Implementação de passeios quânticos em duas dimensões

Author(s)

João Fernando Doriguello Diniz

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Física Gleb Wataghin
• Defense date: 2016-06-17

Examining board members

Marcos César de Oliveira; Alberto Vazquez Saa; Alfredo Miguel Ozório de Almeida

• Advisor: Marcos César de Oliveira

Abstract

Quantum walks are the quantum counterpart to classic random walks and have a crucial role in the design of efficient quantum algorithms that overcome classic algorithms. During the last years a great effort has been dedicated to implement quantum walks experimentally. However, bi-dimensional quantum walk implementations are still scarce and it is precisely starting from two dimensions that there exists some computational gain. This dissertation is based on this necessity to propose a physical system capable of implementing a two-dimensional quantum walk: a superconducting qubit capacitively coupled to a mechanical oscillator. This system has already been studied in the literature and was shown to adequately generate a one-dimensional quantum walk. The dissertation was thus centred in generalizing this system by coupling a second mechanical resonator to the qubit and in demonstrating that this resulting system is theoretically capable of simulating a two-dimensional quantum walk. Simulations of the probability distribution with and without decoherence were conducted. Moreover, we studied the recent connection between relativistic quantum mechanics and quantum walks; more specifically, we revised the resemblance between the Klein-Gordon and Dirac equations and the quantum walk time evolution equations (AU)

• FAPESP's process: 14/12617-5 - Implementation of two-dimensional quantum walks
• Grantee: João Fernando Doriguello Diniz
• Support Opportunities: Scholarships in Brazil - Master