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Dissertations / Theses on the topic 'Quantum computing'
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Zimokos, K. R. "Quantum computing." Thesis, Sumy State University, 2014. http://essuir.sumdu.edu.ua/handle/123456789/45442.
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Computers built on the principles of quantum physics promise a revolution on the order of the invention of the microprocessor or the splitting of the atom. The vast increase in power could revolutionize fields as disparate as medicine, space exploration, and artificial intelligence.
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Дядечко, Алла Миколаївна, Алла Николаевна Дядечко, Alla Mykolaivna Diadechko, Артем Володимирович Дмітрієв, Артем Владимирович Дмитриев, and Artem Volodymyrovych Dmitriiev. "Quantum computing." Thesis, Видавництво СумДУ, 2010. http://essuir.sumdu.edu.ua/handle/123456789/16434.
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Quantum algorithms can perform a select set of tasks vastly more efficiently than any classical algorithms, but for many tasks it has been proven that quantum algorithms provide no advantage.
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Nutz, Thomas. "Semiconductor quantum light sources for quantum computing." Thesis, Imperial College London, 2018. http://hdl.handle.net/10044/1/63931.
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Semiconductor quantum dots can be used as sources of entangled single photons, which constitute a crucial resource for optical quantum computing. We present theoretical research on entanglement verification and nuclear spin physics, leading to results that are relevant to both experimental work and the theory of quantum optics and mesoscopic quantum systems. Optical quantum computing requires large entangled photonic states, yet characterizing even few-photon states is a challenge in current experiments due to low photon detection efficiencies. We present a lower bound on a measure of computational usefulness of a potentially large quantum state that requires only measured values of three-photon correlations. Hence this bound provides a simple and applicable benchmarking method for quantum dot experiments. We then turn to the critical issue of the interaction between electron and nuclear spins in quantum dots. This interaction gives rise to decoherence that stands in the way of generating entangled photons as well as nuclear phenomena that might help to overcome this challenge. We formulate a quantum mechanical model of the nuclear spin system in a quantum dot driven by continuous-wave laser light. Based on the analytical steady state solution of this model we predict a novel nuclear spin effect, giving rise to nuclear spin polarization that counteracts the effect of an external magnetic field. Beyond the decoherence problem nuclear spins give rise to randomly time-varying transition energies. A quantum mechanical model of this noise as well as the effect of photon scattering is developed, leading to the insight that optical driving can continuously probe the electron transition energy and thereby prevent it from changing.
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Heidebrecht, Andreas. "Quantum state engineering for spin quantum computing." [S.l. : s.n.], 2006. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-29410.
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Stock, Ryan. "Silicon-based quantum optics and quantum computing." Thesis, Cardiff University, 2018. http://orca.cf.ac.uk/111871/.
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In this thesis is presented a brief review of quantum computing, the DiVincenzo criteria, and the possibility of using a solid state system for building a quantum computing architecture. Donor electron systems in silicon are discussed, before chalcogen, \deep", double donors are suggested as a good candidate for fulfilment of the criteria; the optically driven Stoneham proposal, where the spin-spin interaction between two donor electron spin qbits is mediated by the optically controlled, excited, state of a third donor electron, forms the basis of this [1]. Coherence lifetimes are established as a vital requirement of a quantum bit, but radiative lifetimes must also be long. If the spin-spin interaction between qbits is decreased, or turned off, by the de-excitation of the mediating donor electron then the coherence of the qbit is rendered irrelevant; de-excitation will ruin quantum computations that depend upon an interaction that only happens when the mediating electron is in an excited state. Effective mass theory is used to estimate excited state donor, 2P, wavefunctions for selenium doped silicon, and recent Mott semiconductor to metal transition doping data [2] is used to scale the spatial extent of the 1S(A1) ground state wavefunction. Using these wavefunctions, the expected radiative lifetimes are then calculated, via Fermi's golden rule, to be between 9 ns and 17 ns for the 2P0 state, and 12 ns to 20 ns for the 2P_1 state. Fourier Transform InfraRed (FTIR) absorbance spectroscopy is used to determine the optical transitions for selenium donors in silicon, this has allowed agreement between literature, measured, and effective mass theory energy values for the particular samples measured. FTIR time resolved spectroscopy has then been used to measure the radiative emission spectrum of selenium doped silicon samples at 10-300K, following a 1220 nm laser pulse. Fitting to the exponentially decaying emission data, selenium radiative lifetimes as long as 80 ns are found; for the 2P0 to 1S(A1) transition in an atomic selenium donor complex at 10K. A factor of between 4 and 8 agreement is found between calculated and measured radiative lifetimes. This offers the possibility of nanosecond scale donor electron coherence times for chalcogen dopants in silicon.
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Johnsen, Sverre Gullikstad. "Towards optical quantum computing." Thesis, Norwegian University of Science and Technology, Department of Physics, 2003. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-2256.
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Tsampardoukas, Christos. "Ion trap quantum computing." Monterey, California. Naval Postgraduate School, 2011. http://hdl.handle.net/10945/10704.
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Richard Feynman first proposed the idea of quantum computers thirty years ago. Since then, efforts have been undertaken to realize large-scale, fault-tolerant quantum computers that can factor large numbers much more quickly than classical computers, which would have significant implications for computer security. While there is no universally agreed upon technology for experimentally realizing quantum computers, many researchers look to ion traps as a promising technology. This thesis focuses on ion traps, how they fulfill the Divincenzo criteria, what obstacles must be overcome, and recent achievements in this field. We examine the physical principles of a linear Paul trap, including the confining potential and its quantum dynamics. In addition, we built a mechanical analogue of an ion trap for pedagogical purposes, and we provide an analysis of its trapping potential and compare it to a real ion trap, the Paul trap. Furthermore, we provide guidance for building a course module on ion trap based quantum computing; our guidance is based on course materials from several institutions.
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Duncan, Ross. "Types for quantum computing." Thesis, University of Oxford, 2006. http://ora.ox.ac.uk/objects/uuid:c2901ae8-9386-4dbf-879d-e37bbc2692bd.
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Wang, Qian. "Quantum tunneling, quantum computing, and high temperature superconductivity." Texas A&M University, 2003. http://hdl.handle.net/1969.1/1638.
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In this dissertation, I have studied four theoretical problems in quantum tunneling, quantum computing, and high-temperature superconductivity.
I have developed a generally-useful numerical tool for analyzing impurity-induced resonant-state images observed with scanning tunneling microscope (STM) in high temperature superconductors. The integrated tunneling intensities on all predominant sites have been estimated. The results can be used to test the predictions of any tight-binding model calculation.
I have numerically simulated two-dimensional time-dependent tunneling of a Gaussian wave packet through a barrier, which contains charged ions. We have found that a negative ion in the barrier directly below the tunneling tip can deflect the tunneling electrons and drastically reduce the probability for them to reach the point in the target plane directly below the tunneling tip.
I have studied an infinite family of sure-success quantum algorithms, which are introduced by C.-R. Hu [Phys. Rev. A {\bf 66}, 042301 (2002)], for solving a generalized Grover search problem. Rigorous proofs are found for several conjectures made by Hu and explicit equations are obtained for finding the values of two phase parameters which make the algorithms sure success.
Using self-consistent Hartree-Fock theory, I have studied an extended Hubbard model which includes quasi-long-range Coulomb interaction between the holes (characterized by parameter V). I have found that for sufficiently large V/t, doubly-charged-antiphase-island do become energetically favored localized objects in this system for moderate values of U/t, thus supporting a recent conjecture by C.-R. Hu [Int. J. Mod. Phys. B {\bf 17}, 3284 (2003)].
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Meyer, Carola. "Endohedral fullerenes for quantum computing." [S.l. : s.n.], 2003. http://www.diss.fu-berlin.de/2003/296/index.html.
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Bresler, Yony. "Stochastic simulations of quantum computing." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=106525.
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A method for for simulating quantum computing circuits using stochastic processes is described and analyzed. Circuits are transformed into a complex action from which observables are computed. These averages are evaluated using Monte Carlo and complex Langevin methods. The transformation can be applied to any circuit with an input product state, and results in equations that are polynomial in storage. This method is unique in allowing for an efficient simulation that is also general. Three sample circuits are simulated. Standard simulations techniques are shown to yield poor estimates of the observables. An improved method is proposed by adding a coupling term to the action to stabilize the system. Results for this improved method are shown to be more accurate. Feasibility and future directions are discussed.<br>Une méthode pour simuler des circuits de calcul quantique par des processus stochastiques est décrite et analysée. Les circuits sont transformés en une action complexe par laquelle les observables sont calculés. Ces moyennes sont évaluées à l'aide de Monte Carlo et de méthodes complexes de Langevin. La transformation peut être appliquée sur n'importe quel circuit avec un état de produits d'entrée. Celle-ci résulte en équations qui sont polynomiales dans le stockage. Cette méthode est unique, car elle permet une simulation efficace et est à la fois généralisée. Trois circuits d'échantillonnage sont simulés. Les techniques de simulations courantes démontrent inadéquatement les estimations des observables. Une méthode améliorée est donc proposée par l'ajout d'un terme de couplage à l'action pour stabiliser le système. Les résultats démontrés via la méthode améliorée sont plus fiables. La faisabilité et les orientations futures sont discutées.
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Metz, Jeremy. "Quantum Computing With Macroscopic Heralding." Thesis, Imperial College London, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.484422.
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Campbell, Earl T. "Distrubuting entanglement for quantum computing." Thesis, University of Oxford, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.504315.
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Nickerson, Naomi. "Practical fault-tolerant quantum computing." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/31475.
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Quantum computing has the potential to transform information technology by offering algorithms for certain tasks, such as quantum simulation, that are vastly more efficient than what is possible with any classical device. But experimentally implementing practical quantum information processing is a very difficult task. Here we study two important, and closely related, aspects of this challenge: architectures for quantum computing, and quantum error correction Exquisite quantum control has now been achieved in small ion traps, in nitrogen-vacancy centres and in superconducting qubit clusters, but the challenge remains of how to scale these systems to build practical quantum devices. In Part I of this thesis we analyse one approach to building a scalable quantum computer by networking together many simple processor cells, thus avoiding the need to create a single complex structure. The difficulty is that realistic quantum links are very error prone. Here we describe a method by which even these error-prone cells can perform quantum error correction. Groups of cells generate and purify shared resource states, which then enable stabilization of topologically encoded data. Given a realistically noisy network (10% error rate) we find that our protocol can succeed provided that all intra-cell error rates are below 0.8%. Furthermore, we show that with some adjustments, the protocols we employ can be made robust also against high levels of loss in the network interconnects. We go on to analyse the potential running speed of such a device. Using levels of fidelity that are either already achievable in experimental systems, or will be in the near-future, we find that employing a surface code approach in a highly noisy and lossy network architecture can result in kilohertz computer clock speeds. In Part II we consider the question of quantum error correction beyond the surface code. We consider several families of topological codes, and determine the minimum requirements to demonstrate proof-of-principle error suppression in each type of code. A particularly promising code is the gauge color code, which admits a universal transversal gate set. Furthermore, a recent result of Bombin shows the gauge color code supports an error-correction protocol that achieves tolerance to noisy measurements without the need for repeated measurements, so called single-shot error correction. Here, we demonstrate the promise of single-shot error correction by designing a decoder and investigating its performance. We simulate fault-tolerant error correction with the gauge color code, and estimate a sustainable error rate, i.e. the threshold for the long time limit, of ~0.31% for a phenomenological noise model using a simple decoding algorithm.
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Wardrop, Matthew Phillip. "Quantum Gates for Quantum Dots." Thesis, The University of Sydney, 2015. http://hdl.handle.net/2123/14938.
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Since the mid-20th century it has been understood that a general-purpose quan- tum computer would be able to efficiently solve problems that will forever be out-of-reach for conventional computers. Since then, many quantum algorithms have been developed with applications in a wide range of domains including cryptography, simulations, machine learning and data analysis. While this has resulted in substantial attention being paid to the development of quantum com- puters, the best architectures to use in their fabrication is not yet clear. Semiconductor quantum dot devices are a particularly promising candidate for use in quantum computing architectures, as it is anticipated that once the funda- mental building blocks are implemented, they might be massively scalable using the existing lithography techniques of the semiconductor industry. So far, how- ever, it is not yet clear how best to implement the high-fidelity gates required for general-purpose quantum computation. In this thesis, we present and characterise novel theoretical proposals for fast, simple and high-fidelity two-qubit gates using magnetic (exchange) coupling for specific semiconductor quantum dot qubits; namely, the singlet-triplet and resonant-exchange qubits. These two-qubit operations are simple enough that it is feasible for them to be implemented in experiments of the near future. Success- ful implementations would significantly extend the experimentally demonstrable frontier of semi-conductor quantum dot devices as relevant to their use in uni- versal quantum computing architectures. We also develop simple parameter estimation schemes by which it is possible to substantially mitigate the dominant sources of error for our proposed gates; namely, low-frequency charge and magnetic noise. We develop the techniques in the context of pseudo-static magnetic field gradient fluctuations in singlet- triplet qubits, and demonstrate that these techniques lead to a several orders of magnitude improvement in single-qubit coherence times. With minimal effort this could be ported to other qubit architectures.
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Xu, Huizhong. "Quantum computing with Josephson junction circuits." College Park, Md. : University of Maryland, 2004. http://hdl.handle.net/1903/1885.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2004.<br>Thesis research directed by: Physics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Evans, Julia. "The algebra of topological quantum computing." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=107687.
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Topological quantum computing is an approach to the problem of implementingquantum gates accurately and robustly. The idea is to exploit topological propertiesof certain quasiparticles called anyons to obtain a proposed implementation of quan-tum computing which is inherently fault-tolerant. The mathematical structure thatdescribes anyons is that of modular tensor categories. These modular tensor cate-gories can be constructed from the representations of certain algebraic objects calledquantum groups. In this thesis we give an explanation of modular tensor categoriesand quantum groups as they relate to topological quantum computing. It is intendedthat it can be read with some basic knowledge of algebra and category theory. Thehope is to give a concrete account accessible to computer scientists of the theory ofmodular tensor categories obtained from quantum groups. The emphasis is on thecategory theoretic and algebraic point of view rather than on the physical point ofview.<br>Le calcul quantique topologique est une approche au problème d'implementationde circuits quantique d'une façon robuste et precisé. L'idée s'agit d'exploiter certaines propriétés de quasiparticules, dites "anyons", pour obtenir une implémentation du calcul quantique qui est intrinsequement tolerante aux pannes. La structure mathématique qui décrit ces anyons est celle des catégories modulaires. Ces objets peuvent être construites à partir de représentations de certaines algèbres, appelées groupes quantiques. Dans ce mémoire, nous donnerons une exposition des catégories modulaires, des groupes quantiques et du lien qu'ils partagent avec le calcul quantique. Le mémoire ne devrait requérir qu'une connaissance de base en algèbre et en théorie des categories. L'espoir étant de donner un model concret pour les informaticiens de la théorie de catégories obtenus à partir de groupes quantiques. L'emphase sera sur le point de vu algèbrique et catégorique plutôt que celui physique.
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Casson, Ian. "Linking polymetallic rings for quantum computing." Thesis, University of Manchester, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.503018.
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Ioannou, L. M. "Computing finite-dimensional bipartite quantum separability." Thesis, University of Cambridge, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.604939.
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In Chapter 2, I apply polyhedral theory to prove easily that the set of separable states is not a polytope; for the sake of completeness, I then review the role of polytopes in nonlocality. Next, I give a novel treatment of entanglement witnesses and define a new class of entanglement witnesses, which may prove to be useful beyond the examples given. In the last section, I briefly review the five basic convex body problems given in [1] (Groetschel et al., 1988), and their application to the quantum separability problem. In Chapter 3, I treat the separability problem as a computational decision problem and motivate its approximate formulations. After a review of basic complexity-theoretic notions, I discuss the computational complexity of the separability problems: I discuss the issue of NP-completeness, giving an alternative definition of the separability problem as an NP-hard problem in NP. I finish the chapter with a comprehensive survey of deterministic algorithm solutions to the separability problem, including one that follows from a second NP formulation. Chapters 1 and 3 motivate a new interior-point algorithm which, given the expected values of a subset of an orthogonal basis of observables of an otherwise unknown quantum state, searches for an entanglement witnesses in the span of the subset of observables. When all the expected values are known, the algorithm solves the separability problem. In Chapter 4, I give the motivation for the algorithm and show how it can be used in a particular physical scenario to detect entanglement (or decade separability) of an unknown quantum state using as few quantum resources as possible. I then explain the intuitive idea behind the algorithm and relate it to the standard algorithms of its kind. I end the chapter with a comparison of the complexities of the algorithms surveyed in Chapter 3. Finally, in Chapter 5, I present the details of the algorithm and discuss its performance relative to standard methods.
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Zhang, Jinying. "Fullerene Compounds for Quantum Computing Architectures." Thesis, University of Oxford, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.531661.
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Pérez, Salinas Adrián. "Algorithmic strategies for seizing quantum computing." Doctoral thesis, Universitat de Barcelona, 2021. http://hdl.handle.net/10803/673255.
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Quantum computing is an emergent technology with prospects to solve problems nowadays intractable. For this purpose it is a requirement to build computers capable to store and control quantum systems without losing their quantum properties. However, these computers are hard to achieve, and in the near term there will only be Noisy Intermediate-Scale Quantum (NISQ) computers with limited performance. In order to seize quantum computing during the NISQ era, algorithms with low resource demands and capable to return approximate solutions are explored.
This thesis presents two different algorithmic strategies aiming to contribute to the plethora of algorithms available for NISQ devices, namely re-uploading and strategy. Each strategy takes advantage of different features of quantum computing, namely the superposition and the density of the Hilbert space in re-uploading, and entanglement among different partitions of the system in unary, to overcome a variety of obstacles. In both cases, the strategies are general and can be applied in a range of scenarios. Some examples are also provided in this thesis.
First, the re-uploading is designed as a meeting point between quantum computing and machine learning. Machine learning is a set of techniques to build computer programs capable to learn how to solve a problem through experience, without being explicitly programmed for it. Even though the re-uploading is not the first attempt to join quantum computers and machine learning, this approach has certain properties that make it different from other methods.
In particular, the re-uploading approach consists in introducing data into a classical algorithms in different stages along the process. This is a main difference with respect to standard methods, where data is uploaded at the beginning of the procedure. In the re-uploading, data is accompanied by tunable classical parameters that are optimized by a classical method according to a cost function defining the problem. The joint action of data and tunable parameters grant the quantum algorithm a great flexibility to learn a given behavior from sampling target data. The more re- uploadings are used, the better results can be obtained.
In this thesis, re-uploading is presented by means of a set of theoretical results supporting its capabilities, and simulations and experiments to benchmark its performance in a variety of problems.
The second algorithmic strategy is unary. This strategy describes a problem making use of only a small part of the available computational space. Thus, the computational capabilites of the computer are not optimal. In exchange, the operations required to execute a certain task become simpler. As a consequence, the retrieved results are more resilient to noise and decoherence, and meaningful. Therefore, a trade-off between efficiency and resillience against noise arises. NISQ computers benefit from this circumstance, especially in the case of small problems, where even quantum advantage and advantage over standard algorithms can be achieved.
In this thesis, unary is used to solve a typical problem in finance called option pricing, which is of interest for real world applications. Options are contracts to buy the right to buy/sell a given asset at certain time and price. The holder of the option will only exercise this right in case of profit. Option pricing concists in estimating this profit by handling stochastic evolution models.
This thesis aims to contribute to the growing number of algorithms available for NISQ computers and pave the way towards new quantum technologies.<br>La computación cuántica es una tecnología emergente con potencial para resolver problemas hoy impracticables. Para ello son necesarios ordenadores capaces de mantener sistemas cuánticos y controlarlos con precisión. Sin embargo, construir estos ordenadores es complejo y a corto plazo solo habrá ordenadores pequeños afectados por el ruido y sujetos a ruido (NISQ). Para aprovechar los ordenadores NISQ se exploran algoritmos que requieran pocos recursos cuánticos mientras proporcionan soluciones aproximadas a los problemas que enfrentan.
En esta tesis se estudian dos propuestas para algoritmos NISQ: re-uploading y unary. Cada estrategia busca tomar ventaja de diferentes características de la computación cuántica para superar diferentes obstáculos. Ambas estrategias son generales y aplicables en diversos escenarios.
En primer lugar, re-uploading está diseñado como un puente entre la computación cuántica y el aprendizaje automático (Machine Learning). Aunque no es el primer intento de aplicar la cuántica al aprendizaje automático, re-uploading tiene ciertas características que lo distinguen de otros métodos. En concreto, re-uploading consiste en introducir datos en un algoritmo cuántico en diferentes puntos a lo largo del proceso. Junto a los datos se utilizan también parámetros optimizables clásicamente que permiten al circuito aprender cualquier comportamiento. Los resultados mejoran cuantas más veces se introducen los datos. El re-uploading cuenta con teoremas matemáticos que sustentan sus capacidades, y ha sido comprobado con éxito en diferentes situaciones tanto simuladas como experimentales.
La segunda estrategia algorítmica es unary. Consiste en describir los problemas utilizando solo parte del espacio de computación disponible dentro del ordenador. Así, las capacidades computacionales del ordenador no son óptimas, pero a cambio las operaciones necesarias para una cierta tarea se simplifican. Los resultados obtenidos son resistentes al ruido, y mantienen su significado, y se produce una compensación entre eficiencia y resistencia a errores. Los ordenadores NISQ se ven beneficiados de esta situación para problemas pequeños. En esta tesis, unary se utiliza para resolver un problema tíıpico de finanzas, incluso obteniendo ventajas cuánticas en un problema aplicable al mundo real.
Con esta tesis se espera contribuir al crecimiento de los algoritmos disponibles para ordenadores cuánticos NISQ y allanar el camino para las tecnologías venideras.
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Gimeno-Segovia, Mercedes. "Towards practical linear optical quantum computing." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/43936.
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Quantum computing promises a new paradigm of computation where information is processed in a way that has no classical analogue. There are a number of physical platforms conducive to quantum computation, each with a number of advantages and challenges. Single photons, manipulated using integrated linear optics, constitute a promising platform for universal quantum computation. Their low decoherence rates make them particularly favourable, however the inability to perform deterministic two-qubit gates and the issue of photon loss are challenges that need to be overcome. In this thesis we explore the construction of a linear optical quantum computer based on the cluster state model. We identify the different necessary stages: state preparation, cluster state construction and implementation of quantum error correcting codes, and address the challenges that arise in each of these stages. For the state preparation, we propose a series of linear optical circuits for the generation of small entangled states, assessing their performance under different scenarios. For the cluster state construction, we introduce a ballistic scheme which not only consumes an order of magnitude fewer resources than previously proposed schemes, but also benefits from a natural loss tolerance. Based on this scheme, we propose a full architectural blueprint with fixed physical depth. We make investigations into the resource efficiency of this architecture and propose a new multiplexing scheme which optimises the use of resources. Finally, we study the integration of quantum error-correcting codes in the linear optical scheme proposed and suggest three ways in which the linear optical scheme can be made fault-tolerant.
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Brown, Katherine Louise. "Using the qubus for quantum computing." Thesis, University of Leeds, 2011. http://etheses.whiterose.ac.uk/1687/.
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In this thesis I explore using the qubus for quantum computing. The qubus is an architecture of quantum computing, where a continuous variable ancilla is used to generate operations between matter qubits. I concentrate on using the qubus for two purposes - quantum simulation, and generating cluster states. Quantum simulation is the idea of using a quantum computer to simulate a quantum system. I focus on conducting a simulation of the BCS Hamiltonian. I demonstrate how to perform the necessary two qubit operations in a controlled fashion using the qubus. In particular I demonstrate an O(N3) saving over an implementation on an NMR computer, and a factor of 2 saving over a naıve technique. I also discuss how to perform the quantum Fourier transform on the qubus quantum computer. I show that it is possible to perform the quantum Fourier transform using just, 24⌊N/2⌋ + 7N − 6, this is an O(N) saving over a naıve method. In the second part of the thesis, I move on, and consider generating cluster states using the qubus. A cluster state, is a universal resource for one-way or measurement-based computation. In one-way computation, the pre-generated, entangled resource is used to perform calculations, which only require local corrections and measurement. I demonstrate that the qubus can generate cluster states deterministically, and in a relatively short time. I discuss several techniques of cluster state generation, one of which is optimal, given the physical architecture we are using. This can generate an n × m cluster in only 3nm − 2n − 2m + 4 operations. The alternative techniques look at generating a cluster using layers or columns, allowing it to be built dynamically, while the cluster is used to perform calculations. I then move on, and discuss problems with error accumulation in the generation process.
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Kult, David. "Quantum Holonomies : Concepts and Applications to Quantum Computing and Interferometry." Doctoral thesis, Uppsala University, Quantum Chemistry, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8185.
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<p>Quantum holonomies are investigated in different contexts.</p><p>A geometric phase is proposed for decomposition dependent evolution, where each component of a given decomposition of a mixed state evolves independently. It is shown that this geometric phase only depends on the path traversed in the space of decompositions.</p><p>A holonomy is associated to general paths of subspaces of a Hilbert space, both discrete and continuous. This opens up the possibility of constructing quantum holonomic gates in the open path setting. In the discrete case it is shown that it is possible to associate two distinct holonomies to a given path. Interferometric setups for measuring both holonomies are</p><p>provided. It is further shown that there are cases when the holonomy is only partially defined. This has no counterpart in the Abelian setting.</p><p>An operational interpretation of amplitudes of density operators is provided. This allows for a direct interferometric realization of Uhlmann's parallelity condition, and the possibility of measuring the Uhlmann holonomy for sequences of density operators.</p><p>Off-diagonal geometric phases are generalized to the non-Abelian case. These off-diagonal holonomies are undefined for cyclic evolution, but must contain members of non-zero rank if all standard holonomies are undefined. Experimental setups for measuring the off-diagonal holonomies are proposed.</p><p>The concept of nodal free geometric phases is introduced. These are constructed from gauge invariant quantities, but do not share the nodal point structure of geometric phases and off-diagonal geometric phases. An interferometric setup for measuring nodal free geometric phases is provided, and it is shown that these phases could be useful in geometric quantum computation.</p><p>A holonomy associated to a sequence of quantum maps is introduced. It is shown that this holonomy is related to the Uhlmann holonomy. Explicit examples are provided to illustrate the general idea.</p>
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Estarellas, Pascual. "Spin chain systems for quantum computing and quantum information applications." Thesis, University of York, 2018. http://etheses.whiterose.ac.uk/20556/.
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One of the most essential processes in classical computation is that related to the information manipulation; each component or register of a computer needs to communicate to others by exchanging information encoded in bits and transforming it through logical operations. Hence the theoretical study of methods for information transfer and processing in classical information theory is of fundamental importance for telecommunications and computer science, along with study of errors and robustness of such proposals. When adding the quantum ingredient, there arises a whole new set of paradigms and devices, based on manipulations of \emph{qubits}, the quantum analogues of conventional data bits. Such systems can show enormous advantage against their classical analogues, but at the same time present a whole new set of technical and conceptual challenges to overcome. The full and detailed understanding of quantum processes and studies of theoretical models and devices therefore provide the first logical steps to the future technological exploitation of these new machines. In this line, this thesis focuses on spin chains as such theoretical models, formed by series of coupled qubits that can be applied to a wide range of physical systems, and its several potential applications as quantum devices. In this work spin chains are presented as reliable devices for quantum communication with high transfer fidelities, entanglement generation and distribution over distant parties and protected storage of quantum information. Methods to design these tools to have some robustness against errors and noise are provided, giving optimism for future quantum technologies.
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Lovett, Neil Brian. "Application of quantum walks on graph structures to quantum computing." Thesis, University of Leeds, 2011. http://etheses.whiterose.ac.uk/1689/.
Full textAbstract:
Quantum computation is a new computational paradigm which can provide fundamentally faster computation than in the classical regime. This is dependent on finding efficient quantum algorithms for problems of practical interest. One of the most successful tools in developing new quantum algorithms is the quantum walk. In this thesis, we explore two applications of the discrete time quantum walk. In addition, we introduce an experimental scheme for generating cluster states, a universal resource for quantum computation. We give an explicit construction which provides a link between the circuit model of quantum computation, and a graph structure on which the discrete time quantum walk traverses, performing the same computation. We implement a universal gate set, proving the discrete time quantum walk is universal for quantum computation, thus confirming any quantum algorithm can be recast as a quantum walk algorithm. In addition, we study factors affecting the efficiency of the quantum walk search algorithm. Although there is a strong dependence on the spatial dimension of the structure being searched, we find secondary dependencies on other factors including the connectivity and disorder (symmetry). Fairly intuitively, as the connectivity increases, the efficiency of the algorithm increases, as the walker can coalesce on the marked state with higher probability in a quicker time. In addition, we find as disorder in the system increases, the algorithm can maintain the quantum speed up for a certain level of disorder before gradually reverting to the classical run time. Finally, we give an abstract scheme for generating cluster states. We see a linear scaling, better than many schemes, as doubling the size of the generating grid in our scheme produces a cluster state which is double the depth. Our scheme is able to create other interesting topologies of entangled states, including the unit cell for topological error correcting schemes.
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Dewaele, Nicholas. "Quantum Computing With Quantum Dots Using The Heisenberg Exchange Interaction." OpenSIUC, 2014. https://opensiuc.lib.siu.edu/theses/1600.
Full textAbstract:
One of the most promising systems for creating a working quantum computer is the triple quantum dots in a linear semiconductor. One of the biggest advantages is that we are able to perform Heisenberg exchange gates on the physical qubits. These exchanges are both fast and relatively low energy. Which means that they would be excellent for producing fast and accurate operations. In order to prevent leakage errors we use a 3 qubit DFS to encode a logical qubit. Here we determine the theoretical time dependent affects of applying the Heisenberg exchange gates in the DFS basis as well as the effect of applying multiple exchange gates at the same time. we also find that applying two heisenberg exchange gates at the same time is an effective way of implementing a leakage elimination operator.
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Holladay, Robert Tyler. "Steepest-Entropy-Ascent Quantum Thermodynamic Modeling of Quantum Information and Quantum Computing Systems." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/94630.
Full textAbstract:
Quantum information and quantum computing (QIQC) systems, relying on the phenomena of superposition and entanglement, offer the potential for vast improvements in certain computations. A practical QC realization requires maintaining the stored information for time-scales long enough to implement algorithms. One primary cause of information loss is decoherence, i.e., the loss of coherence between two energy levels in a quantum system. This work attributes decoherence to dissipation occurring as the system evolves and uses steepest-entropy-ascent quantum thermodynamics (SEAQT) to predict the evolution of system state. SEAQT asserts that, at any instant of time, the system state evolves such that the rate of system entropy change is maximized while conserving system energy. With this principle, the SEAQT equation of motion is applicable to systems in any state, near or far from stable equilibrium, making SEAQT particularly well suited for predicting the dissipation occurring as quantum algorithms are implemented. In the present research, the dynamics of qubits (quantum-bits) using the SEAQT framework are first examined during common quantum gates (combinations of which form algorithms). This is then extended to modeling a system of multiple qubits implementing Shor's algorithm on a nuclear-magnetic-resonance (NMR) QC. Additionally, the SEAQT framework is used to predict experimentally observed dissipation occurring in a two-qubit NMR QC undergoing a so called ``quenching'' process. In addition, several methods for perturbing the density or so-called ``state'' operator used by the SEAQT equation of motion subject to an arbitrary set of expectation value constraints are presented. These are then used as the basis for randomly generating states used in analyzing the dynamics of entangled, non-interacting systems within SEAQT. Finally, a reservoir interaction model is developed for general quantum systems where each system locally experiences a heat interaction with an external reservoir. This model is then used as the basis for developing a decoherence control scheme, which effectively transfers entropy out of the QIQC system as it is generated, thus, reducing the decoherence. Reservoir interactions are modeled for single qubits and the control scheme is employed in modeling an NMR QC and shown to eliminate nearly all of the noise caused by decoherence/dissipation.<br>Doctor of Philosophy<br>Quantum computers (QCs) have the potential to perform certain tasks much more efficiently than today0 s supercomputers. One primary challenge in realizing a practical QC is maintaining the stored information, the loss of which is known as decoherence. This work attributes decoherence to dissipation (a classical analogue being heat generated due to friction) occurring while an algorithm is run on the QC. Standard quantum modeling approaches assume that for any dissipation to occur, the QC must interact with its environment. However, in this work, steepest-entropy-ascent quantum thermodynamics (SEAQT) is used to model the evolution of the QC as it runs an algorithm. SEAQT, developed by Hatsopolous, Gyftopolous, Beretta, and others over the past 40 years, supplements the laws of quantum mechanics with those of thermodynamics and in contrast to the standard quantum approaches does not require the presence of an environment to account for the dissipation which occurs. This work first applies the SEAQT framework to modeling single qubits (quantum bits) to characterize the effect of dissipation on the information stored on the qubit. This is later extended to a nuclear-magnetic-resonance (NMR) QC of 7 qubits. Additionally, SEAQT is used to predict experimentally observed dissipation in a two-qubit NMR QC. Afterwards, several methods for constrained perturbations of a QC0 s state are presented. These methods are then used with SEAQT to analyze the effect of dissipation on the entanglement of two qubits. Finally, a model is derived within the SEAQT framework accounting for a qubit interacting with its environment, which is at a constant temperature. This model is then used to develop a method for limiting the decoherence and shown to significantly lowering the resulting error due to decoherence.
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Pius, Einar. "Parallel quantum computing : from theory to practice." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/15857.
Full textAbstract:
The term quantum parallelism is commonly used to refer to a property of quantum computations where an algorithm can act simultaneously on a superposition of states. However, this is not the only aspect of parallelism in quantum computing. Analogously to the classical computing model, every algorithm consists of elementary quantum operations and the application of them could be parallelised itself. This kind of parallelism is explored in this thesis in the one way quantum computing (1WQC) and the quantum circuit model. In the quantum circuit model we explore arithmetic circuits and circuit complexity theory. Two new arithmetic circuits for quantum computers are introduced in this work: an adder and a multiply-adder. The latter is especially interesting because its depth (i.e. the number of parallel steps required to finish the computation) is smaller than for any known classical circuit when applied sequentially. From the complexity theoretical perspective we concentrate on the classes QAC0 and QAC0[2], the quantum counterparts of AC0 and AC0[2]. The class AC0 comprises of constant depth circuits with unbounded fan-in AND and OR gates and AC0[2] is obtained when unbounded fan-in parity gates are added to AC0 circuits. We prove that QAC0 circuits with two layers of multi-qubit gates cannot compute parity exactly. This is a step towards proving QAC0 6= QAC0[2], a relation known to hold for AC0 and AC0[2]. In 1WQC, computation is done through measurements on an entangled state called the resource state. Two well known parallelisation methods exist in this model: signal shifting and finding the maximally delayed general flow. The first one uses the measurement calculus formalism to rewrite the dependencies of an existing computation, whereas the second technique exploits the geometry of the resource state to find the optimal ordering of measurements. We prove that the aforementioned methods result in same depth computations when the input and output sizes are equal. Through showing this equivalence we reveal new properties of 1WQC computations and design a new algorithm for the above mentioned parallelisations.
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Naydenov, Boris N. "Encapsulation of endohedral fullerenes for quantum computing." [S.l.] : [s.n.], 2006. http://www.diss.fu-berlin.de/2006/659/index.html.
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Li, Huidong, and 李輝東. "The reversibility and determinism in quantum computing." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B31228306.
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Rosenberg, Nathanial Owen. "Cryptology Management in a Quantum Computing Era." Thesis, Monterey, California. Naval Postgraduate School, 2012. http://hdl.handle.net/10945/7407.
Full textAbstract:
Todays most efficient and widely used cryptographic standards such as RSA rely on the difficulty of factoring large numbers to resist cryptanalysis. Asymmetric cryptography is used in a plethora of sensitive operations from online bank transactions to international e-commerce, and the Department of Defense also uses asymmetric cryptography to transmit sensitive data. Quantum computers have the potential to render obsolete widely deployed asymmetric ciphers essential to the secure transfer of information. Despite this, alternatives are not in place. The goal of this study is to understand the alternatives to classical asymmetric cryptography that can be used as substitutes should quantum computers be realized. This study explores quantum-resistant alternatives to traditional ciphers and involves experimenting with available implementations of ciphers described the post-quantum literature as well as developing our own implementations based on descriptions of algorithms in the literature. This study provides an original implementation of hash-based digital signature and detailed instructions on its use as well as customization of the NTRU lattice-based cryptography suite, including the use of NTRU and AES together in a hybrid cryptographic protocol. This thesis will make recommendations on future work necessary to prepare for the emergence of large-scale, fault-tolerant quantum computers.
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Lee, James. "Photon sources for linear optical quantum computing." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/287474.
Full textAbstract:
Quantum photonic technologies have many exciting applications including secure commu- nication, quantum enhanced measurement and quantum computing. Linear optical quantum computing (LOQC) is a technology of particular interest - especially given that recent progress in on-chip waveguide technology removes the requirement for complex and costly bulk optics setups and state-of-the-art detectors have detection efficiencies of over 90%. Arguably the largest remaining technological hurdle for LOQC is the development of a suitable photon source. A suitable source would produce single, indistinguishable photons deterministically. Additionally, it would be beneficial if the generated photons were entangled, as this can significantly reduce the degree of multiplexing needed to implement LOQC. Quantum dots are a suitable candidate system for these photon sources as they exhibit bright single photon emission and can act as the interface between light and a trapped spin qubit. These properties have resulted in proposals to generate multi-photon entangled states suitable for use in LOQC. This thesis presents some of the progress we have made towards the creation of a suitable photon source. After introducing the background material, we demonstrate pulsed resonant excitation using a single-electron-charged quantum dot. Deterministic excitation is demonstrated by performing Rabi oscillations and Ramsey interference in the excitonic population. We also investigate Ramsey interference in a Faraday geometry magnetic field and observe a variety of beats and oscillations in the interferograms. We develop a model to explain our results and conclude that controlling the phase between the two Ramsey interference pulses allows a degree of control over the state of the trapped spin. We then also demonstrate the coherent optical manipulation of a trapped spin in a Voigt geometry magnetic field. Once we have presented the manipulation of the excitonic state and the state of the trapped spin, we proceed to investigate the properties of the light produced by the resonant excitation of a quantum dot. Hong Ou Mandel interference experiments allow us to probe the indistinguishability of the photons resulting from the resonant excitation of the negative trion transition. Repeating the measurement using light generated from a similar system (this time with a trapped hole rather than a trapped electron) that is embedded in a micropillar cavity, we find that the cavity enhancement of the transition results is higher indistinguishabilities. We make use of this bright source of indistinguishable photons to perform an on-chip quantum enhanced measurement and observe the phase superresolution associated with N00N states. In the final experimental chapter, we propose and implement a scheme to generate multi- qubit single photon states. We show that by repeatedly driving a micropillar-cavity-enhanced Raman transition of a single-hole-charged quantum dot in a Voigt geometry magnetic field it is possible to coherently superpose a photon across multiple time bins. The scheme is conceptually similar to proposed schemes for producing multi-photon entangled states. Lastly, we propose a scheme that makes use of the capabilities shown in the three experimental chapters to overcome several of the experimental difficulties associated with generating multi-photon entangled states.
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Cao, Yameng. "Semiconductor light sources for photonic quantum computing." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/56619.
Full textAbstract:
The isolation of qubits from decoherence is crucial to the prospect of building revolutionary quantum devices. This work is devoted to an optical study of the decoherence on spin qubits in self-assembled quantum dots. This thesis contributes towards a complete understanding of quantum decoherence, of which highlighted discoveries include bypassing the spectral diffusion in neutral quantum dot emission lines; observing for the first time the self-polarization phenomenon of nuclear spins, via the resonance-locking effect on a negatively charged quantum dot; and revealing the limiting factors on hole spin dephasing, by measuring polarization correlations on a positively charged quantum dot. Three studies were conducted using two different spectroscopy techniques. For the first study, the spectral diffusion of emission line due to random electrostatic fluctuations was revealed, by scanning a neutral quantum dot transition across the laser resonance. Exciting the quantum dot resonantly bypassed this problem, paving the way for an on-demand antibunched source that generates narrow-band photons. For the second study, evidences supporting the spontaneous self-polarization of nuclear spins were observed for the first time, since it was predicted nearly four decades ago by M. Dyankonov and V.I. Perel. The self-polarization phenomenon is a remarkable demonstration of dynamic nuclear spin polarization since it manifests without the ground state electron being spin-polarized. In the last study, factors limiting the hole spin lifetime was inferred from measuring polarization correlation of successively emitted photons from a positively charged quantum dot. Evidences support a strong dependence on the carrier repopulation rate and the single electron spin dephasing in the upper state, due to the Overhauser field. In combination with the observation of spontaneous nuclear polarization, this opens the possibility of an electron spin sensor, which can indirectly probe the nuclear field.
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Sheldon, Sarah (Sarah Elizabeth). "Second order error correction in quantum computing." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44834.
Full textAbstract:
Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Nuclear Science and Engineering, 2008.<br>Includes bibliographical references (leaf 23).<br>Error correction codes are necessary for the development of reliable quantum computers. Such codes can prevent the lost of information from decoherence caused by external perturbations. This thesis evaluates a five qubit code for correcting second order bit-flip errors. The code consists of encoding, decoherence, decoding, and error correction steps. This work analyzes the proposed code using geometric algebra methods and examines the state of the system after each step in the process.<br>by Sarah Sheldon.<br>S.B.
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Kruger, Markus Gustav. "On evolutionary algorithms for effective quantum computing." Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/20095.
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Thesis (MSc)--Stellenbosch University, 2012.<br>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].<br>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].
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Shojaei, Borzoyeh. "Antimonide-Based Compound Semiconductors for Quantum Computing." Thesis, University of California, Santa Barbara, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10195560.
Full textAbstract:
<p> Quantum information science has made significant progress over the last several decades, but the eventual form a quantum computer will take has yet to be determined. Several physical systems have been shown to operate as quantum bits, or qubits, but each faces a central challenge: the qubit must be sufficiently isolated from its environment to maintain quantum coherence while simultaneously having sufficient coupling to the environment to allow quantum mechanical interactions for manipulation and measurement. An approach to achieve these conflicting requirements is to create qubits that are insensitive to small perturbing interactions within their environment by using topological properties of the physical system in which the qubits are formed. This dissertation presents studies on low-dimensional semiconductor heterostructures of InAs, GaSb and AlSb fabricated by molecular beam epitaxy with focus on relevant properties for their utilization in forming a topologically protected (TP) qubit. </p><p> The theoretical basis regarding the semiconductor characteristics suitable for realizing TP qubits stipulates the need for strong spin-orbit coupled semiconductors with high carrier mobility. A comparative study of InAs/AlSb heterostructures wherein structure parameters were systematically varied led to a greater understanding of the limits to mobility in InAs quantum wells. Magnetotransport measurements using a dual-gated device geometry and a comparison of experiment to models of carrier mobility as a function of carrier density were used to identify dominant scattering mechanisms in these heterostructures. </p><p> The development of dual-gated devices and high quality InAs channels with AlSb barriers led to a demonstration of the gate control of spin-orbit coupling in a high mobility InAs/AlSb quantum well in which the gate-tuned electron mobility exceeded 700,000 cm<sup>2</sup>/V·s. Analysis of low temperature magnetoresistance oscillations indicated the zero field spin-splitting could be tuned via the Rashba effect while keeping the two-dimensional electron gas charge density constant. </p><p> Findings from the work on InAs quantum wells were applied to investigations on InAs/GaSb bilayers, a system predicted to be a two-dimensional topological insulator (TI). The temperature and magnetic field dependence of the resistance in dual-gated InAs/GaSb heterostructures gate-tuned to the predicted TI regime were found consistent with conduction through a disordered two-fluid system. The impact of disorder on the formation of topologically protected edge states and an insulating bulk was considered. Potential fluctuations in the band structure for realistic levels of disorder in state-of-the-art heterostructures were calculated using a gated heterostructure model. Potential fluctuations were estimated to be sufficiently large such that conduction in the predicted TI regime was likely dominated by tunneling between localized electron and hole charge fluctuations, corresponding to a symplectic metallic phase rather than a topological insulator. The implications are that future efforts must address defects and disorder in this system if the TI regime is to be achieved. </p>
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Al-Latifi, Yasir. "Optimizing numerical modelling of quantum computing hardware." Thesis, Umeå universitet, Institutionen för fysik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-182659.
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Quantum computers are being developed to solve certain problems faster than classical computers. Instead of using classical bits, they use quantum bits (qubits) that utilize quantum effects. At Chalmers University of Technology, researchers have already built a quantum chip consisting of two superconducting transmon qubits and are trying to build systems with more qubits. To assist in that process, they make numerical simulations of the quantum systems. However, these simulations face an intrinsic computational limitation: the Hilbert space of the system grows exponentially with the number of qubits. In order to mitigate the problem: the simulations should be made as efficient as possible, by applying certain approximations, while still obtaining accurate results. The aim of this project is to compare several of these approximations, to see how accurate they are and how fast they run on a classical computer. This is done by modelling the qubits as quantum anharmonic oscillators and testing several cases: varying the energy levels of the qubits, increasing the number of qubits, and testing the rotating-wave approximation (RWA). These cases were tested by implementing two-qubit gates on the system. The simulations were all made using the Python library QuTiP. The results show that one should simulate using at least one energy level higher than the maximum energy level required for the gate to function. For larger systems, the RWA will make a big difference in simulation times, while still giving relatively accurate results. When using the RWA, the number of levels used does not seem to affect the results significantly and one could therefore use the lowest possible energy levels that can simulate the system.
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ZORZI, Margherita. "Lambda calculi and logics for quantum computing." Doctoral thesis, Università degli Studi di Verona, 2009. http://hdl.handle.net/11562/337380.
Full textAbstract:
In questa tesi proponiamo diversi risultati originali riguardo i lambda
calcoli e le logiche per le computazioni quantistiche. Il lavoro `e diviso
in tre parti.
Nella prima parte richiamiamo alcune nozioni fondamentali di algebra
lineare, logica e computazione quantistica.
La seconda parte volge l’attenzione ai lambda calcoli quantistici.
Introdurremo dapprima Q, un lambda calcolo quantistico con controllo
classico. Studieremo le sue proprie`a classiche, come la confluenza e
la Subject Reduction, proseguendo poi con un’importante propriet`a
quantistica, chiamata standardizzazione. In seguito sar`a studiato il
potere espressivo di Q, attraverso la provata equivalenza con il formalismo
delle famiglie di circuiti quantistici.
A partire da Q, sar`a poi definito e studiato il sottolinguaggio SQ, ispirato
alla Soft Linear Logic ed intrinsecamente polytime.
Sia Q sia SQ non hanno nella sintassi un operatore di misurazione,
e quindi un’implicita misurazione viene assunta alla fine delle computazioni.
I problemi relativi alla misura sono studiati in un terzo lambda calcolo
chiamato Q*, che estende Q con un operatore di misura. Partendo
dall’osservazione che un esplicito operatore di misura interrompe
l’evoluzione altrimenti deterministica del calcolo, importando un comportamento
probabilistico, sono stati definiti dei nuovi strumenti tecnici
quali le computazioni probabilistiche e gli stati misti. Proveremo
un forte teorema di confluenza, valido anche nell’importante caso delle
computazioni infinite.
Nella terza parte della tesi studieremo invece due sistemi modali
etichettati, chiamati rispettivamente MSQS e MSpQS, che permettono
di ragionare qualitativamente sulle computazioni quantistiche. I due
sistemi rappresentano un possibile punto di partenza verso un nuovo
modello per ragionare qualitativamente sulle trasformazioni
computazionali degli stati quantistici, viste come modelli di Kripke.
1<br>In this thesis we propose several original results about lambda calculi
and logics for quantum computing. The work is divided into three
parts.
The first one is devoted to recall the main notions about linear
algebra, logics and quantum computing.
The second and main part focalizes on quantum lambda calculi.
We start with Q, a quantum lambda calculus with classical control.
We study its classical properties, such as confluence and Subject Reduction.
We go on with an important quantum property of Q, called
standardization, and successively, we study the expressive power of the
proposed calculus, by proving the equivalence with the computational
model of quantum circuit families.
From the calculus Q, subsequently a sublanguage of Q called SQ is
defined and studied: SQ is inspired to the Soft Linear Logic and it is
a quantum lambda calculus intrinsically poly-time.
Since Q and SQ have not an explicit measurement operator in the
syntax, an implicit measurement at the end of the computations is assumed.
Measurement problems are explicitly studied in a third quantum
lambda calculus called Q*, an extension of Q with a measurement
operator. Starting from the observation that an explicit measurement
operator breaks the deterministic evolution of the computation by importing
a probabilistic behavior, new technical instruments, such as
the probabilistic computations and the mixed states are defined. We
prove a confluence result for the calculus, also for the relevant case of
infinite computations.
In the last part of the thesis, we propose two labeled modal deduction
systems able to describe quantum computations from a qualitative
point of view. The two systems, called respectively MSQS and MSpQS,
represent a starting point toward a new model to deal (in a qualitative
way) with computational quantum structures, seen as Kripke models.
1
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Rohling, Niklas [Verfasser]. "Quantum Computing with Spin and Valley Qubits in Quantum Dots / Niklas Rohling." Konstanz : Bibliothek der Universität Konstanz, 2015. http://d-nb.info/1095134507/34.
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Pooley, Matthew Anthony. "Components for quantum computing based on optical transitions in single quantum dots." Thesis, University of Cambridge, 2013. https://www.repository.cam.ac.uk/handle/1810/245335.
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The optically active nature of direct bandgap semiconductors makes them well suited for applications in quantum optics. Semiconductor quantum dots (QDs) are particularly promising, due to their discrete atom-like energy levels. In this thesis, transitions between these energy levels are used to investigate the effects of electric and magnetic fields on the energy structure of single QDs, with a view to developing applications in the field of quantum computing. In the work presented here a novel method of creating entangled photon pair emitters is presented, in which an electric field is used to tune the energy structure of single QDs to allow the fidelity of the emitted entangled state to be increased. In addition, a technique for the creation of energy-tunable entangled photon pairs is proposed and shown to be feasible with current technology. Furthermore, the potential of QDs to act as an interface between photonic and spin qubits is explored. Application of a time varying electric field is used to dynamically tune the QD energy levels, allowing the evolution of excitons confined within single QDs to be manipulated. Using this system a controlled phase rotation of the exciton spin state is implemented. Finally, indistinguishable single photons, emitted by the radiative decay of the exciton state, are used to generate the input state for an integrated photonic two-qubit quantum logic gate. This is the first demonstration of a two-qubit gate using on-demand single photons. It is also the first demonstration of such a gate with all components realised using semiconductor materials.
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Vranckx, Stéphane. "Dynamical study of diatomics : applications to astrochemistry, quantum control and quantum computing." Doctoral thesis, Universite Libre de Bruxelles, 2014. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209261.
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In this work, we theoretically study the properties of diatomic molecular systems, their dynamics, and the control thereof through the use of laser fields. We more specifically study three compounds:<p>1) HeH+, a species of great astrochemical importance which is thought to be the first molecular species to have formed in the universe;<p>2) CO2+, a metastable dication of particular interest in quantum control experiments due to its long-lived lowest vibrational level;<p>3) 41K87Rb, a polar molecule that can be formed at very low temperature and trapped, making it a good candidate for quantum computing schemes.<p>First, we use ab initio methods to compute accurate potential energy curves for the lowest singlet and triplet states of HeH+ as well as the potential energy curves, transition dipole moments and nonadiabatic radial couplings of the ground 3Π state of CO2+ and of its 11 lowest 3Σ- states.<p>In a second step, we use this ab initio data to compute the photodissociation and radiative association cross sections for the a and b 3Σ+ states of HeH+, as well as the values of the corresponding rate constants for astrophysical environments. The photodissociation cross sections from the lowest vibrational level of CO2+ is also determined.<p>Going one step further, we optimize laser control fields that drive the photodissociation dynamics of HeH+ and CO2+ towards specific channels. We compare two field optimization methods: a Møller operator-based Local Control approach and Optimal Control Theory. In both cases, we add a constraint that minimizes the area of the optimized fields.<p>Finally, we focus on one of the potential applications of high-fidelity laser control: the use of small molecular systems as quantum computers. We more specifically study the potential implementation of both intra- and intermolecular logic gates on data encoded in hyperfine states of trapped ultracold polar 41K87Rb molecules, opening interesting perspectives in terms of extensibility.<p>/<p>Dans cette thèse, nous étudions théoriquement les propriétés de molécules diatomiques, leur dynamique de réaction ainsi que le contrôle de cette dynamique à l'aide de champs laser. Notre travail porte plus spécifiquement sur trois espèces :<p>1) HeH+, un composé-clé en astrochimie considéré comme la première espèce moléculaire qui s'est formée dans l'univers ;<p>2) CO2+, un dication métastable qui se prête bien à des expériences de contrôle quantique en raison du relativement long temps de vie de son état vibrationnel le plus bas ;<p>3) 41K87Rb, une molécule polaire qui présente la particularité de pouvoir être formée à très basse température et piégée, ce qui en fait un bon support physique potentiel pour la réalisation d'un ordinateur quantique moléculaire. <p>Nous utilisons tout d'abord des méthodes de calcul ab initio afin d'obtenir les courbes d'énergie potentielle des premiers états singulets et triplets de HeH+ avec un haut de degré de précision, ainsi que les courbes d'énergie potentielle, les moments dipolaires de transition et les couplages non-adiabatiques radiaux de l'état fondamental 3Π de CO2+ et de ses 11 premiers états 3Σ-.<p>Ensuite, nous utilisons ces données ab initio pour calculer les sections efficaces de photodissociation et d'association radiative des états a et b 3Σ+ de HeH+, ainsi que les constantes cinétiques associées à ces processus dans les conditions rencontrées dans des environnements astrophysiques. Les sections efficaces de photodissociation du niveau vibrationnel le plus bas de CO2+ sont également calculées. <p>Nous allons ensuite un cran plus loin en optimisant des champs laser qui guident la dynamique de photodissociation de HeH+ et CO2+ vers des canaux de dissociation spécifiques. Nous comparons deux méthodes d'optimisation de ces champs: une approche de contrôle local basée sur les opérateurs de Møller et la théorie du contrôle optimal. Dans le deux cas, nous incluons une contrainte qui minimise l'aire des champs. <p>Enfin, nous nous concentrons sur l'une des applications possibles du contrôle laser à haute fidélité :l'utilisation de petits systèmes moléculaires comme ordinateurs quantiques. Nous étudions plus spécifiquement l'implémentation possible d'opérations logiques intra- et intermoléculaires sur des données encodées dans des états hyperfins de molécules de 41K87Rb piégées, ce qui ouvre des perspectives intéressantes en terme d'extensibilité.<br>Doctorat en Sciences<br>info:eu-repo/semantics/nonPublished
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Xu, Guanglei. "Adiabatic processes, noise, and stochastic algorithms for quantum computing and quantum simulation." Thesis, University of Strathclyde, 2018. http://digitool.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=30919.
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Rapid developments in experiments provide promising platforms for realising quantum computation and quantum simulation. This, in turn, opens new possibilities for developing useful quantum algorithms and explaining complex many-body physics. The advantages of quantum computation have been demonstrated in a small range of subjects, but the potential applications of quantum algorithms for solving complex classical problems are still under investigation. Deeper understanding of complex many-body systems can lead to realising quantum simulation to study systems which are inaccessible by other means. This thesis studies different topics of quantum computation and quantum simulation. The first one is improving a quantum algorithm in adiabatic quantum computing, which can be used to solve classical problems like combinatorial optimisation problems and simulated annealing. We are able to reach a new bound of time cost for the algorithm which has a potential to achieve a speed up over standard adiabatic quantum computing. The second topic is to understand the amplitude noise in optical lattices in the context of adiabatic state preparation and the thermalisation of the energy introduced to the system. We identify regimes where introducing certain type of noise in experiments would improve the final fidelity of adiabatic state preparation, and demonstrate the robustness of the state preparation to imperfect noise implementations. We also discuss the competition between heating and dephasing effects, the energy introduced by non-adiabaticity and heating, and the thermalisation of the system after an application of amplitude noise on the lattice. The third topic is to design quantum algorithms to solve classical problems of fluid dynamics. We develop a quantum algorithm based around phase estimation that can be tailored to specific fluid dynamics problems and demonstrate a quantum speed up over classical Monte Carlo methods. This generates new bridge between quantum physics and fluid dynamics engineering, can be used to estimate the potential impact of quantum computers and provides feedback on requirements for implementing quantum algorithms on quantum devices.
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Hnatenko, O. S. "Quantum computing. Quantum information technologies as the basis for future learning platforms." Thesis, ISMA University of Applied Science, Riga, Latvia, 2021. https://openarchive.nure.ua/handle/document/16270.
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This paper presents the place of quantum technologies in the modern information world. The technique of quantum computing is described. Also presented is a new model of a qubit based on a nanolaser with frequency stabilization, which emits at different wavelengths, which corresponds to its different states. Thus, the work proposes a scheme of a qubit, which underlies quantum technologies and quantum computers. Quantum computing is a thousand times faster than existing ones. In the future this technology will be able to solve problems that are beyond the power of modern computers, which means it will become the basis for learning and understanding the world more broadly.
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Wanzambi, Ellinor, and Stina Andersson. "Quantum Computing: Implementing Hitting Time for Coined Quantum Walks on Regular Graphs." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-444818.
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In recent years, quantum walks have been widely researched and haveshown exciting properties. One such is a quadratic speed-up in hittingtime compared to its classical counterpart. In this paper, we design aquantum circuit for the MNRS algorithm, which finds a marked node in agraph with a quantum walk, and use it to find a hitting time for themarked nodes in the walk. We do this by implementing the circuit on IBMquantum simulators and show that the execution on a noise-free simulatorresults in hitting times that agree with the theoretical expectations.We also run the algorithm on a mock backend that simulates the noise ofthe IBM Melbourne computer. As expected, the noise has an extensiveimpact on the output, resulting in outcomes far from the noise-freesimulation.IT 21
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O'Hara, John. "Quantum light with quantum dots in III-V photonic integrated circuits : towards scalable quantum computing architectures." Thesis, University of Sheffield, 2017. http://etheses.whiterose.ac.uk/20113/.
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The work in this thesis is motivated by the goal of creating scalable quantum computers, and equally by the physical understanding that develops alongside and follows from this. The fields of physics and technology are symbiotic, and quantum information processing is a prime example. The field has the potential to test quantum mechanics in new and profound ways. Here we approach the technological problem by building upon the foundations laid by the semiconductor chip manufacturing industry. This architecture is based on the III-V semiconductors Gallium Arsenide and Indium Arsenide. Combining the two we can create chip-embedded atom-like light sources -- quantum dots -- that can produce quantum photonic states in lithographically etched nanoscale waveguides and cavities. We demonstrate the integration of quantum light sources and single-mode beam splitters in the same on-chip device. These are the two primary ingredients that are needed to produce the entangled states that are the basis of this type of quantum computing. Next we look at the quantum light source in more detail, showing that with cavity-enhancement we can significantly mitigate the detrimental dephasing associated with nanostructures. The source can be used as a means to produce coherently scattered photons in the waveguides. More importantly, the on-demand photons obtained from pulsed excitation are more indistinguishable and thus more suitable for quantum information carrying and processing. Through experiments and simulations, we investigate some aspects of single-photon sources under pulsed excitation, including emission rate, emission number probabilities, and indistinguishability. A new technique to measure very short lifetimes is demonstrated and examined theoretically. Finally we look at preliminary steps to extend the platform further. The inclusion of photonic crystals and superconducting nanowires provides on-chip filters and detectors, and etched diode structures enable electrical excitation and tunability of the circuit components. These show some clear paths that the work can continue to evolve along.
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Sauer, Jacob A. "Cold Atom Manipulation for Quantum Computing and Control." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/4809.
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Devices that exploit the properties of quantum mechanics for their operation can offer unique advantages over their classical counterparts. Interference of matter waves can be used to
dramatically increase the rotational sensitivity of gyroscopes. Complete control of the quantum evolution of a system could produce a new powerful computational device known as a quantum computer. Research into these technologies offers a deeper
understanding of quantum mechanics as well as exciting new insights into many other areas of science. Currently, a limiting factor in many quantum devices using neutral atoms is accurate motional control over the atoms. This thesis describes two recent advancements in neutral atom motional control using both magnetic and electromagnetic confining fields. Part I reports on the demonstration of the first storage ring for neutral atoms. This storage ring may one day provide the basis for the world's most
sensitive gyroscope. Part II describes the optical delivery of neutral atoms into the mode of a high-finesse cavity for applications in quantum computing and communication.
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Alfares, Fawzan S. "Novel optimisation algorithms based on quantum computing principles." Thesis, Brunel University, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.415136.
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Imreh, Gergely. "Implementing Segmented ion Trap designs For Quantum Computing." Thesis, University of Oxford, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.490084.
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With all the key elements of quantum computing in ion traps demonstrated by the research community, the focus is now placed on building more sophisticated traps with larger numbers of ions to allow practical scale information processing. One promising avenue is to store ions in and shuttle them between many independent traps which serve as potential interaction sites.
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Mendoza, Gabriel J. "Optical quantum computing with active multiplexing and switching." Thesis, University of Bristol, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.687435.
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Linear optical quantum computing (LOQC) benefits from photonic qubits with low decoherence, simple optical elements for qubit manipulation, and a developing integrated platform. The cost of the LOQC approach is the non-deterministic nature of many of the processes, including single-photon generation, which arises from parametric heralded sources and the lack of direct interaction between photons. Active multiplexing - repeating a generation process in time or space and rerouting to single modes using an optical switching network-has been proposed to overcome this challenge and could enable scalable quantum photonics. This thesis explores optical quantum computing, and quantum photonics in general, using active multiplexing and switching, starting from the single-photon source and extending to large-scale architectures. A theoretical framework for time and space multiplexed single photon sources is provided, and a proof-of-principle experimental implementation of a time and space multiplexed source using bulk and fiber components is demonstrated. Multiplexing heralded entangled states is explored theoretically, and a new technique to minimize active switching requirements in some scenarios- relative bin multiplexing- is introduced. Component level architectures for fully fault-tolerant LOQC using active switching are presented, as well as first estimates of their loss/ error thresholds and resource costs. An integrated silicon all-optical switch based on the Kerr effect is simulated and designed. Optical multiplexing using active switching is shown to be a promising approach to break through the current experimental limits in quantum photonics and enable larger experiments in the near future. With sufficient development, optical multiplexing is also a feasible alternative to quantum matter-based schemes for large-scale quantum photonics and computing.