A Quantum Leap Into the Future of Computer Science

Paulo Tiago Gouveia Saldanha

Key information

Authors:

Paulo Tiago Gouveia Saldanha (Paulo Tiago Gouveia Saldanha)

Supervisors:

Filipa Isabel Rodrigues Prudêncio; Carlos Manuel dos Reis Paiva (Carlos Manuel dos Reis Paiva)

Published in

11/24/2022

Abstract

For the last one hundred years, the field of quantum mechanics came from a target of criticism and doubt to an everyday reality. The paradigm of this theory changed in 1964 when John Stewart Bell showed that quantum mechanics was incompatible with any classical theory, including local realism. Bell's theorem was one of the biggest breakthroughs in quantum physics for which started to get applications in many fields of our society, including computer science. Quantum computation is an area based on the principles of quantum physics, focused to solve problems that are too complex for classical computers. The potential in this area is astonishing, for which researchers around the globe are very committed to exploit all its advantages. This dissertation is centered on quantum computing and for that reason it starts by giving some essential tools for those who are not so familiar with quantum mechanics (but with a previous background on linear algebra). Some basic concepts like quantum bits, quantum entanglement and quantum superposition are early introduced to better understand a posteriori definitions. After that, the field of quantum computation is exploited, where notions like quantum gates, no-cloning theorem, superdense coding, quantum teleportation, cryptographic protocols, error corrections and Simon's quantum algorithm will be looked in depth. Finally, a brief overview on category theory is done by giving some essential concepts namely, category, object, morphism, functor and natural transformations, in order to analyze a novel way to present (trough diagrams) quantum computation and quantum information: quantum picturalism.