Single-qubit dynamics

Determining the density matrix of a qubit in closed and open quantum systems when considering free evolution and weak measurements

Bachelor thesis (2022)

Authors

B.A. Witmer Electrical Engineering, Mathematics and Computer Science

Contributors

Y.M. Blanter QN/Blanter Group - AS (supervisor 1)
M.P.T. Caspers Analysis - EEMCS (supervisor 2)
J.M. Thijssen QN/Thijssen Group - AS (coach)
D. de Laat Discrete Mathematics and Optimization - EEMCS (coach)
Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright: © 2022 Brian Witmer
Quantum Mechanics Qubits Density matrix
More Info
expand_more

Published Date

11-08-2022

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

Quantum technology is evolving faster than ever. Currently, all eyes are on the quantum computer, the promising computer that can solve problems which are unsolvable for regular computers. In order to understand this new technology, it is necessary to understand the qubit, the basic unit of quantum information. This can be done by means of the density matrix: a mathematical representation of the state of a system. The aim of this thesis is to find the density matrix of a single qubit in closed (isolated) and open quantum systems. In the case of a closed system, an alternating sequence of two processes with different Hamiltonians is considered, which both last a fixed amount of time after one another. These systems have been solved using a direct formula for a 2 × 2 matrix with distinct eigenvalues raised to the power n for any n ∈ N. In the case of an open system, dissipation is taken into account compared to a single process in a closed system. These open systems have been solved numerically using the Lindblad master equation and the spin-boson model to model the environment as a bath of bosons. However, the use of multiple approximations and assumptions questions the validity of the results for ’strong’ interactions. Suggestions for further research include investigating quantitatively when the Lindblad equation is valid to use and solve open quantum systems using different models for the environment.