Phd in MODELS FOR ECONOMICS AND FINANCE

Thesis title: Quantum Computing: a new computational paradigm. The case of optimization problems

The term “Quantum Technologies” indicates a class of highly innovative technologies in which principles underlying Quantum Mechanics are used to actively manipulate the quantum states of matter. Quantum Computing, a pioneering field of computer science, has introduced a new computing paradigm that allows for an exponential increase in computational capabilities and the resolution of complex problems whose solution cannot be determined by classical systems, including HPC (High Performance Computing) and Artificial Intelligence technologies. In the remainder of this paper, we intend to delve deeper into the topic of Quantum Computing, with particular attention to the application of this technology in solving optimization problems. The QUBO (Quadratic Unconstrained Binary Optimization) formulation and the Ising Model will be analyzed, highlighting their use in the context of the optimization problems mentioned above. In addition, an overview of the implementation of these models on the main quantum hardware, namely the Quantum Gate Array and the Quantum Annealer and on Quantum-Inspired methods, will be provided, thus offering an overall view of the potential of this technology. In conclusion, some applications of the optimization algorithms discussed in this work will be analyzed, in relation to financial problems. A report by McKinsey & Co. highlights that the financial sector is set to be the first to benefit from quantum computing, not only in the medium and long term, but also in the short term. A wide range of financial optimization issues could significantly benefit from these techniques, with particular reference to Portfolio Optimization and Credit Rating Identification, topics that will be explored in this research work.