Design and Implementation of Quantum Algorithms in the Noisy Intermediate Scale Quantum Era

Quantum computing is an emerging paradigm that leverages the principles of quantum mechanics to perform calculations potentially more efficiently than classical computing. It is currently at a crucial stage of its development. Despite its rapid advancement and adoption in both academia and industry, there are still significant theoretical and practical challenges that must be overcome before quantum computing can materialize on a large scale. An essential step on this path is the identification of problems that are intractable for classical algorithms, but can be efficiently solved by a quantum computer, thus demonstrating quantum advantage. Although there are various technologies for the implementation of quantum computers, all are affected to a greater or lesser extent by the presence of errors in the qubits. Therefore, it is common to perform a classical post-processing of the results to mitigate these errors. This thesis focuses on the development of quantum algorithms to address problems in fields as varied as Condensed Matter Physics, Game Theory, and Quantum Machine Learning. In addition, advanced error mitigation techniques are presented that allow their implementation on current quantum devices.