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.

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.

One of today’s challenges to realise computing based on quantum mechanics is to reliably and scalably encode information in quantum systems. Here, we present a photon source to on-demand deliver photonic quantum bits of information based on a strongly coupled atom-cavity system. The source operates intermittently for periods of up to 100 <i>μ</i>s, with a single-photon repetition rate of 1 MHz, and an intra-cavity production efficiency of up to 85%. Our ability to arbitrarily control the photons’ wavepackets and phase profiles, together with long coherence times of 500 ns, allows to store time-bin encoded quantum information within a single photon. To do so, the spatio-temporal envelope of a single photon is sub-divided in d time bins which allows for the delivery of arbitrary qu-d-its. This is done with a fidelity of > 95% for qubits, and 94% for qutrits verified using a newly developed time-resolved quantum-homodyne measurement technique. Additionally, we combine two separate fields of quantum physics by using our deterministic single-photon source to seed linear optics quantum computing (LOQC) circuits. As a step towards quantum networking, it is shown that this photon source can be combined with quantum gates, namely a chip-integrated beam splitter, a controlled-NOT (CNOT) gate as well as a CNOT4 gate. We use this CNOT4 gate to entangle photons deterministically emitted from our source and observe non-classical correlations between events separated by periods exceeding the travel time across the chip by three orders of magnitude. Additionally, we use time-bin encoded qubits to systematically study the de- and re-phasing of quantum states as well as the the effects of time-varying internal phases in photonic quantum circuits.

No description available.

Mapping of earth resources, environmental monitoring, and many other systems require high-resolution wide-area imaging. Since images often have to be captured at night or in inclement weather conditions, a capability is provided by Synthetic Aperture Radar (SAR). SAR systems exploit radar signal's long-range propagation and utilize digital electronics to process complex information, all of which enables high-resolution imagery. This gives SAR systems advantages over optical imaging systems, since, unlike optical imaging, SAR is effective at any time of day and in any weather conditions. Moreover, advanced technology called Interferometric Synthetic Aperture Radar (InSAR), has the potential to apply phase information from SAR images and to measure ground surface deformation. However, given the current state of technology, the quality of InSAR data can be distorted by several factors, such as image co-registration, interferogram generation, phase unwrapping, and geocoding. Image co-registration aligns two or more images so that the same pixel in each image corresponds to the same point of the target scene. Super-Resolution (SR), on the other hand, is the process of generating high-resolution (HR) images from a low-resolution (LR) one. SR influences the co-registration quality and therefore could potentially be used to enhance later stages of SAR image processing. Our research resulted in two major contributions towards the enhancement of SAR processing. The first one is a new learning-based SR model that can be applied with SAR, and similar applications. A second major contribution is utilizing the devised model for improving SAR co-registration and InSAR interferogram generation, together with methods for evaluating the quality of the resulting images. In the case of phase unwrapping, the process of recovering unambiguous phase values from a two-dimensional array of phase values known only modulo $2\pi$ rad, our research produced a third major contribution. This third major contribution is the finding that quantum annealers can resolve problems associated with phase unwrapping. Even though other potential solutions to this problem do currently exist - based on network programming for example - network programming techniques do not scale well to larger images. We were able to formulate the phase unwrapping problem as a quadratic unconstrained binary optimization (QUBO) problem, which can be solved using a quantum annealer. Since quantum annealers are limited in the number of qubits they can process, currently available quantum annealers do not have the capacity to process large SAR images. To resolve this limitation, we developed a novel method of recursively partitioning the image, then recursively unwrapping each partition, until the whole image becomes unwrapped. We tested our new approach with various software-based QUBO solvers and various images, both synthetic and real. We also experimented with a D-Wave Systems quantum annealer, the first and only commercial supplier of quantum annealers, and we developed an embedding method to map the problem to the D-Wave 2000Q_6, which improved the result images significantly. With our method, we were able to achieve high-quality solutions, comparable to state-of-the-art phase-unwrapping solvers. / Graduate

[pt] Interferometria tem sido utilizada para estudar uma variedade de efeitos físicos, desde os experimentos iniciais de Michelson e Morley que forneceram evidências para a teoria da relatividade restrita até os aparelhos de detecção de ondas gravitacionais utilizado no Laser Interferometer Gravitational-Wave Observatory (LIGO). O Propósito dessa dissertação é entender como explorar anyons e suas características únicas para construir interferômetros. Anyons são quasipartículas bi-dimensionais conhecidas por apresentarem estatística fracionária e possuírem aplicações em modelos de computação quântica. Para estudar sua utilidade no contexto de interferometria nós apresentamos uma perspectiva de computação quântica para experimentos de interferência. Em seguida, introduzimos modelos anyônicos e suas aplicações em computação quântica universal. Propomos um circuito quântico que implementa um certo tipo de interferômetro, e como realizá-lo em diferentes modelos anyônicos. Finalmente, discutimos um modelo de computação quântica baseado em ótica linear de anyons fermiônicos que permitiria a criação de uma versão lógica do nosso interferômetro em termos de um interferômetro físico. / [en] Interferometry has been used to study a variety of physical effects, from the early experiments of Michelson and Morley that provided evidence to special relativity to the more recent gravity-wave detection devices used by the Laser Interferometer Gravitational-Wave Observatory (LIGO) experiment. The purpose of this thesis is to understand how one can exploit anyons and its unique characteristics to build interferometers, and understand whether there are immediate advantages in doing so. Anyons are two-dimensional quasiparticles known for their unusual fractional statistics and applications in quantum computing models. To study their usefulness in the context of interferometry, we present a quantum computational approach to interference experiments. Next we give an introduction to anyon models and how they can be used to perform universal quantum computing. We propose a quantum circuit which implements a certain type of interferometer, and how it can be realized in different anyon models. Finally, we discuss a quantum computing model based on linear optics with fermionic anyons that would enable the creation of a logical version of our interferometer in terms of a physical interferometer.

Quantum computing is an emerging field with potential applications in machine learning. This research project aimed to compare the performance of a quantum kernel to that of a classical kernel in machine learning binary classification tasks. Two Support Vector Machines, a popular classification model, was implemented for the respective Variational Quantum kernel and the classical Radial Basis Function kernel and tested on the same sets of artificial quantum-based testing data. The results show that the quantum kernel significantly outperformed the classical kernel for the specific type of data and parameters used in the study. The findings suggest that quantum kernels have the potential to improve machine learning performance for certain types of problems, such as search engines and self-driving vehicles. Further research is, however, needed to confirm their utility in general situations. / Kvantberäkning är ett växande forskningsområde med möjliga tillämpningar inom maskininlärning. I detta forskningsprojekt jämfördes prestandan hos en klassisk kärna med den hos en kvantkärna i binär klassificering för maskininlärninguppgifter, och implikationerna av resultaten diskuterades. Genom att implementera två stödvektormaskiner, en populär klassifikationsmodell, för respektive variabel kvantkärna och klassisk radiell basfunktionskärna kunde vi direkt testa båda kärnorna på samma uppsättning av artificiella kvant-baserad testdata. Resultaten visar på betydande prestandafördelar för kvantkärnan jämfört med den klassiska kärnan när det gäller denna specifika typ av data och de parametrar som användes i vår studie. Vi drar slutsatsen att kvantkärnor inom maskininlärning har potential att överträffa klassiska kärnor, men att mer forskning krävs för att fastställa om detta har någon nytta i allmänna situationer. Om det finns betydande prestandafördelar kan det finnas många tillämpningar, till exempel för sökmotorer och självkörande fordon.

Quantum Computation is the quest for more efficient technologies. It can in principal be applied to Complex quantum systems, Quantum chemical systems, Cyber-security, Finance and AI. However, the introductory course in Quantum Mechanics at the Luleå University of Technology (F0047T) does not provide an introduction to Quantum Computation. This thesis investigates educational material and summarizes introductory concepts to Quantum Computation in the form of a compendium, as well as laboratory tasks in the form of simulation exercises as a potential integration of Quantum Computation into the course. The constructed compendium includes a historical overview, applications, introductory level Quantum Computation theory, Quantum Computational algorithms and a section of the Nobel prize in Physics 2022 which is relevant to both fields. An alternative proof of one of the algorithms, the Deutsch Jozsa Algorithm, presented in the compendium was created, which utilizes mathematics more in-line with the course. If the laboratory tasks were to be incorporated into the course, they would replace one of the current three laboratory tasks. Auxiliary aims for the laboratory tasks were thus imposed. These were: be of similar length/difficulty as the three laboratory tasks separately, be inspirational, be within the theoretical scope of the compendium and focus on quantum phenomenon. The laboratory tasks were chosen to center around Quantum Entanglement and the Deutsch Jozsa Algorithm which are to be preformed using IBM's Quantum Logic Circuit simulator 'Quantum Composer'. Both these tasks focus on Quantum phenomenon and are within the theoretical scope of the compendium. The length/difficulty and inspirational aspects of the tasks needs to be verified in a continuation study.

Quantum computers have the potential to solve certain problems in minutes that would otherwise take classical computers thousands of years due to the exponential speed-up certain quantum algorithms have over classical algorithms. In order to leverage such quantum algorithms, it is necessary for them to run on quantum devices. Examples of such devices include, but are not limited to, semiconductor and superconducting qubits, and semiconductor single and entangled photon emitters. The conventional method of constructing a semiconductor qubit is to apply gates on a semiconductor surface to localize electrons, where the electronic spin states are mapped to a qubit basis. Examples of this include the spin qubit where the spin-1/2 states of a single electron is the qubit basis and the gated singlet-triplet qubit where the states of two coupled electrons are mapped to a qubit basis. In general, gated semiconductor spin qubits are subject to decoherence from the environment which alters the electronic wavefunction by entanglement with the nuclear spins and phonons in the lattice compromising the stability of the qubit. Semiconductor nanostructures can also be designed as photon emitters. Self-assembled quantum dots are an example of such nanostructures and have been shown to emit single photons through exciton recombination and entangled photons through biexciton-exciton cascade. The difficulty in designing photon sources using self-assembled quantum dots is that the size and shape varies from dot to dot, implying that the electronic and magnetic properties also vary. In this thesis, I present the design of a single photon emitter using an InAsP quantum dot embedded in an InP nanowire and the design of a singlet-triplet qubit that is topologically protected from decoherence using an array of such quantum dots embedded in an InP nanowire. The advantage of using quantum dot nanowires over self-assembled quantum dots as photon emitters is that the quantum dot thickness, radius and composition can be controlled deterministically using a technique known as vapour-liquid-solid epitaxy which allows the emission spectrum to be engineered. Using a microscopic model, I simulated an InAsP quantum dot embedded in a nanowire with upwards of millions of atoms and showed that the emission spectrum came in agreement with the actual InAsP/InP quantum dot nanowires that were fabricated at the National Research Council of Canada. Moreover, I showed that altering the distribution of As atoms in the quantum dot can cause dramatic change in the emission spectrum. For the design of the topologically protected singlet-triplet qubit, I demonstrated that the ground state of an array of such quantum dots embedded in an InP nanowire, with four electrons in each dot, is four-fold degenerate and is topologically protected from higher energy states, making the ground state robust against perturbations. This state is known as the Haldane phase and can be understood in terms of two spin-1/2 quasiparticles at each edge of the array. Though the spectral gap in my simulation was of the order of 1 meV, this work provides insight into the potential design of a room temperature operating Haldane qubit where the spectral gap is of the order of room temperature.