This thesis is concerned with the development of an intermediate magnetic field "clock-qubit" in ⁴³Ca⁺ at 146G and techniques to manipulate this qubit using microwaves and lasers. While ⁴³Ca⁺ has previously been used as a qubit, its relatively complicated level structure - with a nuclear spin of 7/2 and low-lying D-states -- makes cooling it in the intermediate field an intimidating prospect. As a result, previous experiments have used small magnetic fields of a few gauss where coherence times are limited and off-resonant excitation is a significant source of experimental error. We demonstrate a simple scheme that allows ⁴³Ca⁺ to be cooled in the intermediate field without any additional experimental complexity compared with low fields. Using the clock-qubit, we achieve a coherence time of T^*<sub style='position:relative;left:-.5em;'>2</sub> = 50 (10)s - the longest demonstrated in any single qubit. We also demonstrate a combined state preparation and measurement error of 6.8(6)x 10^-4 - the lowest achieved for a hyperfine trapped ion qubit [NVG⁺13] - and single-qubit logic gates with average errors of 1.0(3) x 10^-6 - more than an order of magnitude better than the previous record [BWC⁺11]. These results represent the state-of-the-art in the field of single-qubit control. Moreover, we achieve them all in a single scalable room-temperature ion trap using experimentally robust techniques and without relying on the use of narrow-linewidth lasers, magnetic field screening or dynamical decoupling techniques. We also present work on a recent scheme [OWC⁺11] to drive two-qubit gates using microwaves. We have constructed an ion trap with integrated microwave circuitry to perform these gates. Using this trap, we have driven motional sideband transitions, demonstrating the spin-motion coupling that underlies the two-qubit gate. We present an analysis of likely sources of experimental error during a future two-qubit gate and the design and preliminary characterisation of apparatus to minimise the main error contributions. Using this apparatus, we hope to perform a two-qubit gate in the near future.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The goal of this thesis is to present evolutionary algorithms, and demonstrate their applicability in quantum computing. As an introduction to evolutionary algorithms, it is applied to the simple but still challenging (from a computational viewpoint) Travelling Salesman Problem (TSP). This example is used to illustrate the e ect of various parameters like selection method, and maximum population size on the accuracy and e ciency of the evolutionary algorithms. For the sample problem, the 48 continental state capitals of the USA, solutions are evolved and compared to the known optimal solution. From this investigation tournament selection was shown to be the most e ective selection method, and that a population of 200 individuals per generation gave the most e ective convergence rates. In the next part of the thesis, evolutionary algorithms are applied to the generation of optimal quantum circuits for the following cases: The identity transformation : Picked for its simplicity as a test of the correct implementation of the evolutionary algorithm. The results of this investigation showed that the solver program functions correctly and that evolutionary algorithms can indeed nd valid solutions for this kind of problem. The work by Ding et al. [16] on optimal circuits for the two-qubit entanglement gate, controlled-S gate as well as the three qubit entanglement gate are solved by means of EA and the results compared. In all cases similar circuits are produced in fewer generations than the application of Ding et al. [16]. The three qubit quantum Fourier transform gate was also attempted, but no convergence was attained. The quantum teleportation algorithm is also investigated. Firstly the nature of the transformation that leads to quantum teleportation is considered. Next an e ective circuit is sought using evolutionary algorithms. The best result is one gate longer than Brassard [11], and seven gates longer than Yabuki [61]. / AFRIKAANSE OPSOMMING: Die doel van hierdie tesis is om evolusionêre algoritmes te ondersoek en hulle toepaslikheid op kwantumkomputasie te demonstreer. As 'n inleiding tot evolusionêre algoritmes is die eenvoudige, maar steeds komputasioneel uitdagende handelsreisigerprobleem ondersoek. Die invloed van die keuse van 'n seleksie metode, sowel as die invloed van die maksimum aantal individue in 'n generasie op die akkuraatheid en e ektiwiteit van die algoritmes is ondersoek. As voorbeeld is die 48 kontinentale hoofstede van die state van die VSA gekies. Die oplossings wat met evolusionêre algoritmes verkry is, is met die bekende beste oplossings vergelyk. Die resultate van hierdie ondersoek was dat toernooi seleksie die mees e ektiewe seleksie metode is, en dat 200 individue per generasie die mees e ektiewe konvergensie tempo lewer. Evolusionêre algoritmes word vervolgens toegepas om optimale oplossings vir die volgende kwantumalgoritmes te genereer: Die identiteitstransformasie: Hierdie geval is gekies as 'n eenvoudige toepassing met 'n bekende oplossing. Die resultaat van hierdie toepassing van die program was dat dit korrek funksioneer, en vinnig by die korrekte oplossings uitkom. Vervolgens is daar ondersoek ingestel na vier van die gevalle wat in Ding et al. [16] bespreek word. Die spesi eke transformasies waarna gekyk is, is 'n optimale stroombaan vir twee kwabis verstrengeling, 'n beheerde-S hek, 'n drie kwabis verstrengelings hek, en 'n drie kwabis kwantum Fourier transform hek. In die eerste drie gevalle stem die oplossings ooreen met die van Ding et al. [16], en is die konvergensie tempo vinniger. Daar is geen oplossing vir die kwantum Fourier transform verkry nie. Laastens is daar na die kwantumteleportasiealgoritme gekyk. Die eerste stap was om te kyk na die transformasie wat in hierdie geval benodig word, en daarna is gepoog om 'n e ektiewe stroombaan te evolueer. Die beste resultaat was een hek langer as Brassard [11], en sewe hekke langer as Yabuki [61].

The purpose of this thesis is the theoretical study of interference and correlation effects in multimode and continuum mode quantum systems. We are concerned with interference effects in multiport devices which in a sense are generalised Mach-Zehnder interferometers. It is shown how these multimode devices can be employed for the study of negative result and interaction free measurements. Interference and coherence effects are also studied in relation to the radiation fields generated by atoms through the process of spontaneous emission. Besides first order interference, higher order coherence effects are investigated with the aid of Glauber's photodetection theory and it is found that detectors that lie in spacelike regions may display nonclassical correlations under certain conditions. It is well known that the vanishing of field commutators between regions that cannot be connected by subluminal signals reflects the locality of quantum field theory. But is it possible that these spacelike regions exhibit correlations that violate Bell type inequalities? This is the main question and principal concern of the thesis and the answer is affirmative, nonclassical correlations between spacelike regions are indeed possible. A scheme of four detectors that lie in spacelike points was also studied. In this case we do not consider the radiation field but a free scalar field in vacuum state. Nevertheless the virtual quanta of this field may induce nonclassical correlations if the intervals between the detectors are spacelike but small enough. The fundamental reason for this fact is the nonvanishing of the Feynman propagator outside the light cone. Since this propagator is decaying expotentially with the distance it is demonstrated that for large spacelike intervals field correlations obey classical inequalities. We should also note that different inertial observers will agree on the violation or not of these inequalities since the results are manifestly Lorentz invariant.

The potential impact of quantum computing has stimulated a worldwide effort to develop the necessary experimental and theoretical resources. In the race for the quantum computer, several candidate systems have emerged, but the ultimate system is still unclear. We study theoretically how to realize atomic Fock states both for fermionic and bosonic atoms, mainly in one-dimensional optical traps. We demonstrate a new approach of quantum computing based on ultracold fermionic atomic Fock states in optical traps. With the Pauli exclusion principle, producing fermionic atomic Fock states in optical traps is straightforward. We find that laser culling of fermionic atoms in optical traps can produce a scalable number of ultra-high fidelity qubits. We show how each qubit can be independently prepared, and how to perform the required entanglement operations and detect the qubit states with spatially resolved, single-atom detection with adiabatic trap-splitting and fluorescence imaging. On the other hand, bosonic atoms have a strong tendency to stay together. One must rely on strong repulsive interactions to produce bosonic atomic Fock states. To simulate the physical conditions of producing Fock states with ultracold bosonic atoms, we study a many-boson system with arbitrary interaction strength using the Bethe ansatz method. This approach provides a general framework, enabling the study of Fock state production over a wide range of realistic experimental parameters. / text

Single atoms are promising candidates for physically implementing quantum bits, the fundamental unit of quantum information. We have built an apparatus for cooling, trapping and imaging single rubidium atoms in microscopic optical tweezers. The traps are formed from a tightly focused off-resonant laser beam, which traps atoms using the optical dipole force. The traps have a diameter of ~1 &mu;m and a depth of ~1 mK. The novelty of our approach is the use a digital mirror device (DMD) to generate multiple independently movable tweezers from a single laser beam. The DMD consists of an array of micro-mirrors that can be switched on and off, thus acting as a binary amplitude modulator. We use the DMD to imprint a computer-generated hologram on the laser beam, which is converted in to the desired arrangement of traps in the focal plane of a lens. We have developed fast algorithms for calculating binary holograms suitable for the DMD. In addition, we use this method to measure and correct for errors in the phase of the wavefront caused by optical aberrations, which is necessary for producing diffraction-limited focal spots. Using this apparatus, we have trapped arrays of up to 20 atoms with arbitrary geometrical arrangements. We exploit light-assisted collisions between atoms to ensure there is at most one atom per trapping site. We measure the temperature of the atoms in the traps to be 12 &mu;K, and their lifetime to be 1.4 s. Finally, we demonstrate the ability to select individual atoms from an array and transport them over a distance of 14μm with laser cooling, and 5 &mu;m without.

<p>Atomic ions trapped in microfabricated surface traps can be utilized as a physical platform with which to build a quantum computer. They possess many of the desirable characteristics of such a device, including high fidelity state preparation and readout, universal logic gates, and long coherence times, and can be readily entangled with each other through photonic interconnects. The use of optical cavities integrated with trapped ion qubits as a photonic interface presents the possibility for order of magnitude improvements in performance in several key areas for their use in quantum computation. The first part of this thesis describes the design and fabrication of a novel surface trap for integration with an optical cavity. The trap is custom made on a highly reflective mirror surface and includes the capability of moving the ion trap location along all three trap axes with nanometer scale precision. The second part of this thesis demonstrates the suitability of small microcavities formed from laser ablated, fused silica substrates with radii of curvature in the 300-500 micron range for use with the mirror trap as part of an integrated ion trap cavity system. Quantum computing applications for such a system include dramatic improvements in the photon entanglement rate of up to 10 kHz, the qubit measurement time down to 1 microsecond, and the qubit measurement error rate down to the 1e-5 range. The final part of this thesis describes a performance simulator for exploring the physical resource requirements and performance demands to scale a quantum computer to sizes capable of implementing quantum algorithms beyond the limits of classical computation.</p> / Dissertation

Cavity quantum electrodynamics (cavity QED) with single atoms and single photons provides a promising route toward scalable quantum information processing (QIP) and computing. A strongly coupled atom-cavity system should act as a universal quantum interface, allowing the generation and storage of quantum information. This thesis describes the realisation of an atom-cavity system used for the production and manipulation of single photons. These photons are shown to exhibit strong sub-Poissonian statistics and indistinguishability, both prerequisites for their use in realistic quantum systems. Further, the ability to control the temporal shape and internal phase of the photons, as they are generated in the cavity, is demonstrated. This high degree of control presents a novel mechanism enabling the creation of arbitrary photonic quantum bits.

A descoberta do algoritmo de Shor, para a fatoração de inteiros em tempo polinomial, motivou esforços rumo a implementação de um computador quântico. Ele é capaz de quebrar os principais criptossistemas de chave pública usados hoje (RSA e baseados em curvas elípticas). Estes fornecem diversos serviços de segurança, tais como confidencialidade e integridade dos dados e autenticação da fonte, além de possibilitar a distribuição de uma chave simétrica de sessão. Para quebrar estes criptossistemas, um computador quântico grande (2000 qubits) é necessário. Todavia, alternativas começaram a ser investigadas. As primeiras respostas vieram da própria mecânica quântica. Apesar das propriedades interessantes encontradas na criptografia quântica, um criptossistema completo parece inatingível, principalmente devido as assinaturas digitais, essenciais para a autenticação. Foram então propostos criptossitemas baseadas em problemas puramente clássicos que (acredita-se) não são tratáveis por computadores quânticos, que são chamadas de pós-quânticas. Estes sistemas ainda sofrem da falta de praticidade, seja devido ao tamanho das chaves ou ao tempo de processamento. Dentre os criptossistemas pós-quânticos, destacam-se o McEliece e o Niederreiter. Por si só, nenhum deles prevê assinaturas digitais, no entanto, as assinaturas CFS foram propostas, complementandos. Ainda que computadores quânticos de propósito geral estejam longe de nossa realidade, é possível imaginar um circuito quântico pequeno e dedicado. A melhoria trazida por ele seria a diferença necessária para tornar essas assinaturas práticas em um cenário legitimamente pós-quântico. Neste trabalho, uma arquitetura híbrida quântica/clássica é proposta para acelerar algoritmos criptográficos pós-quânticos. Dois coprocessadores quânticos, implementando a busca de Grover, são propostos: um para auxiliar o processo de decodificação de códigos de Goppa, no contexto do criptossistema McEliece; outro para auxiliar na busca por síndromes decodificáveis, no contexto das assinaturas CFS. Os resultados mostram que em alguns casos, o uso de um coprocessador quântico permite ganhos de até 99; 7% no tamanho da chave e até 76; 2% em tempo de processamento. Por se tratar de um circuito específico, realizando uma função bem específica, é possível manter um tamanho compacto (300 qubits, dependendo do que é acelerado), mostrando adicionalmente que, caso computadores quânticos venham a existir, eles viabilizarão os criptossistemas pós-quânticos antes de quebrar os criptossistemas pré-quânticos. Adicionalmente, algumas tecnologias de implementação de computadores quânticos são estudadas, com especial enfoque na óptica linear e nas tecnologias baseadas em silício. Este estudo busca avaliar a viabilidade destas tecnologias como potenciais candidatas à construção de um computador quântico completo e de caráter pessoal. / The discovery of the Shor algorithm, which allows polynomial time factoring of integers, motivated efforts towards the implementation of a quantum computer. It is capable of breaking the main current public key cryptosystems used today (RSA and those based on elliptic curves). Those provide a set of security services, such as data confidentiality and integrity and source authentication, and also the distribution of a symmetric session key. To break those cryptosystem, a large quantum computer (2000 qubits) is needed. Nevertheless, cryptographers have started to look for alternatives. Some of which came from quantum mechanics itself. Despite some interesting properties found on quantum cryptography, a complete cryptosystem seems intangible, specially because of digital signatures, necessary to achieve authentication. Cryptosystems based on purely classical problems which are (believed) not treatable by quantum computers, called post-quantum, have them been proposed. Those systems still lacks of practicality, either because of the key size or the processing time. Among those post-quantum cryptosystems, specially the code based ones, the highlights are the McEliece and the Niederreiter cryptosystems. Per se, none of these provides digital signatures, but, the CFS signatures have been proposed, as a complement to them. Even if general purpose quantum computers are still far from our reality, it is possible to imagine a small dedicated quantum circuit. The benefits brought by it could make the deference to allow those signatures, in a truly post-quantum scenario. In this work, a quantum/classical hybrid architecture is proposed to accelerate post-quantum cryptographic algorithms. Two quantum coprocessors, implementing the Grover search, are proposed: one to assist the decoding process of Goppa codes, in the context of the McEliece and Niederreiter cryptosystems; another to assist the search for decodable syndromes, in the context of the CFS digital signatures. The results show that, for some cases, the use of the quantum coprocessor allows up to 99; 7% reduction in the key size and up to 76; 2% acceleration in the processing time. As a specific circuit, dealing with a well defined function, it is possible to keep a small size (300 qubits), depending on what is accelerated), showing that, if quantum computers come to existence, they will make post-quantum cryptosystems practical before breaking the current cryptosystems. Additionally, some implementation technologies of quantum computers are studied, in particular linear optics and silicon based technologies. This study aims to evaluate the feasibility of those technologies as potential candidates to the construction of a complete and personal quantum computer.

An optomechanical system consists of an optical cavity coupled to a mechanical oscillator. The system used for this work was a silica microsphere. In a silica microsphere, the optical cavity is formed by light that is confined by total internal reflection while circulating around the equator of the sphere. The mechanical oscillator is the mechanical breathing motion of the sphere itself. The optical cavity and mechanical oscillator are coupled by radiation pressure and by the mechanical oscillator physically changing the length of the optical cavity. The optomechanical analog to electromagnetically induced transparency (EIT), known as optomechanically induced transparency (OMIT), has previously been studied in its steady state. One topic of this dissertation is an experimental study of OMIT in the time domain. The results of these experimental demonstrations continue comparisons between EIT and OMIT, while also building a foundation for optomechanical light storage. In OMIT, an off-resonance control laser controls the interaction between on-resonance light and the mechanical oscillator. Optomechanical light storage makes use of this arrangement to store an optical signal as a mechanical excitation, which is then retrieved at a later time as an optical signal. This is done by using two temporally separated off-resonance control laser pulses. This technique is extremely flexible in frequency and displays a storage lifetime on the order of microseconds. Use of optomechanical systems for quantum mechanical applications is hindered by the thermal background noise of the mechanical oscillator. Addressing this issue by first cooling the mechanical oscillator is costly and fraught with difficulties. The final topic presented in this dissertation deals with this issue through the use of an optomechanical dark mode. Two optical modes can interact with the same mechanical mode. The dark mode is a state that couples the two optical modes but is decoupled from the mechanical oscillator. While our specific optomechanical system is limited by its somewhat modest optomechanical cooperativity, this conversion process can, in principle, preserve the quantum state of the signal, even at room temperature, opening the possibility for this technique to be applied in quantum information processing.

Made available in DSpace on 2015-03-04T18:50:13Z (GMT). No. of bitstreams: 1 Apresentacao.pdf: 108219 bytes, checksum: 5d45885c1cb3a3bd5830f6b0e8711721 (MD5) Previous issue date: 2006-03-23 / Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Main memory limitations can lower the performance of segmentation applications for large images or even make it undoable. In this work we integrate the T-Surfaces model and Out-of-Core isosurface generation methods in a general framework for segmentation of large image volumes. T-Surfaces is a parametric deformable model based on a triangulation of the image domain, a discrete surface model and an image threshold. Isosurface generation techniques have been implemented through an Out-of-Core method that uses a kd-tree structure, called Meta-Cell technique. By using the Meta-Cell framework, we present an Out-of-Core version of a segmentation method based on T-Surfaces and isosurface extraction. The Gradient Vector Flow (GVF) is an approach based on Partial Differential Equations. This method has been applied together with snake models for image segmentation through boundary extraction. The key idea is to use a diffusion-reaction PDE in order to generate a new external force field that makes snake models less sensitivity to initialization as well as improves the snakes ability to move into boundary concavities. In this work, we firstly review basic results about global optimization conditions of the GVF and numerical considerations of usual GVF schemes. Besides, we present an analytical analysis of the GVF and a frequency domain analysis, which gives elements to discuss the dependency from the parameter values. Also, we discuss the numerical solution of the GVF based in a SOR method. We observe that the model can be used for Multiply Connected Domains and applied an image processing approach in order to increase the GVF efficiency. / Limitações de memória principal podem diminuir a performance de aplicativos de segmentação de imagens para grandes volumes ou mesmo impedir seu funcionamento. Nesse trabalho nós integramos o modelo das T-Superfícies com um método de extração de iso-superfícies Out-of-Core formando um esquema de segmentação para imagens de grande volume. A T-Superficie é um modelo deformável paramétrico baseado em uma triangulação do domínio da imagem, um modelo discreto de superfície e um threshold da imagem. Técnicas de extração de isso-superfícies foram implementadas usando o método Out-of-Core que usa estruturas kd-tree, chamadas técnicas de Meta-Células. Usando essas técnicas, apresentamos uma versão Out-of-Core de um método de segmentação baseado nas T-Superfícies e em iso-superfícies. O fluxo do Vetor Gradiente (GVF) é um campo vetorial baseado em equações diferenciais parciais. Esse método é aplicado em conjunto com o modelo das Snakes para segmentação de imagens através de extração de contorno. A idéia principal é usar uma equação de difusão-reação para gerar um novo campo de força externa que deixa o modelo menos sensível a inicialização e melhora a habilidade das Snakes para extrair bordas com concavidades acentuadas. Nesse trabalho, primeiramente serão revistos resultados sobre condições de otimização global do GVF e feitas algumas considerações numéricas. Além disso, serão apresentadas uma análise analítica do GVF e uma análise no domínio da frequência, as quais oferecem elementos para discutir a dependência dos parâmetros do modelo. Ainda, será discutida a solução numérica do GVF baseada no método de SOR. Observamos também que o modelo pode ser estendido para Domínios Multiplamente Conexos e aplicamos uma metodologia de pré-processamento que pode tornar mais eficiente o método.