As part of my MS thesis, I am working on modifying the existing quantum algorithm to run on the current Noisy Intermediate Scale Quantum Computer. In this project, we are interested in the Quantum amplitude estimation algorithm, which promises a quadratic speed-up compared to the classical Monte Carlo algorithm.

The mini project was a part of the course Numerical Methods and programming.  The project implements numerical techniques like polynomial regression, RK 4 and Euler methods for modelling human population based on the data avialable at the world bank. 

Graphene is a very unusual material with carriers(massless fermions) that exhibit an effective "speed of light" in the low energy range of <0.5 eV; these massless fermions exhibit various Quantum electrodynamics(QED) phenomena at this energy range which many researchers are exploring. But before doing that, we should understand and stimulate the band structure of graphene.In this project, we propose to study the band structure of graphene using the tight-binding model. Initially, we will consider only the nearest neighbour hopping and analyse the band structure. Further, we can also consider the second nearest neighbour hopping and study the difference it causes to the band structure. We first explore the electronic properties by obtaining the analytical solution of the wave function by solving the Schrodinger equation.We construct the Hamiltonian matrix using the nearest neighbour interaction and use this Hamiltonian to get the energy dispersion relation. We have used Wolfram Mathematica and python programming language to draw the band structure of graphene using tight binding approximation method.