Íons aprisionados como plataforma para computação quântica: aprendizado de máquina quântica em variáveis contínuas e implementação de algoritmos quânticos

Abstract

This work initially investigates the use of trapped ions as a platform for quantum computing in both the digital and continuous-variable paradigms. In the context of continuous variables, we use the vibrational modes of the ions as bosonic degrees of freedom and show how different choices of frequencies, detunings, and phases of the applied fields enable the realization of single- and two-mode Gaussian operations, as well as non-Gaussian operations of the \emph{trisqueezing} and Kerr types. These operations are numerically validated by comparing the evolution produced by the full interaction Hamiltonian with the ideal target states. In particular, we incorporate the dependence of the Rabi frequency on the phonon number into the description of the Kerr interaction and employ this operation as the non-Gaussian element of a quantum neural network applied to classical function regression tasks and to the variational preparation of unstructured quantum states in the Fock basis. In the context of digital quantum computing, we formulate a product allocation problem for gravity-flow racks as an unconstrained quadratic binary optimization problem, map it onto an Ising-type Hamiltonian, and implement a version of the Quantum Approximate Optimization Algorithm adapted to the operations available on a trapped-ion processor, thereby enabling an analysis of the current possibilities and limitations of variational algorithms applied to an industrial problem. In addition to their application to computing, we investigate trapped ions as a platform for the controlled study of physical phenomena. In this context, we analyze an interference mechanism between interactions produced by electromagnetic and mechanical waves, mediated by the electronic and vibrational degrees of freedom of the ions. We show how the relative phase between these interactions can enhance or cancel electronic population transfer and extend this description to ion chains subjected to propagating mechanical pulses. This study highlights the role of the ion as a common material system capable of coupling waves of different natures and allows interference to be discussed in terms of the transition amplitudes produced in the system responsible for their detection. Thus, the contributions of this thesis encompass both the development and application of quantum operations and algorithms and the use of trapped ions to investigate interaction and interference phenomena in controlled quantum systems.