Quantum computing and theoretical computer science

Author(s)

Alex Bredariol Grilo

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Computação
• Defense date: 2014-11-04

Examining board members

Arnaldo Vieira Moura; Franklin de Lima Marquezino; Ricardo Dahab

• Advisor: Arnaldo Vieira Moura

Abstract

Quantum Computing is a relatively new area and it is not well known, mainly among Computer Scientists. It has emerged while physicists tried to simulate Quantum Systems with classical computers efficiently, which has been conjectured impossible. Then, a new computational model that uses the quantum structure of matter to perform computations has been theorized in order to perform these operations. We intend in this work to study the influences of Quantum Computing in Theoretical Computer Science. In order to achieve this goal, we start by presenting the basics of Quantum Computing to Theoretical Computer Science readers with no previous knowledge in this area, removing any initial barriers for a clean understanding of the topic. We will then follow by showing innovations in Theoretical Computer Science introduced by Quantum Computation. We start by showing the main Quantum Algorithms, that exemplify advantages of the new computational model. Among these algorithms, we will present the Shor Algorithm that factors numbers in polynomial time. We follow with more advanced topics in Quantum Computability and Complexity. We study Quantum Finite Automata Models that work with quantum and classical states, focusing on comparing their computational power with Deterministic Finite Automata. In Complexity Theory, we study the question if for languages in QMA, the quantum analogue of NP, zero probability error can be achieved in yes-instances (AU)

• FAPESP's process: 12/06648-0 - Quantum Computing and Theoretical Computer Science
• Grantee: Alex Bredariol Grilo
• Support Opportunities: Scholarships in Brazil - Master