L'approximation adiabatique en mécanique quantique stipule que si un système quantique évolue assez lentement, alors il demeurera dans le même état propre. Récemment, une faille dans l'application de l'approximation adiabatique a été découverte. Les limites du théorème seront expliquées lors de sa dérivation. Ce mémoire à pour but d'optimiser la probabilité de se maintenir dans le même état propre connaissant le système initial, final et le temps d'évolution total. Cette contrainte sur le temps empêche le système d'être assez lent pour être adiabatique. Pour solutionner ce problème, une méthode variationnelle est utilisée. Cette méthode suppose connaître l'évolution optimale et y ajoute une petite variation. Par après, nous insérons cette variation dans l'équation de la probabilité d'être adiabatique et développons en série. Puisque la série est développée autour d'un optimum, le terme d'ordre un doit nécessairement être nul. Ceci devrait nous donner un critère sur l'évolution la plus adiabatique possible et permettre de la déterminer. Les systèmes quantiques dépendants du temps sont très complexes. Ainsi, nous commencerons par les systèmes ayant des énergies propres indépendantes du temps. Puis, les systèmes sans contrainte et avec des fonctions d'onde initiale et finale libres seront étudiés. / The adiabatic approximation in quantum mechanics states that if the Hamiltonian of a physical system evolves slowly enough, then it will remain in the instantaneous eigenstate related to the initial eigenstate. Recently, two researchers found an inconsistency in the application of the approximation. A discussion about the limit of this idea will be presented. Our goal is to optimize the probability to be in the instantaneous eigenstate related to the initial eigenstate knowing the initial and final system, with the total time of the experiment fixed to $T$. This last condition prevents us from being slow enough to use the adiabatic approximation. To solve this problem, we turn to the calculus of variation. We suppose the ideal evolution is known and we add a small variation to it. We take the result, put it in the probability to be adiabatic and expand in powers of the variation. The first order term must be zero. This enables us to derive a criterion which will give us conditions on the ideal Hamiltonian. Those conditions should define the ideal Hamiltonian. Time dependent quantum systems are very complicated. To simplify the problem, we will start by considering systems with time independent energies. Afterward, the general case will be treated.

The ultimate goal in the rapidly burgeoning field of spintronics is to realize semiconductor-based devices that utilize the spin degree of freedom of a single charge carrier (electron or hole) or an ensemble of such carriers to achieve novel and/or enhanced device functionalities such as spin based light emitting devices, spin transistors and femto-Tesla magnetic field sensors. These devices share a common feature: they all rely on controlled transport of spins in semiconductors. A prototypical spintronic device has a transistor-like configuration in which a semiconducting channel is sandwiched between two contacts (source and drain) with a gate electrode sitting on top of the channel. Unlike conventional charge-based transistors, the source electrode of a spin transistor is a ferromagnetic (or half-metallic) material which injects spin polarized electrons in the channel. During transit, the spin polarizations of the electrons are controllably rotated by a gate electric field mediated spin-orbit coupling effect. The drain contact is ferromagnetic (or half-metallic) as well and the transmission probability of an electron through this drain electrode depends on the relative orientation of electron spin polarization and the (fixed) magnetization of the drain. When the spins of the electrons are parallel to the drain magnetization, they are transmitted by the drain resulting in a large device current (ON state of spin FET). However, these electrons will be completely blocked if their spins are antiparallel to the drain magnetization, and ideally, in this situation device current will be zero (OFF state of spinFET). Thus, if we vary the gate voltage, we can modulate the channel current by controlling the spin orientations of the electrons with respect to the drain magnetization. This is how transistor action is realized (Datta-Das model). However, during transport, electrons' velocities change randomly with time due to scattering and hence different electrons experience different spin-orbit magnetic fields. As a result, even though all electrons start their journey with identical spin orientations, soon after injection spins of different electrons point along different directions in space. This randomization of initial spin polarization is referred to as spin relaxation and this is detrimental to the spintronic devices. In particular, for Datta-Das transistor, this will lead to inefficient gate control and large leakage current in the OFF state of the spinFET. The aim of this work is to understand various spin relaxation processes that are operative in semiconductor nanostructures and to indicate possible ways of minimizing them. The theoretical aspect of this work (Chapters 2-5) focuses on the D'yakonov-Perel' process of spin relaxation in a semiconductor quantum wire. This process of spin relaxation occurs because during transport electron spin precesses like a spinning top about the spin-orbit magnetic field. We show that the conventional drift-diffusion model of spin transport, which has been used extensively in literature, completely breaks down in case of a quantum confined system (e.g. a quantum wire). Our approach employs a semi-classical model which couples the spin density matrix evolution with the Boltzmann transport equation. Using this model we have thoroughly studied spin relaxation in a semiconductor quantum wire and identified several inconsistencies of the drift-diffusion formalism.The experimental side of this work (Chapters 6-8) deals with two different issues: (a) performing spin transport experiments in order to extract spin relaxation length and time in various materials (e.g. Cu, Alq3) under one-dimensional confinement, and (b) measurement of the ensemble spin dephasing time in self-assembled cadmium sulfide quantum dots using electron spin resonance technique. The spin transport experiment, as described in Chapter 7 of this dissertation, shows that the spin relaxation time in organic semiconductor (Alq3) is extremely long, approaching a few seconds at low temperatures. Alq3 is the chemical formula of tris- 8 hydroxy-quinoline aluminum, which is a small molecular weight organic semiconductor. This material is extensively used in organic display industry as the electron transport and emission layer in green organic light emitting diodes. The long spin relaxation time in Alq3 makes it an ideal platform for spintronics. This also indicates that it may be possible to realize spin based organic light emitting diodes which will have much higher internal quantum efficiency than their conventional non-spin counterparts. From spin transport experiments mentioned above we have also identified Elliott-Yafet mode as the dominant spin relaxation mechanism operative in organic semiconductors. Electron spin resonance experiment performed on self-assembled quantum dots (Chapter 8) allows us to determine the ensemble spin dephasing time (or transverse spin relaxation time) of electrons confined in these systems. In quantum dots electrons are strongly localized in space. Surprisingly, the ensemble spin dephasing time shows an increasing trend as we increase temperature. The most likely explanation for this phenomenon is that spin dephasing in quantum dots (unlike quantum wells and wires) is dominated by nuclear hyperfine interaction, which weakens progressively with temperature. We hope that our work, which elaborates on all of the above mentioned topics in great detail, will be a significant contribution towards the current state of knowledge of subtle spin-based issues operative in nanoscale device structures, and will ultimately lead to realization of novel nano-spintronic devices.

Le sujet porte sur une classe de codes correcteurs d erreurs dits codes cycliques tordus, et ses applications a l'Informatique quantique et aux codes quasi-cycliques. Les codes cycliques classiques ont une structure d'idéaux dans un anneau de polynômes. Ulmer a introduit en 2008 une généralisation aux anneaux dits de polynômes tordus, une classe d'anneaux non commutatifs introduits par Ore en 1933. Dans cette thèse on explore le cas du corps a quatre éléments et de l'anneau produit de deux copies du corps a deux éléments. / The topic of the thesis is the study of skew cyclic codes, with application to Quantum Computing and quasi-cyclic codes. Classical cyclic codes have a natural structure of ideals in a polynomial ring. This was generalized by Ulmer in 2008 to skew polynomial rings, a class of non commutative rings introduced by Ore in 1933. The latter codes are not classically cyclic if the alphabet ring admits a non trivial automorphism. In this work is explored the cases of the finite field of order four and of a product ring of two copies of the finite field of order two.

Nesta dissertação estudamos, no âmbito teórico, algumas propostas recentes de processamento de informação quântica passiva, isto é, descartando protocolos de correção de erros. Recorrendo à criação de subespaços livres de decoerência através de um sistema físico de quatro spins acoplados ao resto do universo por um agente degenerado, mostramos ser possível construir um conjunto universal de portas lógicas (C-NOT, T e Hadamard) neste mesmo subespaço, alcançando, por conseguinte, a realização de qualquer operação computacional, insensivelmente ao resto do universo. Partimos de um hamiltoniano geral com interações individuais de cada spin com campos externos, além de acoplamentos controlados entre pares de spins. Experimentalmente, hamiltonianos deste tipo são comuns no contexto de junções Josephson, motivo pelo qual tratamos esta implementação em um capítulo especial. Introduzindo perturbativamente ao hamiltoniano operadores espúrios ao subespaço livre de decoerência, incluímos sensibilidade do sistema frente ao ambiente, criando a possibilidade da incursão de erros através de mecanismos de dissipação. Tais mecanismos foram investigados em termos da intensidade do parâmetro de acoplamento entre o sistema e o ambiente, revelando uma clara evidência teórica do Efeito Zenão Quântico, através da excelente concordância entre resultados de operações realizadas em subespaços livres de decoerência e operações realizadas em sistemas fortemente acoplados ao resto do universo. Neste sentido, selecionamos a fidelidade como medida de distância entre um estado em evolução a partir de um certo estado inicial do subespaço livre de decoerência (e submetido a dissipação), e um estado em evolução regida pela mesma operação quântica e a partir das mesmas condições iniciais no caso ideal, livre de decoerência. Essa abordagem explícita permitiu-nos obter a razão necessária entre os parâmetros associados a perturbação (que remove o estado do subespaço original) e acoplamento (entendido como a freqüência entre as medidas promovidas pelo resto do universo), para alcançar a eficiência desejada na realização de uma certa porta lógica. Tecnicamente, o trabalho envolveu vários resultados matemáticos novos e operacionalmente úteis, levando a simplificações importantes durante os cálculos envolvidos. / In this dissertation we studied theoretical aspects of some recent proposals of passive quantum information processing, that is, discarding error correction protocols. Falling back upon the creation of decoherence-free subspaces through a physical system of four spins coupled to the rest of the universe by a degenerate agent, we showed to be possible to build a universal set of logical quantum gates (C-NOT, T and Hadamard) in this same subspace, reaching, consequently, the accomplishment of any computational operation, callously to the rest of the universe. We started from a general Hamiltonian with individual interactions of each spin with external fields, besides controlled couplings between spin pairs. Experimentally, Hamiltonians like this are common in the context of Josephson junctions and, therefore, we treated this implementation in a special chapter. Perturbatively introducing spurious operators to the hamiltonian in the decoherence-free subspace, we included sensibility of the system to the environment, creating the possibility of the incursion of errors through dissipation mechanisms. Such mechanisms were investigated in terms of the intensity of the coupling parameter between the system and the environment, revealing an obvious theoretical evidence of the Quantum Zeno Effect, through the excellent agreement between the results of operations accomplished in decoherence-free subspace and operations accomplished in systems strongly coupled to the rest of the universe. In this sense, we selected the fidelity as the distance measure between a state in evolution starting from a certain initial state of the decoherence-free subspace (and submitted to the dissipation), and a state in evolution governed by the same quantum operation and starting from the same initial conditions in the ideal decoherence-free case. This explicit approach allowed us to obtain the necessary quotient between the associated disturbance parameter (that removes the state from the original subspace) and coupling parameter (understood as the frequency between the measurements promoted by the rest of the universe), to reach the efficiency desired in the accomplishment of a logic gate. Technically, the work involved several new operationally useful mathematical results, leading to important simplifications during the involved calculations.

Made available in DSpace on 2015-03-04T18:50:52Z (GMT). No. of bitstreams: 1 thesis.pdf: 6097890 bytes, checksum: 7eea019378a8126c37befefac84557cb (MD5) Previous issue date: 2007-06-15 / Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Caminhos aleatórios clássicos são essenciais para a Física, a Matemática, a Ciência da Computação e muitas outras áreas. Há uma grande expectativa que a sua versão quântica seja ainda mais poderosa, uma vez que o caminhante quântico se espalha quadraticamente mais rápido que o seu análogo clássico. Neste trabalho, estudamos o comportamento do caminhante quântico em uma e duas dimensões, além de generalizarmos o formalismo de ligações interrompidas para duas ou mais dimensões. Em uma dimensão, analisamos o comportamento do caminhante quântico, que além das duas possibilidades de deslocamento usuais, direita e esquerda, também permanece na posição atual. Em duas dimensões, apresentamos um estudo detalhado do comportamento do caminhante no plano e quando há descoerência gerada pela quebra aleatória das ligações para as posições vizinhas com uma certa probabilidade para cada uma das direções. Quando essa probabilidade de quebra é diferente nas duas direções encontramos um resultado não trivial que representa uma transição do caso 2-D descorente para o caso 1-D coerente. Também utilizamos o formalismo de ligações interrompidas para modelar o comportamento de um caminhante quântico que passa por uma e por duas fendas. Realizamos simulações com com as principais moedas e observamos conclusivamente os padrões de interferência e difração.

Made available in DSpace on 2015-03-04T18:51:17Z (GMT). No. of bitstreams: 1 thesisMarquezino.pdf: 1984026 bytes, checksum: aab2f346b43ad780233318adb7219d76 (MD5) Previous issue date: 2010-02-26 / Conselho Nacional de Desenvolvimento Cientifico e Tecnologico / 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. / 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.

Submitted by Maria Cristina (library@lncc.br) on 2015-09-23T18:31:34Z No. of bitstreams: 1 tese_pedro.pdf: 954527 bytes, checksum: e9834fab8c799933912f185f0a422658 (MD5) / Approved for entry into archive by Maria Cristina (library@lncc.br) on 2015-09-23T18:31:58Z (GMT) No. of bitstreams: 1 tese_pedro.pdf: 954527 bytes, checksum: e9834fab8c799933912f185f0a422658 (MD5) / Made available in DSpace on 2015-09-23T18:32:21Z (GMT). No. of bitstreams: 1 tese_pedro.pdf: 954527 bytes, checksum: e9834fab8c799933912f185f0a422658 (MD5) Previous issue date: 2015-04-22 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / Optimization algorithms are known to have a wide range of applications in various areas of knowledge. Thus, any improvement in the performance of optimization algorithms generate great impact in solving various problems. Thus, this work indroduces the area of quantum algorithms for global optimization (maximization/minimization) of continuous functions through different quantum search methods and classical local optimization algorithms. In this case, the use of search quantum algorithms is tied directly to performance with respect to the classical method: using a quantum computer can find an element in an unsorted database using only $O(\sqrt{N})$ queries. / Algoritmos de otimização são conhecidos por apresentarem uma vasta gama de aplicações em diversas áreas do conhecimento. Desta forma, qualquer melhoria no desempenho dos algoritmos de otimização gera grande impacto na resolução de diversos problemas. Neste sentido, este trabalho introduz a área de algoritmos quânticos para a otimização global (maximização/minimização) de funções contínuas através de diferentes métodos quânticos de busca e algoritmos clássicos de otimização local. Neste caso, a utilização de algoritmos quânticos de busca está diretamente associada ao desempenho com relação ao método clássico: usando um computador quântico pode-se encontrar um elemento em um banco de dados não-ordenado usando apenas $O(\sqrt{N})$ consultas.

String diagrams turn algebraic equations into topological moves that have recurring shapes, involving the sliding of one diagram past another. We individuate, at the root of this fact, the dual nature of polygraphs as presentations of higher algebraic theories, and as combinatorial descriptions of "directed spaces". Operations of polygraphs modelled on operations of topological spaces are used as the foundation of a compositional universal algebra, where sliding moves arise from tensor products of polygraphs. We reconstruct several higher algebraic theories in this framework. In this regard, the standard formalism of polygraphs has some technical problems. We propose a notion of regular polygraph, barring cell boundaries that are not homeomorphic to a disk of the appropriate dimension. We define a category of non-degenerate shapes, and show how to calculate their tensor products. Then, we introduce a notion of weak unit to recover weakly degenerate boundaries in low dimensions, and prove that the existence of weak units is equivalent to a representability property. We then turn to applications of diagrammatic algebra to quantum theory. We re-evaluate the category of Hilbert spaces from the perspective of categorical universal algebra, which leads to a bicategorical refinement. Then, we focus on the axiomatics of fragments of quantum theory, and present the ZW calculus, the first complete diagrammatic axiomatisation of the theory of qubits. The ZW calculus has several advantages over ZX calculi, including a computationally meaningful normal form, and a fragment whose diagrams can be read as setups of fermionic oscillators. Moreover, its generators reflect an operational classification of entangled states of 3 qubits. We conclude with generalisations of the ZW calculus to higher-dimensional systems, including the definition of a universal set of generators in each dimension.

The decline of Moore's law has catalyzed a significant effort to identify beyond-CMOS devices and architectures for the coming decades. A multitude of classical and quantum systems have been proposed to address this challenge, and spintronics has emerged as a promising approach for these post-Moore systems. Many of these architectures are tailored specifically for applications in combinatorial optimization and machine learning. Here we propose the use of spintronics for such applications by exploring two distinct but related computing paradigms. First, the use of spin-currents to manipulate and control quantum information is investigated with demonstrated high-fidelity gate operation. This control is accomplished through repeated entanglement and measurement of a stationary qubit with a flying-spin through spin-torque like effects. Secondly, by transitioning from single-spin quantum bits to larger spin ensembles, we then explore the use of stochastic nanomagnets to realize a probabilistic system that is intrinsically governed by Boltzmann statistics. The nanomagnets explore the search space at rapid speeds and can be used in a wide-range of applications including optimization and quantum emulation by encoding the solution to a given problem as the ground state of the equivalent Boltzmann machine. These applications are demonstrated through hardware emulation using an all-digital autonomous probabilistic circuit.

<p>The effects of open system evolution on single particle interferometry, quantum computation, and the adiabatic approximation are investigated.</p><p>Single particle interferometry: Three concepts concerning completely positive maps (CPMs) and trace preserving CPMs (channels), named subspace preserving (SP) CPMs, subspace local channels, and gluing of CPMs, are introduced. SP channels preserve probability weights on given orthogonal sum decompositions of the Hilbert space of a quantum system. Subspace locality determines what channels act locally with respect to such decompositions. Gluings are the possible total channels obtainable if two evolution devices, characterized by channels, act jointly on a superposition of a particle in their inputs. It is shown that gluings are not uniquely determined by the two channels. We determine all possible interference patterns in single particle interferometry for given channels acting in the interferometer paths. It is shown that the standard interferometric setup cannot distinguish all gluings, but a generalized setup can.</p><p>Quantum computing: The robustness of local and global adiabatic quantum search subject to decoherence in the instantaneous eigenbasis of the search Hamiltonian, is examined. In both the global and local search case the asymptotic time-complexity of the ideal closed case is preserved, as long as the Hamiltonian dynamics is present. In the case of pure decoherence, where the environment monitors the search Hamiltonian, it is shown that the local adiabatic quantum search performs as the classical search with scaling N, and that the global search scales like N^3/2 , where N is the list length. We consider success probabilities p<1 and prove bounds on the run-time with the same scaling as in the conditions for the p → 1 limit.</p><p>Adiabatic evolution: We generalize the adiabatic approximation to the case of open quantum systems in the joint limit of slow change and weak open system disturbances. </p>