Método de dinâmicas efetivas aplicado na análise da interação qubit-qubit em dispositivos supercondutores: a interação qubit-qubit no contexto da computação quântica

Abstract

In this dissertation, we approach some aspects of quantum computing. At first, we detail the Deutsch-Jozsa algorithm and show how to implement it in real IBM quantum computers, available free of charge via remote access on the IBM-Q Experience platform. From the implementation of this algorithm, it was possible to prove its advantage over its classical counterparts, i. e., that it is, in fact, possible to solve problems more efficiently (with fewer steps) when exploring quantum principles, such as superposition states and entangled states, in the computational processes. In the course of the work, we came across some issues that motivated us to develop the second part of our project, particularly the problem involving logical operations with many qubits (known as multi-qubit gates). Such gates can be decomposed into simpler one and two-qubit gates, however introducing much greater complexity to the algorithms. In this sense, we look for efficient ways to implement three-qubit logic gates in superconducting qubit systems. For this purpose, we use a technique to obtain effective Hamiltonians to derive the desired interactions, simplifying the analysis of the system. This approximate method was then confronted with numerical calculations using Hamiltonians without approximation, making it possible to verify the approximations' validity and prove the results obtained analytically. Then, we compare the times needed to implement simple operations, such as the transfer of an excitation (1 qubit of quantum information) between two qubits, both via the so-called "direct" interaction, in which an auxiliary qubit is a mediator of the effective interaction (without it being effectively populated) and via the so-called "indirect" interaction, since the exchange between the qubits requires the transfer of information to the auxiliary qubit during the process. Although the indirect case requires more steps (logic gates), it is more advantageous in terms of processing time. Finally, we analyze the fidelity of the logical operations taking into account the presence of errors (systematic and random) in the auxiliary qubit that mediates the interaction. In the presence of such errors, the exchange of quantum information via the direct process showed better fidelity. In this regime, because of the fewer intermediate steps using a qubit that has faults, it is not necessary to demand such precise control of the system parameters.