Solving combinatorial optimization problems using quantum computing: a case study for the QAP

Quantum computing is one of the most researched areas in computer science and withone of the greatest future prospects thanks to the new discoveries and methodologies thatcan provide approaches of a different kind to tackle problems and find solutions. One ofsuch methodologies is none other than quantum annealing, a metaheuristic focused on thequalities of quantum mechanics. Combinatorial Optimization (CO) problems have always been a hassle to find solutionsin large scale problems owing to their complexity and resource consumption. However,these can be transformed into an equivalent Quadratic Unconstrained Binary Optimization(QUBO) model that is constraint-free and its variables are (binary) decision variables.What is best, QUBO models can be efficiently solve with quantum annealing in a quantumcomputer. The objective of the project will be the study of all the particular functionalities andproperties of each aspect of all the transformation chain for the specific case study withthe QAP problem. The implementation of this problem, its transformation into a QUBOmodel and the solution obtained through quantum annealing are the key points that leadto harness the potential of quantum computing and set its current limits

Solving combinatorial optimization problems using quantum computing: a case study for the QAP

Quantum computing is one of the most researched areas in computer science and withone of the greatest future prospects thanks to the new discoveries and methodologies thatcan provide approaches of a different kind to tackle problems and find solutions. One ofsuch methodologies is none other than quantum annealing, a metaheuristic focused on thequalities of quantum mechanics. Combinatorial Optimization (CO) problems have always been a hassle to find solutionsin large scale problems owing to their complexity and resource consumption. However,these can be transformed into an equivalent Quadratic Unconstrained Binary Optimization(QUBO) model that is constraint-free and its variables are (binary) decision variables.What is best, QUBO models can be efficiently solve with quantum annealing in a quantumcomputer. The objective of the project will be the study of all the particular functionalities andproperties of each aspect of all the transformation chain for the specific case study withthe QAP problem. The implementation of this problem, its transformation into a QUBOmodel and the solution obtained through quantum annealing are the key points that leadto harness the potential of quantum computing and set its current limits

Construcción de clasificadores híbridos clásico-cuánticos para datos imbalanceados

Quantum circuits offer a different approach to process data through quantum operations and measurements of quantum states. At the same time, the increasing number of advances in technology has opened a path to turning these quantum circuits into building blocks of a machine learning model. The transition of data from classical to quantum and reverting it from quantum to classical offers a presumably much more nuanced and diverse form of learning the data instead of using two different scenarios separately. The idea consists on combining these two scenarios meaningfully into a single hybrid classical quantum model and observe how these two settings may offer value instead of only focusing in one or another. Therefore, the challenge consists on dealing with a machine learning problem using three different means; namely, quantum models, classical models and hybrid classical quantum models and make an assessment of the procedure's design, techniques employed and infrastructures built. In particular, the machine learning task belongs to a binary classification problem of an unbalanced dataset. Given that the drive of the comparison between classical and quantum means stems from evaluating and comparing their performance, the already hard and complex underlying pattern representation from the features, owing to the presence of unbalanced class distribution, is an adequate choice. The unbalanced dataset contains a binary classification problem of transactions being either classified as fraud or as valid, the former class being considerably lower in number. Apart from the machine learning approach and the difficulty of the task, the quantum model addition is developed by picturing how the quantum tools brought to the table can be used to achieve a possibly better representation and pattern description of such complicate unbalanced data sets. The main focus is exploring data representation in quantum circuits using different types of embeddings, the variational quantum classifier model for classification, the interpretation of an observable as a Hermitian operator in quantum mechanics and the come and forth between classical and quantum communication