly illustrate the whole process by taking 48 different set of equations and solving them by using the concept of Grover's algorithm. We propose new quantum circuits for each set of equations and design those on the IBM quantum simulator. We run the quantum circuit for one set of equations and obtain the desired results, and hence verify the working of the algorithm.