Quantum algorithms for function optimization

Abstract

[en] Quantum computing has started to become a reality, as many big and small companies are building state of the art quantum computers, with some even offering quantum services to the public, as quantum computers have been proved to offer a significant computational advantage in comparison to classical computers. Often, though, mathematicians and computer scientists have difficulties getting into the field of quantum computing be- cause of their lack of knowledge about quantum physics. In this work, we take on the more applied side of quantum computing using an abstracted mathematical framework, the gate-based quantum computing model, completely separated from the physics behind. We first introduce the intuition behind quantum computing and present the mathematical basis of the aforementioned gate-based model. We review and implement some elemental quantum algorithms and after that then dive into the topic of function optimization. For discrete function optimization, we review Grover Adaptive Search, devise an efficient implementation of the algorithm, run it on a simulator and analyze its computational cost. For continuous function optimization, we summarize the most relevant work regarding the topic and pave the way for others that want to implement the algorithms described.