This is a project with the ambition of demonstrating the possibilities and applications of the quantum approximation optimization algorithm (QAOA). Throughout the paper discussions on the theoretical background and fundamentals of the algorithm will be done by examining the relevant nomenclature. Then a set of possible application problems will be considered where it will be discussed why this specific algorithm is of interest for each individual problem. In the fourth section these problems will concretely be tested via simulations of the QAOA and lastly an analysis of the outcomes will be done.

<p>We demonstrate how quantum machine learning might play a vital role in achieving moderate speedups in machine learning problems and might have scope for providing rich models to describe the distribution underlying the observed data. We work with Restricted Boltzmann Machines to demonstrate the same to supervised learning tasks. We compare the relative performance of contrastive divergence with sampling from Dwave annealer on bars and stripes dataset and then on imabalanced network security data set. Later we do training using Quantum Imaginary Time Evolution, that is well suited for the Noisy Intermediate-Scale Quantum era to perform classification on MNIST data set.  </p>

<p>Optimization and Machine learning (ML) have emerged as two positively disruptive methodologies and have thus resulted in unprecedented applications in several domains of technology. In recent years, ML has forayed into physical sciences and provided promising outcomes thanks to its ability in representing and generalizing complex functions to reveal underlying relations among variables describing a system. By casting ML as an optimization task, we first focus on its application in solving quantum many-body problems. Leveraging the power of quantum computation, we develop hybrid quantum machine learning protocols and implement benchmark tests to calculate the band structures of two-dimensional materials. We also show how this method can be used to estimate the critical point for a quantum phase transition. One  hurdle in such techniques is related to parameter optimization, wherein to obtain the desired result, the parameters have to be optimized, which can be computationally intensive. For a particular class of problem and a choice of algorithm, we deduce a simple parameter setting rule. This rule is projected as a heuristic and is validated numerically for several problem instances. Finally, by venturing into thermal photonics, a framework that takes advantage of the spectral and spatial information of hyperspectral thermal images to establish a completely passive machine perception, titled HADAR is presented. A conventional deep neural network is developed that utilizes the governing equation of HADAR and its performance in semantic segmentation is demonstrated. Altogether, this report establishes the need for creative algorithms that exploit modern hardware to solve complex problems that were previously deemed unsolvable.</p>