Advances in quantum machine learning

Here we discuss advances in the field of quantum machine learning. The following document offers a hybrid discussion; both reviewing the field as it is currently, and suggesting directions for further research. We include both algorithms and experimental implementations in the discussion. The field's outlook is generally positive, showing significant promise. However, we believe there are appreciable hurdles to overcome before one can claim that it is a primary application of quantum computation.Comment: 38 pages, 17 Figure

Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Random Walks: A Review of Algorithms and Applications

A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science. Furthermore, in quantum mechanics, quantum walks can be regarded as quantum analogues of classical random walks. Classical random walks and quantum walks can be used to calculate the proximity between nodes and extract the topology in the network. Various random walk related models can be applied in different fields, which is of great significance to downstream tasks such as link prediction, recommendation, computer vision, semi-supervised learning, and network embedding. In this paper, we aim to provide a comprehensive review of classical random walks and quantum walks. We first review the knowledge of classical random walks and quantum walks, including basic concepts and some typical algorithms. We also compare the algorithms based on quantum walks and classical random walks from the perspective of time complexity. Then we introduce their applications in the field of computer science. Finally we discuss the open issues from the perspectives of efficiency, main-memory volume, and computing time of existing algorithms. This study aims to contribute to this growing area of research by exploring random walks and quantum walks together.Comment: 13 pages, 4 figure

Quantum machine learning for particle physics using a variational quantum classifier

Quantum machine learning aims to release the prowess of quantum computing to improve machine learning methods. By combining quantum computing methods with classical neural network techniques we aim to foster an increase of performance in solving classification problems. Our algorithm is designed for existing and near-term quantum devices. We propose a novel hybrid variational quantum classifier that combines the quantum gradient descent method with steepest gradient descent to optimise the parameters of the network. By applying this algorithm to a resonance search in di-top final states, we find that this method has a better learning outcome than a classical neural network or a quantum machine learning method trained with a non-quantum optimisation method. The classifiers ability to be trained on small amounts of data indicates its benefits in data-driven classification problems