Implementation of a Quantum Algorithm to Estimate the Energy of a Particle in a Finite Square Well Potential on IBM Quantum Computer

TL;DR

This paper demonstrates the implementation of a quantum algorithm using IBM quantum devices and simulators to estimate the energy levels of a particle in a finite square well potential, showcasing the practical application of quantum phase estimation.

Contribution

It presents the first implementation of quantum phase estimation for energy calculation in a finite potential well on IBM quantum hardware and simulators, optimizing circuit size for better results.

Findings

Successful simulation of the system on IBM classical devices.

Partial implementation on 5-qubit quantum devices with reduced circuit complexity.

Circuits achieved some success but showed scattered results due to hardware limitations.

Abstract

In this paper, we implement a quantum algorithm -on IBM quantum devices, IBM QASM simulator and PPRC computer cluster -to find the energy values of the ground state and the first excited state of a particle in a finite square-well potential. We use the quantum phase estimation technique and the iterative one to execute the program on PPRC cluster and IBM devices, respectively. Our results obtained from executing the quantum circuits on the IBM classical devices show that our circuits succeed at simulating the system. However, duo to scattered results, we execute only the iterative phase estimation part of the circuit on the 5 qubit quantum devices to reduce the circuit size and obtain low-scattered results.