Increasing ubiquity of computational resources has enabled simulation of complex electronic systems and modern materials. The PAOFLOW software package is a tool designed to construct and analyze tight binding Hamiltonians from the solutions of DFT calculations. PAOFLOW leverages localized basis sets to greatly reduce computational costs of post-processing QE simulation results, enabling efficient determination of properties such as electronic density, band structures in the presence of electric or magnetic fields, magnetic or spin circular dichroism, spin-texture, Fermi surfaces, spin or anomalous Hall conductivity (SHC or AHC), electronic transport, and more. PAOFLOW's broad functionality is detailed in this work, and several independent studies where PAOFLOW's capabilities directly enabled research on promising candidates for ferroelectric and spintronic based technologies are described. Today, Quantum computers are at the forefront of computational information science. Materials scientists and quantum chemists can use quantum computers to simulate interacting systems of fermions, without having to perform the iterative methods of classical computing. This dissertation also describes a study where the band structure for silicon is simulated for the first time on quantum hardware and broadens this concept for simulating band structures of generic crystalline structures on quantum machines.

Der Variationsquanten-Eigensolver (VQE) ist ein hybrider quanten-klassischer Algorithmus, der dazu dient, den Grundzustand eines Hamiltonians mit Hilfe von Variationsmethoden aufzufinden. Er hat ein breites Spektrum an möglichen Anwendungen, von der Quanten Chemie bis hin zu Gittereichtheorien in der Hamiltonformulierung. VQE stützt sich auf Quantencomputer, um die Energie eines Systems in Form von Schaltkreisparametern zu berechnen und minimiert diese parametrisierte Energie mit einer klassischen Optimierungsroutine. Diese Doktorarbeit bebenutzt als Algorithmus eine Bayes'sche Optimierung (BO). Der Algorithmus wurde speziell für die Minimierung der parametrisierten Energie, wie sie mit einem Quantencomputer berechnet wird, entwickelt. Die BO basiert auf der Gaußschen Prozessregression (GPR) und ist ein Algorithmus zum Auffinden des globalen Minimums einer Black-Box Kostenfunktion, z.~B.~der Energie. Die BO arbeitet mit einer sehr geringen Anzahl von Iterationen selbst bei Verwendung von Daten, die durch statistisches Rauschen beeinflusst sind. Außerdem erwies sich das für diese Arbeit entwickelte GPR-Verfahren als sehr vielseitig, da wir es auch für die Berechnung diskreter Integraltransformationen von verrauschten Daten verwenden konnten. Insbesondere wurde dieses Verfahren zur Rekonstruktion von Parton Verteilungsfunktionen aus Gitter-QCD-Daten verwendet. / The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm used to find the ground state of a Hamiltonian using variational methods. It has a wide range of potential applications, from quantum chemistry to lattice gauge theories in the Hamiltonian formulation. VQE relies on quantum computers to evaluate the energy of the system in terms of circuit parameters, and it minimizes this parametrized energy with a classical optimization routine. This work describes a Bayesian optimization (BO) algorithm specifically designed to minimize the parametrized energy obtained with a quantum computer. BO based on Gaussian process regression (GPR) is an algorithm for finding the global minimum of a black-box cost function, e.g. the energy, with a very low number of iterations even when using data affected by statistical noise. Furthermore, the GPR procedure developed for this work proved to be very versatile as we also used it to compute discrete integral transforms of noisy data. In particular, this procedure was used to reconstruct parton distribution functions from lattice QCD data.

This thesis provides also a detailed stepwise guideline on the data analysis for scanning X-ray diffraction experiments at a modern synchrotron radiation source. / Halbleiterbasierte Spin-Qubits in elektrostatischen Quantenpunkten haben vor Kurzem ein technologisches Niveau erreicht, welches lange Kohärenzzeiten und hohe Fidelitäten ermöglicht. Diese Eigenschaften sind wichtig, um eine große Anzahl von Qubits zu realisieren, welche durch adiabatische Ladungstransporte miteiander verbunden werden sollen. Allerdings können lokale Fluktuationen der Gitterverspannung im aktiven Material die Spinzustände stören, da sie das elektrostatische Potential beeinflussen. Diese Arbeit untersucht die Gitterverspannung in funktionalen Loch-Spin-Qubits und in Bauelementen für kohärenten Elektronentransport, welche auf epitaktischen Ge/Si0.20Ge0.80 und Si/Si0.66Ge0.34 Heterostrukturen mit metallischen Elektroden basieren. Die experimentelle Herausforderung besteht darin, zugleich eine hohe Sensitivität für die Gitterdeformation und eine räumliche Auflösung auf der Nanometerskala zu erreichen. Dies wird durch rasternde Röntgenbeugungsmikroskopie an der Strahllinie ID01/ESRF ermöglicht, welche eine Abbildung des Verspannungstensors mit einer lateralen Auflösung von ≤ 50 nm in bis zu 10 nm-dünnen epitaktischen Quantentöpfen ermöglicht. Die Untersuchung von vier verschiedenen Quantenbauteilen zeigt Modulationen der Gitterverspannung von 10−4 − 10−3 auf, welche durch die Elektroden und die plastische Entspannung der Heterostruktur verursacht sind. Diese Modulationen werden in räumliche Fluktuationen der Bandkantenniveaus von einer Größenordnung von mehreren meV übersetzt, die damit ähnlich zu den Abständen der orbitalen Energieniveaus der Quantenpunkte sind. Folglich stellt diese Arbeit wichtige Informationen für die Realisierung eines skalierbaren Quantenprozessors durch eine Berücksichtigung der lokalen Materialeigenschaften bereit / Semiconductor spin qubits featuring gate-defined electrostatic quantum dots have recently reached a maturity level enabling long spin coherence times and high fidelity. These characteristics are of paramount importance in the realization of large arrays of qubits interconnected by adiabatic charge shuttling. However, spin coherence can be strongly affected by local fluctuations of the lattice strain in the active material, since they impact the electrostatic potential. This work explores strain fluctuations in functional hole spin qubits and coherent electron shuttling devices based on epitaxial Ge/Si0.20Ge0.80 and Si/Si0.66Ge0.34 heterostructures with metallic electrodes. The main experimental challenge is to simultaneously achieve high sensitivity to the lattice deformation together with nanoscale spatial resolution. These requirements are met by Scanning X-ray Diffraction Microscopy at the synchotron beamline ID01/ESRF, which allows spatial mapping with ≤ 50 nm lateral resolution of the strain tensor in quantum well layers as thin as 10 nm. The analysis of four different devices highlights local modulations of the strain tensor components in the range of 10−4 − 10−3 induced by the gate electrodes and the plastic relaxation of the heterostructure. By means of band perturbation calculations, these strain fluctuations are translated into spatial modulations of the band edge energy levels. These perturbations are found to be of a few meV and thus on a similar magnitude as the orbital energy of the quantum dots. As such, this work provides important information for the realization of a scalable quantum processor with coherent interconnects by considering local material properties.

Le domaine des systèmes de référence quantiques, dont les dernière avancées sont brièvement présentées au chapitre 1, est extrêmement pertinent à la compréhension de la dégradation des états quantiques et de l’évolution d’instruments de mesures quantiques. Toutefois, pour arriver à comprendre formellement ces avancées et à apporter une contribution originale au domaine, il faut s’approprier un certain nombre de concepts physiques et mathématiques, in- troduits au chapitre 2. La dégradation des états quantiques est très présente dans le contrôle d’états utiles à l’informatique quantique. Étant donné que ce dernier tente de contrôler des sys- tèmes à deux états, le plus souvent des moments cinétiques, l’analyse des systèmes de référence quantiques qui les mesurent s’avère opportune. Puisque, parmi les plus petits moments ciné- tiques, le plus connu est de s = 1 et que son état le plus simple est l’état non polarisé, l’étude 2 du comportement d’un système de référence mesurant successivement ce type de moments ci- nétiques constitue le premier pas à franchir. C’est dans le chapitre 3 qu’est fait ce premier pas et il aborde les questions les plus intéressantes, soit celles concernant l’efficacité du système de référence, sa longévité et leur maximum. La prochaine étape est de considérer des états de moments cinétiques polarisés et généraux, étape qui est abordée dans le chapitre 4. Cette fois, l’analyse de la dégradation du système de référence est un peu plus complexe et nous pouvons l’inspecter approximativement par l’évolution de certains paramètres pour une certaine classe d’états de système de référence. De plus, il existe une interaction entre le système de référence et le moment cinétique qui peut avoir un effet sur le système de référence tout à fait comparable à l’effet de la mesure. C’est cette même interaction qui est étudiée dans le chapitre 5, mais, cette fois, pour des moments cinétiques de s = 1. Après une comparaison avec la mesure, il devient manifeste que les ressemblances entre les deux processus sont beaucoup moins apparentes, voire inexistantes. Ainsi, cette ressemblance ne semble pas générale et semble accidentelle lorsqu’elle apparaît. / The field of quantum reference frames, which recent progress is briefly presented in chap- ter 1, is extremely relevant when it comes to understanding the deterioration of quantum states and the evolution of quantum measurement instruments. However, to fully understand these advances and to be able to bring an original contribution to this field, one must first understand a number of concepts in physics and mathematics. These concepts are explained in chapter 2. Since the deterioration of quantum states is very present when controlling useful states in quan- tum computing, and since quantum computing attempts to control two-states systems, often angular momenta, analyzing quantum reference frames proves to be relevant. Having s = 1 as 2 the smallest known angular momentum, and since its simplest state is the unpolarized state, the study of a reference frame behavior that measures successively this type of angular momentums is the first step to be taken (chapter 3). The most interesting questions concern the efficiency of the reference frame, its longevity, and the optimization of these two quantities. The next step is to consider polarized and general angular momentum states (chapter 4). This time, analyzing the deterioration of the reference frame proves to be more complex, and can be examined in an approximate manner by looking at the evolution of certain parameters given for a certain class of states of reference frames. Furthermore, the existence of an interaction between the reference frame and the angular momentum can affect the reference frame approximatively as much as the measuring it does. It is this very interaction that is studied in chapter 5, but this time, for s = 1 angular momenta. Comparing this interaction with the measurement shows very clearly that the similarities between the two processes are a lot less visible than with s = 1 , and 2 even perhaps nonexistent. Therefore, the similarity does not seem to be general and appears to be accidental when it is significant.

Dans cette thèse, nous étudions théoriquement les propriétés de molécules diatomiques, leur dynamique de réaction ainsi que le contrôle de cette dynamique à l'aide de champs laser. Notre travail porte plus spécifiquement sur trois espèces :• HeH⁺, un composé-clé en astrochimie considéré comme la première espèce moléculaire qui s'est formée dans l'univers ;• CO²⁺, un dication métastable qui se prête bien à des expériences de contrôle quantique en raison du relativement long temps de vie de son état vibrationnel le plus bas ;• ⁴¹K⁸⁷Rb, une molécule polaire qui présente la particularité de pouvoir être formée à très basse température et piégée, ce qui en fait un bon support physique potentiel pour la réalisation d'un ordinateur quantique moléculaire. Nous utilisons tout d'abord des méthodes de calcul ab initio afin d'obtenir les courbes d'énergie potentielle des premiers états singulets et triplets de HeH⁺ avec un haut de degré de précision, ainsi que les courbes d'énergie potentielle, les moments dipolaires de transition et les couplages non-adiabatiques radiaux de l'état fondamental ³Π de CO²⁺ et de ses 11 premiers états ³Σ⁻.Ensuite, nous utilisons ces données ab initio pour calculer les sections efficaces de photodissociation et d'association radiative des états a et b ³Σ⁺ de HeH⁺, ainsi que les constantes cinétiques associées à ces processus dans les conditions rencontrées dans des environnements astrophysiques. Les sections efficaces de photodissociation du niveau vibrationnel le plus bas de CO²⁺ sont également calculées. Nous allons ensuite un cran plus loin en optimisant des champs laser qui guident la dynamique de photodissociation de HeH⁺ et CO²⁺ vers des canaux de dissociation spécifiques. Nous comparons deux méthodes d'optimisation de ces champs: une approche de contrôle local basée sur les opérateurs de Møller et la théorie du contrôle optimal. Dans le deux cas, nous incluons une contrainte qui minimise l'aire des champs. Enfin, nous nous concentrons sur l'une des applications possibles du contrôle laser à haute fidélité : l'utilisation de petits systèmes moléculaires comme ordinateurs quantiques. Nous étudions plus spécifiquement l'implémentation possible d'opérations logiques intra- et intermoléculaires sur des données encodées dans des états hyperfins de molécules de ⁴¹K⁸⁷Rb piégées, ce qui ouvre des perspectives intéressantes en terme d'extensibilité. / In this work, we theoretically study the properties of diatomic molecular systems, their dynamics, and the control thereof through the use of laser fields. We more specifically study three compounds::• HeH⁺, a species of great astrochemical importance which is thought to be the first molecular species to have formed in the universe; :• CO²⁺, a metastable dication of particular interest in quantum control experiments due to its long-lived lowest vibrational level;:• ⁴¹K⁸⁷Rb, a polar molecule that can be formed at very low temperature and trapped, making it a good candidate for quantum computing schemes.First, we use ab initio methods to compute accurate potential energy curves for the lowest singlet and triplet states of HeH⁺ as well as the potential energy curves, transition dipole moments and nonadiabatic radial couplings of the ground ³Π state of CO²⁺ and of its 11 lowest ³Σ⁻states.In a second step, we use this ab initio data to compute the photodissociation and radiative association cross sections for the a and b ³Σ⁺ states of HeH⁺, as well as the values of the corresponding rate constants for astrophysical environments. The photodissociation cross sections from the lowest vibrational level of CO²⁺ is also determined.Going one step further, we optimize laser control fields that drive the photodissociation dynamics of HeH⁺ and CO²⁺ towards specific channels. We compare two field optimization methods: a Møller operator-based Local Control approach and Optimal Control Theory. In both cases, we add a constraint that minimizes the area of the optimized fields.Finally, we focus on one of the potential applications of high-fidelity laser control: the use of small molecular systems as quantum computers. We more specifically study the potential implementation of both intra- and intermolecular logic gates on data encoded in hyperfine states of trapped ultracold polar ⁴¹K⁸⁷Rb molecules, opening interesting perspectives in terms of extensibility.

Made available in DSpace on 2015-03-04T18:51:16Z (GMT). No. of bitstreams: 1 Tese Demerson.pdf: 742439 bytes, checksum: 534128a7d9b5cfc57f84985cd77ac16d (MD5) Previous issue date: 2009-08-28 / We present a new polynomial-time quantum algorithm that solves the hidden subgroup problem (HSP) for a special class of metacyclic groups, namely Z_{p} \rtimes \Z_{q^s}, with q \mid (p-1) and p/q= \up{poly}(\log p), where p, q are any odd prime numbers and s is any positive integer. This solution generalizes previous algorithms presented in the literature. In a more general setting, without imposing a relation between p and q, we obtain a quantum algorithm with time and query complexity 2^{O(\sqrt{\log p})}. In any case, those results improve the classical algorithm, which needs {\Omega}(\sqrt{p}) queries. We also present quantum algorithms for the HSP over non-abelian groups of order 2^{n+1} which have a cyclic subgroup of index 2 and for some semidirect product \Z_N^m \rtimes \Z_p, where N has a special prime factorization. / Neste trabalho apresentamos um novo algoritmo quântico eficiente para o Problema do Subgrupo Oculto (PSO) sobre uma classe especial de grupos metacíclicos, Z_p \rtimes Z_q^s, com q | (p-1) e p/q= poli(log p), onde p, q são números primos ímpares distintos e s um inteiro positivo qualquer. Em um contexto mais geral, sem impor uma relação entre p e q obtemos um algoritmo quântico com complexidade de tempo 2^{O(\sqrt{log p})}. Em qualquer caso, esses resultados são melhores que qualquer algoritmo clássico para o mesmo fim, cuja complexidade é \Omega(\sqrt{p}). Apresentamos também, algoritmos quânticos para o PSO sobre grupos não abelianos de ordem 2^{n+1} que possuem subgrupos cíclicos de índice 2 e para certos produtos semidiretos de grupos Z_N^m \rtimes Z_p, com m, N inteiros positivos e N fatorado de forma especial.

Many-Body Perturbation Theory is put to test as a method for reliable calculations of the electron-electron interaction in two-dimensional quantum dots. We show that second order correlation gives qualitative agreement with experiments on a level which was not found within the Hartree-Fock description. For weaker confinements, the second order correction is shown to be insufficient and higher order contributions must be taken into account. We demonstrate that all order Many-Body Perturbation Theory in the form of the Coupled Cluster Singles and Doubles method yields very reliable results for confinements close to those estimated from experimental data. The possibility to use very large basis sets is shown to be a major advantage compared to Full Configuration Interaction approaches, especially for more than five confined electrons. Also, the possibility to utilize two-electron correlation in combination with tailor made potentials to achieve useful properties is explored. In the case of a two-dimensional quantum dot molecule we vary the interdot distance, and in the case of a two-dimensional quantum ring we vary the ring radius, in order to alter the spectra. In the latter case we demonstrate that correlation in combination with electromagnetic pulses can be used for the realization of quantum logical gates. / At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 5: Manuscript.

This Thesis focuses on different aspects of quantum computation theory: adiabatic quantum algorithms, decoherence during the adiabatic evolution and quantum simulators. After an overview on the area of quantum computation and setting up the formal ground for the rest of the Thesis we derive a general error estimate for adiabatic quantum computing. We demonstrate that the first-order correction, which has frequently been used as a condition for adiabatic quantum computation, does not yield a good estimate for the computational error. Therefore, a more general criterion is proposed, which includes higher-order corrections and shows that the computational error can be made exponentially small – which facilitates significantly shorter evolution times than the first-order estimate in certain situations. Based on this criterion and rather general arguments and assumptions, it can be demonstrated that a run-time of order of the inverse minimum energy gap is sufficient and necessary. Furthermore, exploiting the similarity between adiabatic quantum algorithms and quantum phase transitions, we study the impact of decoherence on the sweep through a second-order quantum phase transition for the prototypical example of the Ising chain in a transverse field and compare it to the adiabatic version of Grover’s search algorithm. It turns out that (in contrast to first-order transitions) the impact of decoherence caused by a weak coupling to a rather general environment increases with system size (i.e., number of spins/qubits), which might limit the scalability of the system. Finally, we propose the use of electron systems to construct laboratory systems based on present-day technology which reproduce and thereby simulate the quantum dynamics of the Ising model and the O(3) nonlinear sigma model.

<p>Utvecklandet av kvantdatorn är ett ytterst lovande projekt som kombinerar teoretisk och experimental kvantfysik, matematik, teori om kvantinformation och datalogi. Under första steget i utvecklandet av kvantdatorn låg huvudintresset på att skapa några algoritmer med framtida tillämpningar, klargöra grundläggande frågor och utveckla en experimentell teknologi för en leksakskvantdator som verkar på några kvantbitar. Då dominerade förväntningarna om snabba framsteg bland kvantforskare. Men det verkar som om dessa stora förväntningar inte har besannats helt. Många grundläggande och tekniska problem som dekoherens hos kvantbitarna och instabilitet i kvantstrukturen skapar redan vid ett litet antal register tvivel om en snabb utveckling av kvantdatorer som verkligen fungerar. Trots detta kan man inte förneka att stora framsteg gjorts inom kvantteknologin. Det råder givetvis ett stort gap mellan skapandet av en leksakskvantdator med 10-15 kvantregister och att t.ex. tillgodose de tekniska förutsättningarna för det projekt på 100 kvantregister som aviserades för några år sen i USA. Det är också uppenbart att svårigheterna ökar ickelinjärt med ökningen av antalet register. Därför är simulering av kvantdatorer i klassiska datorer en viktig del av kvantdatorprojektet. Självklart kan man inte förvänta sig att en kvantalgoritm skall lösa ett NP-problem i polynomisk tid i en klassisk dator. Detta är heller inte syftet med klassisk simulering. Den klassiska simuleringen av kvantdatorer kommer att täcka en del av gapet mellan den teoretiskt matematiska formuleringen av kvantmekaniken och ett förverkligande av en kvantdator. Ett av de viktigaste problemen i vetenskapen om kvantdatorn är att utveckla ett nytt symboliskt språk för kvantdatorerna och att anpassa redan existerande symboliska språk för klassiska datorer till kvantalgoritmer. Denna avhandling ägnas åt en anpassning av det symboliska språket Mathematica till kända kvantalgoritmer och motsvarande simulering i klassiska datorer. Konkret kommer vi att representera Simons algoritm, Deutsch-Joszas algoritm, Grovers algoritm, Shors algoritm och kvantfelrättande koder i det symboliska språket Mathematica. Vi använder samma stomme i alla dessa algoritmer. Denna stomme representerar de karaktäristiska egenskaperna i det symboliska språkets framställning av kvantdatorn och det är enkelt att inkludera denna stomme i framtida algoritmer.</p> / <p>Quantum computing is an extremely promising project combining theoretical and experimental quantum physics, mathematics, quantum information theory and computer science. At the first stage of development of quantum computing the main attention was paid to creating a few algorithms which might have applications in the future, clarifying fundamental questions and developing experimental technologies for toy quantum computers operating with a few quantum bits. At that time expectations of quick progress in the quantum computing project dominated in the quantum community. However, it seems that such high expectations were not totally justified. Numerous fundamental and technological problems such as the decoherence of quantum bits and the instability of quantum structures even with a small number of registers led to doubts about a quick development of really working quantum computers. Although it can not be denied that great progress had been made in quantum technologies, it is clear that there is still a huge gap between the creation of toy quantum computers with 10-15 quantum registers and, e.g., satisfying the technical conditions of the project of 100 quantum registers announced a few years ago in the USA. It is also evident that difficulties increase nonlinearly with an increasing number of registers. Therefore the simulation of quantum computations on classical computers became an important part of the quantum computing project. Of course, it can not be expected that quantum algorithms would help to solve NP problems for polynomial time on classical computers. However, this is not at all the aim of classical simulation. Classical simulation of quantum computations will cover part of the gap between the theoretical mathematical formulation of quantum mechanics and the realization of quantum computers. One of the most important problems in "quantum computer science" is the development of new symbolic languages for quantum computing and the adaptation of existing symbolic languages for classical computing to quantum algorithms. The present thesis is devoted to the adaptation of the Mathematica symbolic language to known quantum algorithms and corresponding simulation on the classical computer. Concretely we shall represent in the Mathematica symbolic language Simon's algorithm, the Deutsch-Josza algorithm, Grover's algorithm, Shor's algorithm and quantum error-correcting codes. We shall see that the same framework can be used for all these algorithms. This framework will contain the characteristic property of the symbolic language representation of quantum computing and it will be a straightforward matter to include this framework in future algorithms.</p>

Le domaine des systèmes de référence quantiques, dont les dernière avancées sont brièvement présentées au chapitre 1, est extrêmement pertinent à la compréhension de la dégradation des états quantiques et de l’évolution d’instruments de mesures quantiques. Toutefois, pour arriver à comprendre formellement ces avancées et à apporter une contribution originale au domaine, il faut s’approprier un certain nombre de concepts physiques et mathématiques, in- troduits au chapitre 2. La dégradation des états quantiques est très présente dans le contrôle d’états utiles à l’informatique quantique. Étant donné que ce dernier tente de contrôler des sys- tèmes à deux états, le plus souvent des moments cinétiques, l’analyse des systèmes de référence quantiques qui les mesurent s’avère opportune. Puisque, parmi les plus petits moments ciné- tiques, le plus connu est de s = 1 et que son état le plus simple est l’état non polarisé, l’étude 2 du comportement d’un système de référence mesurant successivement ce type de moments ci- nétiques constitue le premier pas à franchir. C’est dans le chapitre 3 qu’est fait ce premier pas et il aborde les questions les plus intéressantes, soit celles concernant l’efficacité du système de référence, sa longévité et leur maximum. La prochaine étape est de considérer des états de moments cinétiques polarisés et généraux, étape qui est abordée dans le chapitre 4. Cette fois, l’analyse de la dégradation du système de référence est un peu plus complexe et nous pouvons l’inspecter approximativement par l’évolution de certains paramètres pour une certaine classe d’états de système de référence. De plus, il existe une interaction entre le système de référence et le moment cinétique qui peut avoir un effet sur le système de référence tout à fait comparable à l’effet de la mesure. C’est cette même interaction qui est étudiée dans le chapitre 5, mais, cette fois, pour des moments cinétiques de s = 1. Après une comparaison avec la mesure, il devient manifeste que les ressemblances entre les deux processus sont beaucoup moins apparentes, voire inexistantes. Ainsi, cette ressemblance ne semble pas générale et semble accidentelle lorsqu’elle apparaît. / The field of quantum reference frames, which recent progress is briefly presented in chap- ter 1, is extremely relevant when it comes to understanding the deterioration of quantum states and the evolution of quantum measurement instruments. However, to fully understand these advances and to be able to bring an original contribution to this field, one must first understand a number of concepts in physics and mathematics. These concepts are explained in chapter 2. Since the deterioration of quantum states is very present when controlling useful states in quan- tum computing, and since quantum computing attempts to control two-states systems, often angular momenta, analyzing quantum reference frames proves to be relevant. Having s = 1 as 2 the smallest known angular momentum, and since its simplest state is the unpolarized state, the study of a reference frame behavior that measures successively this type of angular momentums is the first step to be taken (chapter 3). The most interesting questions concern the efficiency of the reference frame, its longevity, and the optimization of these two quantities. The next step is to consider polarized and general angular momentum states (chapter 4). This time, analyzing the deterioration of the reference frame proves to be more complex, and can be examined in an approximate manner by looking at the evolution of certain parameters given for a certain class of states of reference frames. Furthermore, the existence of an interaction between the reference frame and the angular momentum can affect the reference frame approximatively as much as the measuring it does. It is this very interaction that is studied in chapter 5, but this time, for s = 1 angular momenta. Comparing this interaction with the measurement shows very clearly that the similarities between the two processes are a lot less visible than with s = 1 , and 2 even perhaps nonexistent. Therefore, the similarity does not seem to be general and appears to be accidental when it is significant.