Quantum Algorithms for Condensed-Matter Physics, Number Theory and Quantum Machine Learning

Quantum computing is a novel paradigm that seeks to harness quantum mechanical effects like superposition, entanglement and interference to outperform classical computers based upon bits (i.e zeroes and ones) on certain tasks. Research into the field of quantum algorithms has produced some exponential speed-ups over the best classical algorithms currently known, with potential applications far beyond the academic domain. Yet, the quest for quantum algorithms that dramatically outperform their classical counterparts has proved to be hard. New quantum algorithms are needed, together with a better understanding of the type of problems quantum computers excel at.

In this thesis, we explore the capabilities that quantum computers may offer  to Condensed-Matter Physics, Number Theory and Quantum Machine Learning.