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1
Lovett, Neil Brian. "Application of quantum walks on graph structures to quantum computing." Thesis, University of Leeds, 2011. http://etheses.whiterose.ac.uk/1689/.
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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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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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Quantum holonomies are investigated in different contexts.
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.
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
provided. It is further shown that there are cases when the holonomy is only partially defined. This has no counterpart in the Abelian setting.
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.
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.
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.
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.
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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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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:1) HeH+, a species of great astrochemical importance which is thought to be the first molecular species to have formed in the universe;
2) CO2+, a metastable dication of particular interest in quantum control experiments due to its long-lived lowest vibrational level;
3) 41K87Rb, a polar molecule that can be formed at very low temperature and trapped, making it a good candidate for quantum computing schemes.
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.
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.
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.
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.
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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 :
1) HeH+, un composé-clé en astrochimie considéré comme la première espèce moléculaire qui s'est formée dans l'univers ;
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 ;
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.
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-.
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.
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.
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.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Di, Tiegang. "Entanglement generation and applications in quantum information." Texas A&M University, 2006. http://hdl.handle.net/1969.1/3840.
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This dissertation consists of three sections. In the first section, we discuss the generation
of arbitrary two-qubit entangled states and present three generation methods.
The first method is based on the interaction of an atom with classical and quantized
cavity fields. The second method is based on the interaction of two coupled two-level
atoms with a laser field. In the last method, we use two spin-1/2 systems which
interact with a tuned radio frequency pulse. Using those methods we have generated
two qubit arbitrary entangled states which is widely used in quantum computing and
quantum information. In the second section, we discuss a possible experimental implementation
of quantum walk which is based on the passage of an atom through a
high-Q cavity. The chirality is determined by the atomic states and the displacement
is characterized by the photon number inside the cavity. Our scheme makes quantum
walk possible in a cavity QED system and the results could be widely used on
quantum computer. In the last section, we investigate the properties of teleporting
an arbitrary superposition of entangled Dicke states of any number of atoms (qubits)
between two distant cavities. We also studied teleporting continuous variables of an
optical field. Teleportation of Dicke states relies on adiabatic passage using multiatom
dark states in each cavity and a conditional detection of photons leaking out of both cavities. In the continuous variables teleportation scheme we first reformulate
the protocol of quantum teleportation of arbitrary input optical field states in
the density matrix form, and established the relation between the P-function of the
input and output states. We then present a condition involving squeeze parameter
and detection efficiency under which the P-function of the output state becomes the
Q function of the input state such that any nonclassical features in the input state
will be eliminated in the teleported state. Based on the research in this section we
have made it possible of arbitrary atomic Dicke states teleportation from one cavity
to another, and this teleortation will play an essential role in quantum communication.
Since quantum properties is so important in quantum communication, the
condition we give in this section to distinguish classical and quantum teleportation is
also important.
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CIRILLO, GIOVANNI AMEDEO. "Engineering quantum computing technologies: from compact modelling to applications." Doctoral thesis, Politecnico di Torino, 2022. http://hdl.handle.net/11583/2971119.
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Holleczek, Annemarie. "Linear optics quantum computing with single photons from an atom-cavity system." Thesis, University of Oxford, 2016. http://ora.ox.ac.uk/objects/uuid:d655fa1c-3405-413d-8af8-eecf6212ab74.
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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 μs, 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.
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Venegas-Andraca, Salvador Elías. "Discrete quantum walks and quantum image processing." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427612.
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In this thesis we have focused on two topics: Discrete Quantum Walks and Quantum Image Processing. Our work is a contribution within the field of quantum computation from the perspective of a computer scientist. With the purpose of finding new techniques to develop quantum algorithms, there has been an increasing interest in studying Quantum Walks, the quantum counterparts of classical random walks. Our work in quantum walks begins with a critical and comprehensive assessment of those elements of classical random walks and discrete quantum walks on undirected graphs relevant to algorithm development. We propose a model of discrete quantum walks on an infinite line using pairs of quantum coins under different degrees of entanglement, as well as quantum walkers in different initial state configurations, including superpositions of corresponding basis states. We have found that the probability distributions of such quantum walks have particular forms which are different from the probability distributions of classical random walks. Also, our numerical results show that the symmetry properties of quantum walks with entangled coins have a non-trivial relationship with corresponding initial states and evolution operators. In addition, we have studied the properties of the entanglement generated between walkers, in a family of discrete Hadamard quantum walks on an infinite line with one coin and two walkers. We have found that there is indeed a relation between the amount of entanglement available in each step of the quantum walk and the symmetry of the initial coin state. However, as we show with our numerical simulations, such a relation is not straightforward and, in fact, it can be counterintuitive. Quantum Image Processing is a blend of two fields: quantum computation and image processing. Our aim has been to promote cross-fertilisation and to explore how ideas from quantum computation could be used to develop image processing algorithms. Firstly, we propose methods for storing and retrieving images using non-entangled and entangled qubits. Secondly, we study a case in which 4 different values are randomly stored in a single qubit, and show that quantum mechanical properties can, in certain cases, allow better reproduction of original stored values compared with classical methods. Finally, we briefly note that entanglement may be used as a computational resource to perform hardware-based pattern recognition of geometrical shapes that would otherwise require classical hardware and software.
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Bettonte, Gabriella. "Quantum approaches for Worst-Case Execution-Times analysis of programs." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPASG026.
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L'informatique quantique gagne en popularité dans la communauté informatique. La prise de conscience du potentiel de l'informatique quantique a commencée en 1981, lorsque Richard Feynman a imaginé la construction d'un ordinateur quantique. Cependant, le domaine a connu beaucoup de scepticisme quant à ses capacités pratiques à long terme pour résoudre les problèmes. En particulier, les chercheurs tente de relever le défi de construire des ordinateurs quantiques scalables et fiables. Dernièrement, de nombreuses entreprises ont obtenu des résultats encourageants et ont construit des machines quantiques avec suffisamment de qubits pour commencer à mener des expériences intéressantes dessus. Nous avons choisi l'évaluation du pire temps d'exécution (WCET) comme application de nos recherches sur l'informatique quantique, car elle est cruciale pour diverses applications temps réel. L'analyse WCET garantit que le temps d'exécution d'un programme respecte toutes les contraintes d'ordonnancement et de timing. Dans l'histoire des algorithmes quantiques, l'attention a souvent été accordée aux problèmes avec une structure mathématique particulière. L'évaluation des WCET, à l'opposé, n'est pas un problème a priori favorable au contexte quantique, et possède des solutions classiques efficaces déjà éprouvées. Ainsi, il est intéressant d'explorer l'impact de l'informatique quantique sur ce type de problèmes, dans l'esprit de trouver des domaines nouveaux et concrets dans lesquels l'informatique quantique pourrait apporter sa contribution. Si ce n'est pas le cas, la recherche dans ces domaines spécifiques peut aider à définir les limites des applications qui pourraient bénéficier de l'informatique quantique. Cette thèse présente différentes approches quantiques pour effectuer des évaluations WCETs de programmes pour des modèles simplifiésQuantum computing is gaining popularity in the computer science community. The awareness of the potential of quantum computing started in 1981, when Richard Feynman first speculated about building a quantum computer. However, until recently, the field has known much skepticism about its long-term practical capabilities to solve problems. In particular, researchers are still facing the challenge of building scalable and reliable quantum computers. Lately, many companies have obtained encouraging results and built quantum machines with enough qubits to start conducting interesting experiments. We chose the worst-case execution-time (WCET) evaluation as the application of our research on quantum computing, as it is crucial for various real-time applications. WCET analysis guarantees that a program's execution time matches all the scheduling and timing constraints. In quantum algorithms history, attention was often given to problems with a particular mathematical structure. The WCETs evaluation, as an opposite, is not a particularly quantum-friendly problem, and it has already proven efficient classical solutions. Hence, it is worth exploring the impact of quantum computing on those kinds of problems, with the spirit of finding new and concrete fields to which quantum computing could bring its potential. If not, research on such specific fields will help to set the boundaries of which applications could benefit from quantum computing. This thesis presents different quantum approaches to perform WCETs evaluations of programs under simplified assumptions
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Kissinger, Aleks. "Pictures of processes : automated graph rewriting for monoidal categories and applications to quantum computing." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:61fb3161-a353-48fc-8da2-6ce220cce6a2.
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This work is about diagrammatic languages, how they can be represented, and what they in turn can be used to represent. More specifically, it focuses on representations and applications of string diagrams. String diagrams are used to represent a collection of processes, depicted as "boxes" with multiple (typed) inputs and outputs, depicted as "wires". If we allow plugging input and output wires together, we can intuitively represent complex compositions of processes, formalised as morphisms in a monoidal category. While string diagrams are very intuitive, existing methods for defining them rigorously rely on topological notions that do not extend naturally to automated computation. The first major contribution of this dissertation is the introduction of a discretised version of a string diagram called a string graph. String graphs form a partial adhesive category, so they can be manipulated using double-pushout graph rewriting. Furthermore, we show how string graphs modulo a rewrite system can be used to construct free symmetric traced and compact closed categories on a monoidal signature. The second contribution is in the application of graphical languages to quantum information theory. We use a mixture of diagrammatic and algebraic techniques to prove a new classification result for strongly complementary observables. Namely, maximal sets of strongly complementary observables of dimension D must be of size no larger than 2, and are in 1-to-1 correspondence with the Abelian groups of order D. We also introduce a graphical language for multipartite entanglement and illustrate a simple graphical axiom that distinguishes the two maximally-entangled tripartite qubit states: GHZ and W. Notably, we illustrate how the algebraic structures induced by these operations correspond to the (partial) arithmetic operations of addition and multiplication on the complex projective line. The third contribution is a description of two software tools developed in part by the author to implement much of the theoretical content described here. The first tool is Quantomatic, a desktop application for building string graphs and graphical theories, as well as performing automated graph rewriting visually. The second is QuantoCoSy, which performs fully automated, model-driven theory creation using a procedure called conjecture synthesis.
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Kotiyal, Saurabh. "Design Exploration and Application of Reversible Circuits in Emerging Technologies." Scholar Commons, 2016. http://scholarcommons.usf.edu/etd/6283.
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The reversible logic has promising applications in emerging computing paradigms, such as quantum computing, quantum dot cellular automata, optical computing, etc. In reversible logic gates, there is a unique one-to-one mapping between the inputs and outputs. To generate a useful gate function, the reversible gates require some constant ancillary inputs called ancilla inputs. Also to maintain the reversibility of the circuits some additional unused outputs are required that are referred to as the garbage outputs. The number of ancilla inputs, the number of garbage outputs and quantum cost plays an important role in the evaluation of reversible circuits. Thus minimizing these parameters are important for designing an efficient reversible circuit. Reversible circuits are of highest interest in optical computing, quantum dot cellular automata and quantum computing. The quantum gates perform an elementary unitary operation on one, two or more two-state quantum systems called qubits. Any unitary operation is reversible in nature, and hence, quantum networks are also reversible, to conclude the quantum computers must be built from reversible logic components.
The main contribution of this dissertation is the design exploration and application of reversible circuits in emerging nanotechnologies. The emerging technologies explored in this work are 1) Optical quantum computing 2) Quantum computing.
The first contribution of this dissertation is Mach-Zehnder interferometer based design of all optical reversible binary adder. The all optical reversible adder design is based on two new optical reversible gates referred as optical reversible gate I (ORG-I) and optical reversible gate II (ORG-II) and the existing all optical Feynman gate. The two new reversible gates ORG-I and ORGI-II have been proposed and can implement a reversible adder with a reduced optical cost which is equal to the number of MZI switches required, less propagation delay, and with zero overhead in terms of number of ancilla inputs and the garbage outputs. The proposed all optical reversible adder design based on the ORG-I and ORG-II reversible gates are compared and shown to be better than the other existing designs of reversible adder proposed in the non-optical domain in terms of number of MZI switches, delay, the number of ancilla inputs and the garbage outputs. The proposed all optical reversible adder will be a key component of an all optical reversible arithmetic logical unit (ALU), that is a quite essential component in a wide variety of optical signal processing applications. In the existing literature, the NAND logic based implementation is the only known implementation available for reversible gates and its functions. There is a lack of research in the direction of NOR logic based implementation of reversible gates and functions. The second contribution of this dissertation is the design of NOR logic based n-input and n-output reversible gates, one of which can be efficiently mapped into optical computing using the Mach-Zehnder interferometer (MZI), while the other can be mapped efficiently in optical computing using the linear optical quantum gates. The proposed reversible NOR gates work as a corresponding NOR counterpart of NAND logic based Toffoli gates. The proposed optical reversible NOR logic gates can implement the reversible boolean logic functions with less number of linear optical quantum logic gates with reduced optical cost and propagation delay compared to the implementation using existing optical reversible NAND gates. It is illustrated that an optical reversible gate library having both optical Toffoli gate and the proposed optical reversible NOR gate is superior compared to the library containing only the optical Toffoli gate: (i) in terms of number of linear optical quantum gates when implemented using linear optical quantum computing (LOQC), (ii) in terms of optical cost and delay when implemented using the Mach-Zehnder interferometer. The third contribution of this dissertation is a binary tree-based design methodology for a NxN reversible multiplier. The proposed binary tree-based design methodology for a NxN reversible multiplier performs the addition of partial products in parallel using the reversible ripple adders with zero ancilla bit and zero garbage bit; thereby, minimizing the number of ancilla and garbage bits used in the design. The proposed design methodology shows improvements in terms of number of ancilla inputs and garbage outputs compared to all the existing reversible multiplier designs. The methodology is also extended to the design of NxN reversible signed multiplier based on modified Baugh-Wooley multiplication methodology.
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Michelberger, Patrick Steffen. "Room temperature caesium quantum memory for quantum information applications." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:19c9421d-0276-4c6d-a641-7640d2981da3.
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Quantum memories are key components in photonics-based quantum information processing networks. Their ability to store and retrieve information on demand makes repeat-until-success strategies scalable. Warm alkali-metal vapours are interesting candidates for the implementation of such memories, thanks to their very long storage times as well as their experimental simplicity and versatility. Operation with the Raman memory protocol enables high time-bandwidth products, which denote the number of possible storage trials within the memory lifetime. Since large time-bandwidth products enable multiple synchronisation trials of probabilistically operating quantum gates via memory-based temporal multiplexing, the Raman memory is a promising tool for such tasks. Particularly, the broad spectral bandwidth allows for direct and technologically simple interfacing with other photonic primitives, such as heralded single photon sources. Here, this kind of light-matter interface is implemented using a warm caesium vapour Raman memory. Firstly, we study the storage of polarisation-encoded quantum information, a common standard in quantum information processing. High quality polarisation preservation for bright coherent state input signals can be achieved, when operating the Raman memory in a dual-rail configuration inside a polarisation interferometer. Secondly, heralded single photons are stored in the memory. To this end, the memory is operated on-demand by feed-forward of source heralding events, which constitutes a key technological capability for applications in temporal multiplexing. Prior to storage, single photons are produced in a waveguide-based spontaneous parametric down conversion source, whose bespoke design spectrally tailors the heralded photons to the memory acceptance bandwidth. The faithful retrieval of stored single photons is found to be currently limited by noise in the memory, with a signal-to-noise ratio of approximately 0.3 in the memory output. Nevertheless, a clear influence of the quantum nature of an input photon is observed in the retrieved light by measuring the read-out signal's photon statistics via the g(2)-autocorrelation function. Here, we find a drop in g(2) by more than three standard deviations, from g(2) ~ 1.69 to g(2) ~ 1.59 upon changing the input signal from coherent states to heralded single photons. Finally, the memory noise processes and their scalings with the experimental parameters are examined in detail. Four-wave-mixing noise is determined as the sole important noise source for the Raman memory. These experimental results and their theoretical description point towards practical solutions for noise-free operation.
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Candoli, Davide. "Simulation of NMR/NQR observables and spin control for applications in Quantum Science." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020.
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Il mio progetto di tesi consiste nello sviluppo di un programma per la simulazione numerica di esperimenti di risonanza magnetica/di quadrupolo nucleare (NMR/NQR), con l’obiettivo di realizzare una connessione tra la teoria e le evidenze sperimentali: dopo aver ricostruito la dinamica degli spin nucleari prevista in base alla teoria, il software simula a partire da questa i risultati delle misure, presentandoli in una forma confrontabile con i dati ottenuti in laboratorio. L’intero lavoro è fondato su uno studio completo e approfondito della descrizione quantistica dei fenomeni di interesse, la quale è servita come modello su cui plasmare la struttura del programma. Le simulazioni eseguite sondano buona parte della fenomenologia studiata nei laboratori NMR, abbracciando un ampio spettro di configurazioni che comprende NMR ed NQR pure e reciprocamente perturbate. Il software è stato impiegato anche per la riproduzione delle tecniche sperimentali finalizzate all’implementazione di qubit e quantum gates in sistemi NQR, dimostrandosi uno strumento utile per la ricerca nell’ambito del controllo quantistico ed elaborazione dell’informazione quantistica.
Questo lavoro di tesi è stato realizzato nell'ambito di un progetto di cooperazione internazionale dell'Università di Bologna in collaborazione con la Brown University, Providence (USA).
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Kanchibotla, Bhargava Ram V. "Fabrication and Device Applications of Self Assembled Nanostructures." VCU Scholars Compass, 2009. http://scholarscompass.vcu.edu/etd/2.
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The spin dynamics of electrons in inorganic and organic semiconducting nanostructures has become an area of interest in recent years. The controlled manipulation of an electron’s spin, and in particular its phase, is the primary requirement for applications in quantum information processing. The phase decoheres in a time known as the transverse relaxation time or T2 time. We have carried out a measurement of the ensemble-averaged transverse spin relaxation time (T2*) in bulk and few molecules of the organic semiconductor tris-(8-hydroxyquinolinolato aluminum) or Alq3. The Alq3 system exhibits two characteristic T2* times: the longer of which is temperature independent and the shorter is temperature dependent, indicating that the latter is most likely limited by spin-phonon interaction. Based on the measured data, we infer that the single-particle T2 time in Alq3 is probably long enough to meet Knill's criterion for fault-tolerant quantum computing even at room temperature. Alq3 is also an optically active organic, and we propose a simple optical scheme for spin qubit readout. Moreover, we found that the temperature-dependent T2* time is considerably shorter in bulk Alq3 powder than in few molecules confined in 1–2-nm-sized cavities. Because carriers in organic molecules are localized over individual molecules or atoms but the phonons are delocalized, we believe that this feature is caused by a phonon bottleneck effect. Organic fluorophore molecules, electrosprayed within nanometer sized pores of an anodic alumina film, exhibit unusually large molecule-specific red- or blue-shifts in the fluorescence peak. This molecular specificity allows us to resolve different constituents in a mixture optically, providing a unique new technology for bio- and chemical sensing. We have also observed that the fluorescence efficiency progressively increases with decreasing pore diameter. This trend cannot be explained by the usual photo carrier confinement model since the photo carriers are localized over individual molecules (or atoms) which are much smaller than the pore diameter. A more likely explanation is the metal enhanced fluorescence caused by the plasmon resonance of nanotextured aluminum lying at the bottom of the pores.
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Zafarullah, Ijaz. "Thulium ions in a yttrium aluminum garnet host for quantum computing applications material analysis and single qubit operations /." Thesis, Montana State University, 2008. http://etd.lib.montana.edu/etd/2008/zafarullah/ZafarullahI0508.pdf.
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Rare-earth-doped crystals have been used for optical signal processing and storage applications. In this dissertation, their potential for quantum computing applications is explored. In one quantum computing scheme, information is stored in nuclear spin states and this information is then processed by using optical pulses through the coupling of these nuclear spin states to a common electronic level. To implement this scheme, nuclear spin states and coupling of these nuclear spin states to a common electronic level is required. Preliminary work in rare-earth materials like Pr3+ and Eu3+ has shown promising results regarding their suitability for quantum computing applications. One particular problem with these materials is that their transition wavelengths are only accessible with dye lasers. These lasers are inherently unstable, and currently few available systems exhibit the stability required for quantum computing applications. An alternative choice was to investigate other rare-earth ions like thulium. Thulium has a transition wavelength that can be accessed with diode lasers, which are commercially available, easy to stabilize, and compact. This dissertation is based on our investigations of Tm3+:YAG for quantum computing applications. Investigations involved a detailed characterization of the material. Nuclear spin states, in Tm3+:YAG, were obtained by applying an external magnetic field to the sample. First, interaction of an external magnetic field with the thulium ions at various sites in the crystal was analyzed. This analysis was used to measure the magnetic anisotropy in the material. These results show that it is possible, with the suitable choice of the magnetic orientation and the site in the crystal, to build a working 3-level quantum system. In the demonstration of single qubit operations in Tm3+:YAG, we first theoretically studied the effect of Gaussian spatial beam on the single qubit operations. Later on, we experimentally prepared a single isolated ensemble of ions in the inhomogeneously broadened absorption profile of the medium. This single isolated ensemble of ions was used as a test-bed to implement the single qubit operations. We also isolated two ensembles of ions in the inhomogeneous absorption profile of the medium. The interaction between these two isolated ensembles of ions was also studied.
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Tirukkovalur, Sravya. "A Global Address Space Approach to Automated Data Management for Parallel Quantum Monte Carlo Applications." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1307464186.
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Kukharchyk, Nadezhda [Verfasser], Andreas D. [Akademischer Betreuer] Wieck, and Pavel [Akademischer Betreuer] Bushev. "Focused ion beam implantation of Yttrium orthosilicates with Erbium ions for applications in quantum computing / Nadezhda Kukharchyk. Gutachter: Andreas D. Wieck ; Pavel Bushev." Bochum : Ruhr-Universität Bochum, 2016. http://d-nb.info/1089006853/34.
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Hawash, Maher Mofeid. "Methods for Efficient Synthesis of Large Reversible Binary and Ternary Quantum Circuits and Applications of Linear Nearest Neighbor Model." PDXScholar, 2013. https://pdxscholar.library.pdx.edu/open_access_etds/1090.
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This dissertation describes the development of automated synthesis algorithms that construct reversible quantum circuits for reversible functions with large number of variables. Specifically, the research area is focused on reversible, permutative and fully specified binary and ternary specifications and the applicability of the resulting circuit to the physical limitations of existing quantum technologies.
Automated synthesis of arbitrary reversible specifications is an NP hard, multiobjective optimization problem, where 1) the amount of time and computational resources required to synthesize the specification, 2) the number of primitive quantum gates in the resulting circuit (quantum cost), and 3) the number of ancillary qubits (variables added to hold intermediate calculations) are all minimized while 4) the number of variables is maximized. Some of the existing algorithms in the literature ignored objective 2 by focusing on the synthesis of a single solution without the addition of any ancillary qubits while others attempted to explore every possible solution in the search space in an effort to discover the optimal solution (i.e., sacrificed objective 1 and 4).
Other algorithms resorted to adding a huge number of ancillary qubits (counter to objective 3) in an effort minimize the number of primitive gates (objective 2). In this dissertation, I first introduce the MMDSN algorithm that is capable of synthesizing binary specifications up to 30 variables, does not add any ancillary variables, produces better quantum cost (8-50% improvement) than algorithms which limit their search to a single solution and within a minimal amount of time compared to algorithms which perform exhaustive search (seconds vs. hours). The MMDSN algorithm introduces an innovative method of using the Hasse diagram to construct candidate solutions that are guaranteed to be valid and then selects the solution with the minimal quantum cost out of this subset.
I then introduce the Covered Set Partitions (CSP) algorithm that expands the search space of valid candidate solutions and allows for exploring solutions outside the range of MMDSN. I show a method of subdividing the expansive search landscape into smaller partitions and demonstrate the benefit of focusing on partition sizes that are around half of the number of variables (15% to 25% improvements, over MMDSN, for functions less than 12 variables, and more than 1000% improvement for functions with 12 and 13 variables). For a function of n variables, the CSP algorithm, theoretically, requires n times more to synthesize; however, by focusing on the middle k (k by MMDSN which typically yields lower quantum cost. I also show that using a Tabu search for selecting the next set of candidate from the CSP subset results in discovering solutions with even lower quantum costs (up to 10% improvement over CSP with random selection).
In Chapters 9 and 10 I question the predominant methods of measuring quantum cost and its applicability to physical implementation of quantum gates and circuits. I counter the prevailing literature by introducing a new standard for measuring the performance of quantum synthesis algorithms by enforcing the Linear Nearest Neighbor Model (LNNM) constraint, which is imposed by the today's leading implementations of quantum technology. In addition to enforcing physical constraints, the new LNNM quantum cost (LNNQC) allows for a level comparison amongst all methods of synthesis; specifically, methods which add a large number of ancillary variables to ones that add no additional variables. I show that, when LNNM is enforced, the quantum cost for methods that add a large number of ancillary qubits increases significantly (up to 1200%).
I also extend the Hasse based method to the ternary and I demonstrate synthesis of specifications of up to 9 ternary variables (compared to 3 ternary variables that existed in the literature). I introduce the concept of ternary precedence order and its implication on the construction of the Hasse diagram and the construction of valid candidate solutions. I also provide a case study comparing the performance of ternary logic synthesis of large functions using both a CUDA graphic processor with 1024 cores and an Intel i7 processor with 8 cores. In the process of exploring large ternary functions I introduce, to the literature, eight families of ternary benchmark functions along with a Multiple Valued file specification (the Extended Quantum Specification XQS). I also introduce a new composite quantum gate, the multiple valued Swivel gate, which swaps the information of qubits around a centrally located pivot point.
In summary, my research objectives are as follows:
* Explore and create automated synthesis algorithms for reversible circuits both in binary and ternary logic for large number of variables.
* Study the impact of enforcing Linear Nearest Neighbor Model (LNNM) constraint for every interaction between qubits for reversible binary specifications.
* Advocate for a revised metric for measuring the cost of a quantum circuit in concordance with LNNM, where, on one hand, such a metric would provide a way for balanced comparison between the various flavors of algorithms, and on the other hand, represents a realistic cost of a quantum circuit with respect to an ion trap implementation.
* Establish an open source repository for sharing the results, software code and publications with the scientific community. With the dwindling expectations for a new lifeline on silicon-based technologies, quantum computations have the potential of becoming the future workhorse of computations. Similar to the automated CAD tools of classical logic, my work lays the foundation for creating automated tools for constructing quantum circuits from reversible specifications.
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Yemen, Olfa. "Application des codes cycliques tordus." Phd thesis, Université Nice Sophia Antipolis, 2013. http://tel.archives-ouvertes.fr/tel-00866858.
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Le sujet porte sur une classe de codes correcteurs d erreurs dits codes cycliques tordus, et ses applications a l'Informatique quantique et aux codes quasi-cycliques. Les codes cycliques classiques ont une structure d'idéaux dans un anneau de polynômes. Ulmer a introduit en 2008 une généralisation aux anneaux dits de polynômes tordus, une classe d'anneaux non commutatifs introduits par Ore en 1933. Dans cette thèse on explore le cas du corps a quatre éléments et de l'anneau produit de deux copies du corps a deux éléments.
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Faust, Thomas Benjamin. "On the synthesis, measurement and applications of octanuclear heterometallic rings." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/on-the-synthesis-measurement-and-applications-of-octanuclear-heterometallic-rings(a9697906-50e4-4d0a-9eda-bfd09b9e12f8).html.
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Inorganic macrocycles have stimulated interest in recent years for their magnetic properties, their associated host-guest chemistry and their aesthetically appealing structures. These characteristics have led to suggestions that they could be exploited for the purposes of ion recognition, catalysis, as single molecule magnets, MRI agents, antibacterial agents and as part of larger architectures in a molecular machine. This thesis explores the properties of a group of chromium(III) macrocycles, with functionality tailored towards different pursuits. Firstly the magnetic properties of a newly synthesised family of ring dimers are investigated. The nature of magnetic exchange within each ring leads to a net electronic spin which, it has been proposed, could represent a quantum binary digit within a quantum information processing system. By linking together pairs of rings, the degree of inter ring communication can be determined. Such interactions are important for the correlation of spin as initiation of quantum entanglement, a pre-requisite for quantum computing. The rings can also act as fluoro-metallocrowns, hosting the molecule which templated their formation. A range of rings with different guests are synthesised and their solid and solution state structures are explored. On templating about bulky dialkyl amines hybrid organic-inorganic rotaxanes are formed where the guest is fixed. In contrast when using small amines and alkali metals, exchange of guests is possible. The dynamics of all of these systems are investigated with proton NMR, quite remarkable for such highly paramagnetic complexes.
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Angelsmark, Ola. "Constructing Algorithms for Constraint Satisfaction and Related Problems : Methods and Applications." Doctoral thesis, Linköping : Univ, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-3836.
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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.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/16434
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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.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.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.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.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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Dewaele, Nicholas. "Quantum Computing With Quantum Dots Using The Heisenberg Exchange Interaction." OpenSIUC, 2014. https://opensiuc.lib.siu.edu/theses/1600.
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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.
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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.Doctor of Philosophy
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.
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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.
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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.