Simulação Numérica de Experimentos de Ressonância Magnética de Núcleos Quadrupolares com Aplicações em Computação Quântica - Possa, Denimar (2011)
Nuclear magnetic resonance (NMR) at high magnetic field is oneof the most viabletools for implementing small-scale quantum computation. This fact motivates the studyof other magnetic resonance techniques for similar purposes. In this work we show, byextensively using numerical simulations, how nuclear quadrupole resonance (NQR) atzero external magnetic field can be used to perform basic quantum computing tasks.Specifically, concrete proposals to represent 2 and 3 q-bit states are presented, obtainedin systems of nuclei with spin 3/2 and 7/2, respectively, subjected to a pure quadrupolecoupling to an axially symmetric electric field gradient. Inthe spin 3/2 case, a methodfor quantum state tomography is also described, involving the use of two crossed coilsfor signal detection. Due to the similarity between the NMR and NQR techniques,many procedures used for obtaining pseudopure states and creating logic gates bearresemblance to those commonly used in NMR. However, NQR has some specific featureswhich provide important differences with regard to NMR, especially with respect to thedesign of the radiofrequency (RF) pulses responsible for handling the system. The useof circularly polarized pulses provides a mechanism of selective excitation in NQR withno counterpart in high-field NMR; these selective pulses are much shorter than the longselective pulses normally used in NMR, which is an advantage in terms of computationaltime and also considering the existence of decoherence effects. Another advantage ofNQR compared to high-field NMR is the relatively low cost of NQR spectrometers,which do not require the use of superconducting magnets. A second aim of this workis the development of a computational program for the numerical simulation of generalmagnetic resonance experiments involving quadrupolar nuclei in crystals, without anyrestriction as to the relative magnitude of the Zeeman and quadrupole interactions. Thisallows us to address, within the same theoretical framework, high-field NMR as well aspure NQR experiments, also including intermediate cases inwhich the interactions havecomparable magnitudes. The program, which was developed using the Mathematicapackage, makes use of the interaction picture to compute thetime evolution of the densityoperator under the effects of the relevant nuclear spin interactions and RF pulses. Someconditions specifically required for quantum computing applications are implemented inthe program, such as the possibility of use of elliptically polarized radiofrequency and theinclusion of zero- and first-order terms in the average Hamiltonian expansion. A numberof examples dealing with simple NQR and quadrupole-perturbed NMR experiments arepresented, along with the proposal of experiments to createquantum pseudopure statesand logic gates using pure NQR.