This thesis deals with a series of quantum computer implementation issues from the Kane 31P in 28Si architecture to Shor’s integer factoring algorithm and beyond. The discussion begins with simulations of the adiabatic Kane CNOT and readout gates, followed by linear nearest neighbor implementations of 5-qubit quantum error correction with and without fast measurement. A linear nearest neighbor circuit implementing Shor’s algorithm is presented, then modified to remove the need for exponentially small rotation gates. Finally, a method of constructing optimal approximations of arbitrary single-qubit fault-tolerant gates is described and applied to the specific case of the remaining rotation gates required by Shor’s algorithm.

La physique quantique appliquée à la théorie de l’information se révèle être pleine de promesses pour notre société. Conscients de ce potentiel, des groupes de scientifiques du monde entier ont pour objectif commun de créer un ordinateur utilisant les principes de la mécanique quantique. La premières étape de cet ambitieux cheminement menant à l’ordinateur quantique est la réalisation du bloc de base de l’encodage quantique de l’information, le qubit. Dans le large choix de qubits existants, ceux utilisant un spin sont très attrayants puisqu’ilspeuvent être lus et manipulés de façon cohérente uniquement en utilisant des champs électriques. Enfin, plus un système est isolé, plus son comportement demeure quantique, ce qui fait du spin nucléaire un sérieux candidat dans la course aux long temps de cohérence et donc aux grands nombres d’opérations quantiques.Dans ce contexte, j’ai étudié un transistor de spin moléculaire. Ce dispositif, placé dans un réfrigérateur à dilution assurant des mesures à 40mK, est composé d’une molécule magnétique TbPc2 couplée à des électrodes (source, drain et grille) et à une antenne hyperfréquence. Il nous a permis de lire à l’aide d’une mesure de conductance, à la fois l’état de spin électronique et nucléaire de l’ion Terbium. Ma thèse se focalise sur l’étude de la dynamique de ces spins et plus particulièrement celle du spin nucléaire 3/2 sous l’influence d’un champ micro-onde. La première étape consiste à mesurer la différence d’énergie entreces quatre états de spin nucléaire pour ensuite parvenir à manipuler de façon cohérente ses trois transitions en utilisant uniquement un champ électrique. Pour caractériser davantage les processus de décohérence à l’origine de la perte de phase des états quantique, j’ai réalisé des mesures Ramsey et Hahn-echo révélant des temps de cohérence de l’ordre de 0.3ms. Ces résultats préliminaires montrent que nous sommes en présence de 3 qubits ayant une figure de mérite supérieure à deux milles, répondant ainsi aux attentes suscitées par l’utilisation d’un spin nucléaire comme bloc de base de l’information quantique.Plus que démontrer expérimentalement la dynamique de trois qubits, ces mesures nous prouvent qu’un spin nucléaire intégré dans une géométrie de type transistor à aimant moléculaire est un système à quatre états contrôlé de façon cohérente. Des propositions théoriques démontrent qu’un traitement quantique de l’information, telle que l’application de portes quantiques et la réalisation d’algorithmes, peuvent être implémentées sur un tel système. Je me suis concentré sur un algorithme de recherche. Il s’agit de la succession d’une porteHadamard, qui crée une superposition cohérente de tous les états de spin nucléaire, et une évolution unitaire qui amplifie l’amplitude d’un état désiré. Il permet une accélération quadratique de la recherche d’un élément dans une liste non ordonnée comparée à un algorithme classique. Pendant ma thèse, j’ai apporté la preuve expérimentale de la faisabilité de cet algorithme de Grover sur un système à plusieurs niveaux. La première étape a été de créer une superposition cohérente de 2, 3 et 4 états par l’application d’un pulsation radio-fréquence. Enfin, j’ai mesuré une oscillation cohérente entre une superposition de trois états et un état sélectionné qui est la signature de l’implémentation de l’algorithme de recherche.En résumé, cette thèse expose la première implémentation d’un algorithme quantique de recherche sur un qudit de type aimant moléculaire. Ces résultats, combinés à la grande polyvalence des molécules magnétiques, sont autant de promesses pour la suite de ce défi scientifique qu’est la construction d’un ordinateur quantique moléculaire. / The application of quantum physics to the information theory turns out to be full of promises for our information society. Aware of this potential, groups of scientists all around the world have this common goal to create the quantum version of the computer. The first step of this ambitious project is the realization of the basic block that encodes the quantum information, the qubit. Among all existing qubits, spin based devices are very attractive since they reveal electrical read-out and coherent manipulation. Beyond this, the more isolated a system is, the longer its quantum behaviour remains, making of the nuclear spin a serious candidate for exhibiting long coherence time and consequently high numbers of quantum operation.In this context I worked on a molecular spin transistor consisting of a TbPc2 singlemolecule magnet coupled to electrodes (source, drain and gate) and a microwave antenna. This setup enabled us to read-out electrically both the electronic and the nuclear spin states and to coherently manipulate the nuclear spin of the Terbium ion. I focus during my Ph.D. on the study of the spins dynamic and mainly the 3/2 nuclear spin under the influence of a microwave pulse. The first step was to measure the energy difference between these statesleading in a second time to the coherent manipulation of the three nuclear spin transitions using only a microwave electric field. To further characterize the decoherence processes that break the phase of the nuclear spin states, I performed Ramsey and Hahn-echo measurements. These preliminary results show that we were in presence of three qubits with figure of merit higher than two thousands, thus meeting the expectations aroused by the use of a nuclearspin as the basic block of quantum information.More than demonstrating the qubit dynamic, I demonstrated that a nuclear spin embedded in the molecular magnet transistor is a four quantum states system that can be fully controlled, a qudit. Theoretical proposal demonstrated that quantum information processing such as quantum gates and algorithms could be implemented using a 3/2 spin. I focused on a research algorithm which is a succession of an Hadamard gate, that creates a coherent superposition of all the nuclear spin sates, and an unitary evolution, that amplified the amplitude of a desired state. It allows a quadratic speed-up to find an element in an unordered list compared to classical algorithm. During my Ph.D., I demonstrated the experimental proof of feasibility of this Grover like algorithm applied to a multi-levels system. The first step was to experimentally create coherent superposition of 2, 3 and 4 states. Then I measured coherent oscillations inbetween a 3 state superposition and a selected state which is the signature of the research algorithm implementation.In summary, this Ph.D. exposed the first quantum search algorithm on a single-molecule magnet based qudit. These results combined to the great versatility of molecular magnet holds a lot of promises for the next challenge: building up a scalable molecular based quantum computer.

Simuladores quânticos têm tido um importante papel no estudo e desenvolvimento da computação quântica ao longo dos anos. A simulação de algoritmos quânticos em computadores clássicos é computacionalmente difícil, principalmente devido à natureza paralela dos sistemas quânticos. Para acelerar essas simulações, alguns trabalhos propõem usar hardware paralelo programável como FPGAs, o que diminui consideravelmente o tempo de execução. Contudo, essa abordagem tem três problemas principais: pouca escalabilidade, já que apenas transfere a complexidade do domínio do tempo para o domínio do espaço; a necessidade de re-síntese a cada mudança no algoritmo; e o esforço extra ao projetar o código RTL para simulação. Para lidar com esses problemas, uma arquitetura de um co-processador SIMD é proposta, cujas operações das portas quânticas está baseada no modelo Network of Butterflies. Com isso, eliminamos a necessidade de re-síntese com mudanças pequenas no algoritmo quântico simulado, e eliminamos a influência de um dos fatores que levam ao crescimento exponencial do uso de recursos da FPGA. Adicionamente, desenvolvemos uma ferramenta para geração automática do código RTL sintetizável do co-processador, reduzindo assim o esforço extra de projeto. / Quantum simulators have had a important role on the studying and development of quantum computing throughout the years. The simulation of quantum algorithms on classical computers is computationally hard, mainly due to the parallel nature of quantum systems. To speed up these simulations, some works have proposed to use programmable parallel hardware such as FPGAs, which considerably shorten the execution time. However this approach has three main problems: low scalability, since it only transfers the complexity from time domain to space domain; the need of re-synthesis on every change on the algorithm; and the extra effort on designing the RTL code for simulation. To handle these problems, an architecture of a SIMD co-processor is proposed, whose operations of quantum gates are based on Network of Butterflies model. Thus, we eliminate the need of re-synthesis on small changes on the simulated quantum algorithm, and we eliminated the influence of one of the factors that lead to the exponential growth on the consumption of FPGA resources. Aditionally, we developed a tool to automatically generate the synthesizable RTL code of the co-processor, thus reducing the extra design effort.

Atomic defects in solids offer access to atom-like quantum properties without complex trapping methods while displaying a rich physics due to interactions with their solid-state environment. Such properties have made them an advantageous building block for quantum information processing, in particular to construct a quantum network, where information would be encoded in spins and transferred between nodes through photons. Among defects in solids, the negatively charged silicon-vacancy centre in diamond (SiV$^{−}$) has attracted attention for its very promising optical properties for such a network. In this thesis, we investigate the spin properties of the silicon-vacancy centre as a potential spin-photon interface. First, we use resonant excitation of an SiV$^{−}$ centre in an external magnetic field to selectively address different electronic states and analyse the resulting fluorescence. We find evidence of selection rules in the optical transitions revealing that the centre possesses an electronic spin S = 1/2. Making use of the dependence of such selection rules on the applied magnetic field orientation, we resonantly drive two optical transitions forming a $\Lambda$-scheme. In the double resonance condition, we achieve coherent population trapping, whereby the SiV$^{−}$ is pumped into a dark state corresponding to a superposition of the two addressed ground states of opposite spin. This technique allows us to evaluate the coherence time of the dark state and hence of the spin, while demonstrating the possibility of all-optical control of the spin when a $\Lambda$-scheme is available. We then use resonant optical pulses to initialise and read out the spin state of a single SiV$^{−}$. By tuning a microwave pulse into resonance between two ground states of opposite spin, we demonstrate optically detected magnetic resonance. Subsequently, by varying the duration of a resonant microwave pulse, we achieve coherent control of a single SiV$^{−}$ electronic spin. Through Ramsey interferometry, we measure a spin dephasing time of 115 $\pm$ 9 ns. We then investigate interactions of the SiV$^{−}$ with its environment. We analyse the hyperfine interaction of the SiV$^{−}$ spin with the nuclear spin of $^{29}$Si, with a view to taking advantage of the long-lived nuclear spin in the future. We show that single-phonon-mediated excitations between electronic states of the SiV$^{−}$ are the dominant spin dephasing and population decay mechanism and evaluate how external strain alters optical selection rules and can be used to improve the coherence time of the spin.

Quantum annealing is expected to be a powerful generic algorithm for solving hard combinatorial optimization problems faster than classical computers. Finding the solution to a combinatorial optimization problem is equivalent to finding the ground state of an Ising Hamiltonian. In today's quantum annealers the spins of the Ising Hamiltonian are mapped to superconducting qubits. On the other hand, dissipation processes degrade the success probability of finding the solution. In this thesis we set out to explore a newly proposed architecture for a noise-resilient quantum annealer that instead maps the Ising spins to continuous variable quantum states of light encoded in the field quadratures of a two-photon pumped Kerr- nonlinear resonator based on the proposal by Puri et al. (2017). In this thesis we study the Wigner negativity for this newly proposed architecture and evaluate its performance based on the negativity of the Wigner function. We do this by determining an experimental value to when the presence of losses become too detrimental, such that the Wigner function of the quantum state during the evolution within the anneal becomes positive for all times. Furthermore, we also demonstrate the capabilities of this continuous variable quantum annealer by simulating and finding the best solution of a small instance of the NP-complete subset sum problem and of the number partitioning problem.

Simuladores quânticos têm tido um importante papel no estudo e desenvolvimento da computação quântica ao longo dos anos. A simulação de algoritmos quânticos em computadores clássicos é computacionalmente difícil, principalmente devido à natureza paralela dos sistemas quânticos. Para acelerar essas simulações, alguns trabalhos propõem usar hardware paralelo programável como FPGAs, o que diminui consideravelmente o tempo de execução. Contudo, essa abordagem tem três problemas principais: pouca escalabilidade, já que apenas transfere a complexidade do domínio do tempo para o domínio do espaço; a necessidade de re-síntese a cada mudança no algoritmo; e o esforço extra ao projetar o código RTL para simulação. Para lidar com esses problemas, uma arquitetura de um co-processador SIMD é proposta, cujas operações das portas quânticas está baseada no modelo Network of Butterflies. Com isso, eliminamos a necessidade de re-síntese com mudanças pequenas no algoritmo quântico simulado, e eliminamos a influência de um dos fatores que levam ao crescimento exponencial do uso de recursos da FPGA. Adicionamente, desenvolvemos uma ferramenta para geração automática do código RTL sintetizável do co-processador, reduzindo assim o esforço extra de projeto. / Quantum simulators have had a important role on the studying and development of quantum computing throughout the years. The simulation of quantum algorithms on classical computers is computationally hard, mainly due to the parallel nature of quantum systems. To speed up these simulations, some works have proposed to use programmable parallel hardware such as FPGAs, which considerably shorten the execution time. However this approach has three main problems: low scalability, since it only transfers the complexity from time domain to space domain; the need of re-synthesis on every change on the algorithm; and the extra effort on designing the RTL code for simulation. To handle these problems, an architecture of a SIMD co-processor is proposed, whose operations of quantum gates are based on Network of Butterflies model. Thus, we eliminate the need of re-synthesis on small changes on the simulated quantum algorithm, and we eliminated the influence of one of the factors that lead to the exponential growth on the consumption of FPGA resources. Aditionally, we developed a tool to automatically generate the synthesizable RTL code of the co-processor, thus reducing the extra design effort.

[pt] A dissertação apresenta detalhadamente o algoritmo de fatoração de Shor, tanto em termos de sua execução passo a passo como mediante sua representação em forma de circuito, abordando aspectos tanto de sua parte clássica como de sua parte quântica. Inicialmente são apresentados aspectos de teoria dos números indispensáveis para a compreensão do algoritmo e em seguida são desenvolvidos conceitos e propriedades de mecânica quântica e de informação quântica pertinentes. Em atenção ao caráter eminentemente estocástico do algoritmo realiza-se um estudo de sua fonte estocástica e demonstram-se os principais teoremas que embasam a avaliação de sua probabilidade de sucesso. Desenvolvem-se exemplos de simulação clássica do algoritmo. Finalmente, a eficiência do algoritmo de fatoração de Shor é comparada com a de algoritmos clássicos. / [en] The dissertation presents in detail Shor s factoring algorithm, including its execution step by step and its representation in the form of a circuit, addressing aspects of both its classical and its quantum parts. Aspects of number theory indispensable to understand the algorithm are presented, followed by a development of concepts and properties of quantum mechanics and quantum information. Considering the eminently stochastic character of the algorithm, a study of its stochastic source is carried out and the main theorems that support the evaluation of its probability of success are proved. Examples of classical simulation of the algorithm are developed. Finally, the efficiency of Shor s factoring algorithm is compared with that of classical algorithms.

L'étude des nanoagrégats métalliques supportés sur des oxydes est d'une importance primordiale autant au niveau fondamental que technologique, notamment dans le domaine de l'énergie. Les nanoparticules à base de platine supportées sur alumine Gamma sont largement utilisées comme catalyseurs hétérogènes ultradispersés, en particulier sous atmosphère réductrice d'hydrogène. Leur réactivité et leur sélectivité sont intimement liés à la géométrie locale et à la densité électronique des sites actifs. Ces dernières sont particulièrement ardues à définir, étant donnée la très faible taille des agrégats étudiés (environ 0.8 nm de diamètre). La spectroscopie XANES (X-Ray Absorption Near Edge Structure), nécessitant un rayonnement synchrotron, est un des outils les plus appropriés pour étudier ces systèmes, en particulier in situ, à l'échelle atomique. En effet les spectres XANES sont influencés par la géométrie locale et la symétrie de l'environnement des atomes (en particulier les angles entre les liaisons), le degré d'oxydation, les types de liaisons mis en jeu, et la structure électronique du système. Tous ces facteurs sont néanmoins difficiles à différencier et même à interpréter. Il est donc impossible de déduire de manière précise la structure des particules métalliques par la seule expérience, sans aucune comparaison avec des spectres simulés. La mise en place de modèles théoriques devient alors nécessaire. Nous mettons donc en oeuvre une approche associant expériences XANES haute résolution in situ et simulations quantiques, ces dernières visant à la proposition de modèles structuraux pertinents, à la quantification de la réactivité des agrégats et au calcul des caractéristiques spectrales pour comparaison à l'expérience. L'identification de la morphologie des particules, de l'interaction métal-support et du taux de couverture en H est ainsi rendue possible par l'association de l'expérience et du calcul. La bibliothèque de modèles existants de particules monométalliques de Pt supportées sur de l'alumine Gamma avec ou sans hydrogène adsorbé, est complétée par des modèles hydrogénés sur la face (110) et par des modèles de différentes tailles hydrogénés sur la face (100). Cette bibliothèque devenue assez complète a permis une étude de l'influence de la taille des particules, de leur morphologie, de leur structure électronique, des différentes face de l'alumine Gamma, ainsi que du taux de couverture en hydrogène sur la signature des spectres XANES. Cette première étude des catalyseurs monométalliques de platine, se conclue par la discrimination de certaines morphologies, mais surtout la quantification du taux de couverture en hydrogène des particules. Ensuite, des modèles de particules bimétalliques platine – étain supportés sur la face (100) de l'alumine Gamma sont élaborés avec adsorption d'hydrogène. Ces modèles permettent de mieux comprendre l'influence de l'étain sur la morphologie, les propriétés électroniques et l'interaction avec le support et l'hydrogène de ces agrégats. Différentes compositions ont été explorées, ce qui a apporté des informations sur la dilution du platine par l'étain. L'adsorption d'hydrogène a alors été étudiée sur des agrégats de Pt10Sn3 supportées sur la face (100) de l'alumine Gamma. Bien que de nombreux paramètres ne sont pas encore pris en compte dans ces modèles, la comparaison à l'expérience permet déjà d'avoir une première approximation sur la description de systèmes bimétalliques. / The study of metallic nanoclusters supported on oxides is of paramount fundamental and technological importance, particularly in the field of energy. The nanoparticles based on platinum supported on gamma alumina are widely used as highly dispersed heterogeneous catalysts especially under reducing hydrogen atmosphere. Their reactivity and selectivity are intimately related to the local geometry and the electronic density of active sites. These are particularly difficult to define, given the very small size of the studied particles (about 0.8 nm in diameter). XANES (X-Ray Absorption Near Edge Structure) spectroscopy requiring synchrotron radiation, is one of the most appropriate tools to study these systems, especially in situ, at the atomic scale. Indeed the XANES spectra are influenced by the geometry and symmetry of the atoms local environment (especially angles between bonds), the degree of oxidation, the bond types involved, and the electronic structure of the system . All these factors are nevertheless difficult to differentiate and even to interpret. It is therefore impossible to infer accurately the structure of the metal particles by experience alone, without any comparison with simulated spectra. The establishment of theoretical models becomes necessary. We are implementing an approach that combines high-resolution XANES experiments in situ and quantum simulations, the latter aimed at proposing relevant structural models to quantify the reactivity of the particles and calculating spectral characteristics for comparison to experiment. The identification of the clusters morphologies, the metal-support interaction and the hydrogen coverage is made possible combining experiments and quantum calculations. The library of existing monometallic Pt particles models supported on Gamma alumina with or without adsorbed hydrogen, is refined. New models considering the two main surface of Gamma alumina, the particle size and hydrogen adsorption are developed. This extended library of models enabled a study of the effect of particle size, morphology, electronic structure, different alumina faces, and the hydrogen coverage on the signature of XANES spectra. This first study of monometallic platinum catalysts, concludes with the discrimination of the morphologies, but especially with the quantification of the hydrogen coverage of the particles for each temperature and hydrogen pressure experimental condition. Then, models of bimetallic Platinum-tin particles supported on the (100) Gamma alumina face are performed with hydrogen adsorption. These models provide insights into the effect of tin on the morphology, the electronic properties and the interaction with the support and hydrogen of these clusters. Different compositions were explored, which provided information on the dilution of platinum by tin. The adsorption of hydrogen was then studied on Pt10Sn3 clusters supported on the (100) face of alumina. Although many parameters are not yet included in these models, the comparison to the experience already provides a first approximation to the description of bimetallic systems.

A computação quântica é um modelo computacional baseado nas leis da mecânica quântica, que pode ser utilizado para desenvolver algoritmos mais eficientes que seus correspondentes clássicos. O desenvolvimento de algoritmos quânticos eficientes, no entanto, é uma tarefa altamente desafiadora. Uma abordagem recente que vem se mostrando bem-sucedida é a utilização de caminhadas quânticas. Neste trabalho, estudamos a caminhada quântica no hipercubo, calculando analiticamente sua distribuição estacionária e analisando propriedades de seu mixing time, tanto na situação ideal como na situação com descoerência gerada por ligações interrompidas. Também estudamos a caminhada na malha bidimensional, calculando sua distribuição estacionária analiticamente e explorando a relação entre o mixing time e a complexidade do algoritmo de busca nesse grafo. Desenvolvemos uma ferramenta computacional para simulação numérica de caminhadas quânticas em malhas uni- e bidimensionais com diversas condições de contorno. Finalmente, estudamos alguns algoritmos de busca em grafos e analisamos numericamente o impacto que a descoerência exerce sobre seus desempenhos. / Quantum computing is a model of computation based on the laws of quantum mechanics, which can be used to develop faster algorithms. The development of efficient quantum algorithms, however, is a highly challenging task. A recent successful approach is the use of quantum walks. In this work, we have studied the quantum walk on the hypercube, obtaining the exact stationary distribution and analyzing properties of its mixing time both in the ideal and in the noisy set-ups, with noise generated by broken links. We have also studied the walk in a two-dimensional grid, where we have obtained its stationary distribution analytically and have explored the relation between mixing time and the complexity of the search algorithm for this graph. We have developed a computational tool for numerical simulation of quantum walks in one- and two-dimensional grids with several boundary conditions. Finally, we have studied some algorithms for search on graphs and have numerically analyzed the impact of decoherence over their performances.

Submitted by ANDRE RAMALHO DOS SANTOS null (ramalho_inf@yahoo.com.br) on 2018-02-14T03:20:16Z No. of bitstreams: 1 Dissertação André Ramalho.final.pdf: 2789018 bytes, checksum: d4170ea3aaec8f302b447a0aac5e5986 (MD5) / Approved for entry into archive by Ana Paula Santulo Custódio de Medeiros null (asantulo@rc.unesp.br) on 2018-02-14T16:54:15Z (GMT) No. of bitstreams: 1 santos_ar_me_rcla.pdf: 2620534 bytes, checksum: cb88b11f48c3fc7b2fef3c938febb8e0 (MD5) / Made available in DSpace on 2018-02-14T16:54:15Z (GMT). No. of bitstreams: 1 santos_ar_me_rcla.pdf: 2620534 bytes, checksum: cb88b11f48c3fc7b2fef3c938febb8e0 (MD5) Previous issue date: 2017-11-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Nós estudamos teoricamente como o calor e a eletricidade são afetados pela sobreposição de dois férmions de Majorana (MFs, de Majorana fermions em Inglês), os quais estão isolados nas bordas de um fio topológico de Kitaev, em particular, na forma de “ferradura”. É considerado que esse fio está assimetricamente acoplado a um único ponto quântico (QD, de Quantum dot em Inglês) hibridizado com contatos metálicos. Em baixas temperaturas e dependente do nível de energia desse QD, nós mostramos que ao ajustar a assimetria acima, as respostas ressonantes das condutâncias termoelétricas mudam inesperadamente de forma drástica. Assim, propomos como aplicação, um sintonizador termoelétrico em nanoescala assistido por MFs. / We study theoretically in a topological U-shaped Kitaev wire, with Majorana fermions (MFs) on the edges, how heat and electricity are affected by them when found overlapped. The asymmetric regime of their couplings with a single quantum dot (QD) hybridized with metallic leads is considered. At low temperatures and dependent upon the QD energy level, we show that by tuning this asymmetry, the resonance positions of the thermoelectrical conductances change drastically. Thereby, the tuner of heat and electricity here proposed is constituted.