319 research outputs found

    Validation of frequency and mode extraction calculations from time-domain simulations of accelerator cavities

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    The recently developed frequency extraction algorithm [G.R. Werner and J.R. Cary, J. Comp. Phys. 227, 5200 (2008)] that enables a simple FDTD algorithm to be transformed into an efficient eigenmode solver is applied to a realistic accelerator cavity modeled with embedded boundaries and Richardson extrapolation. Previously, the frequency extraction method was shown to be capable of distinguishing M degenerate modes by running M different simulations and to permit mode extraction with minimal post-processing effort that only requires solving a small eigenvalue problem. Realistic calculations for an accelerator cavity are presented in this work to establish the validity of the method for realistic modeling scenarios and to illustrate the complexities of the computational validation process. The method is found to be able to extract the frequencies with error that is less than a part in 10^5. The corrected experimental and computed values differ by about one parts in 10^$, which is accounted for (in largest part) by machining errors. The extraction of frequencies and modes from accelerator cavities provides engineers and physicists an understanding of potential cavity performance as it depends on shape without incurring manufacture and measurement costs

    Advanced tensor based signal processing techniques for wireless communication systems and biomedical signal processing

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    Many observed signals in signal processing applications including wireless communications, biomedical signal processing, image processing, and machine learning are multi-dimensional. Tensors preserve the multi-dimensional structure and provide a natural representation of these signals/data. Moreover, tensors provide often an improved identifiability. Therefore, we benefit from using tensor algebra in the above mentioned applications and many more. In this thesis, we present the benefits of utilizing tensor algebra in two signal processing areas. These include signal processing for MIMO (Multiple-Input Multiple-Output) wireless communication systems and biomedical signal processing. Moreover, we contribute to the theoretical aspects of tensor algebra by deriving new properties and ways of computing tensor decompositions. Often, we only have an element-wise or a slice-wise description of the signal model. This representation of the signal model does not reveal the explicit tensor structure. Therefore, the derivation of all tensor unfoldings is not always obvious. Consequently, exploiting the multi-dimensional structure of these models is not always straightforward. We propose an alternative representation of the element-wise multiplication or the slice-wise multiplication based on the generalized tensor contraction operator. Later in this thesis, we exploit this novel representation and the properties of the contraction operator such that we derive the final tensor models. There exist a number of different tensor decompositions that describe different signal models such as the HOSVD (Higher Order Singular Value Decomposition), the CP/PARAFAC (Canonical Polyadic / PARallel FACtors) decomposition, the BTD (Block Term Decomposition), the PARATUCK2 (PARAfac and TUCker2) decomposition, and the PARAFAC2 (PARAllel FACtors2) decomposition. Among these decompositions, the CP decomposition is most widely spread and used. Therefore, the development of algorithms for the efficient computation of the CP decomposition is important for many applications. The SECSI (Semi-Algebraic framework for approximate CP decomposition via SImultaneaous matrix diagonalization) framework is an efficient and robust tool for the calculation of the approximate low-rank CP decomposition via simultaneous matrix diagonalizations. In this thesis, we present five extensions of the SECSI framework that reduce the computational complexity of the original framework and/or introduce constraints to the factor matrices. Moreover, the PARAFAC2 decomposition and the PARATUCK2 decomposition are usually described using a slice-wise notation that can be expressed in terms of the generalized tensor contraction as proposed in this thesis. We exploit this novel representation to derive explicit tensor models for the PARAFAC2 decomposition and the PARATUCK2 decomposition. Furthermore, we use the PARAFAC2 model to derive an ALS (Alternating Least-Squares) algorithm for the computation of the PARAFAC2 decomposition. Moreover, we exploit the novel contraction properties for element wise and slice-wise multiplications to model MIMO multi-carrier wireless communication systems. We show that this very general model can be used to derive the tensor model of the received signal for MIMO-OFDM (Multiple-Input Multiple-Output - Orthogonal Frequency Division Multiplexing), Khatri-Rao coded MIMO-OFDM, and randomly coded MIMO-OFDM systems. We propose the transmission techniques Khatri-Rao coding and random coding in order to impose an additional tensor structure of the transmit signal tensor that otherwise does not have a particular structure. Moreover, we show that this model can be extended to other multi-carrier techniques such as GFDM (Generalized Frequency Division Multiplexing). Utilizing these models at the receiver side, we design several types for receivers for these systems that outperform the traditional matrix based solutions in terms of the symbol error rate. In the last part of this thesis, we show the benefits of using tensor algebra in biomedical signal processing by jointly decomposing EEG (ElectroEncephaloGraphy) and MEG (MagnetoEncephaloGraphy) signals. EEG and MEG signals are usually acquired simultaneously, and they capture aspects of the same brain activity. Therefore, EEG and MEG signals can be decomposed using coupled tensor decompositions such as the coupled CP decomposition. We exploit the proposed coupled SECSI framework (one of the proposed extensions of the SECSI framework) for the computation of the coupled CP decomposition to first validate and analyze the photic driving effect. Moreover, we validate the effects of scull defects on the measurement EEG and MEG signals by means of a joint EEG-MEG decomposition using the coupled SECSI framework. Both applications show that we benefit from coupled tensor decompositions and the coupled SECSI framework is a very practical tool for the analysis of biomedical data.Zahlreiche messbare Signale in verschiedenen Bereichen der digitalen Signalverarbeitung, z.B. in der drahtlosen Kommunikation, im Mobilfunk, biomedizinischen Anwendungen, der Bild- oder akustischen Signalverarbeitung und dem maschinellen Lernen sind mehrdimensional. Tensoren erhalten die mehrdimensionale Struktur und stellen eine natĂŒrliche Darstellung dieser Signale/Daten dar. DarĂŒber hinaus bieten Tensoren oft eine verbesserte Trennbarkeit von enthaltenen Signalkomponenten. Daher profitieren wir von der Verwendung der Tensor-Algebra in den oben genannten Anwendungen und vielen mehr. In dieser Arbeit stellen wir die Vorteile der Nutzung der Tensor-Algebra in zwei Bereichen der Signalverarbeitung vor: drahtlose MIMO (Multiple-Input Multiple-Output) Kommunikationssysteme und biomedizinische Signalverarbeitung. DarĂŒber hinaus tragen wir zu theoretischen Aspekten der Tensor-Algebra bei, indem wir neue Eigenschaften und Berechnungsmethoden fĂŒr die Tensor-Zerlegung ableiten. Oftmals verfĂŒgen wir lediglich ĂŒber eine elementweise oder ebenenweise Beschreibung des Signalmodells, welche nicht die explizite Tensorstruktur zeigt. Daher ist die Ableitung aller Tensor-Unfoldings nicht offensichtlich, wodurch die multidimensionale Struktur dieser Modelle nicht trivial nutzbar ist. Wir schlagen eine alternative Darstellung der elementweisen Multiplikation oder der ebenenweisen Multiplikation auf der Grundlage des generalisierten Tensor-Kontraktionsoperators vor. Weiterhin nutzen wir diese neuartige Darstellung und deren Eigenschaften zur Ableitung der letztendlichen Tensor-Modelle. Es existieren eine Vielzahl von Tensor-Zerlegungen, die verschiedene Signalmodelle beschreiben, wie die HOSVD (Higher Order Singular Value Decomposition), CP/PARAFAC (Canonical Polyadic/ PARallel FACtors) Zerlegung, die BTD (Block Term Decomposition), die PARATUCK2-(PARAfac und TUCker2) und die PARAFAC2-Zerlegung (PARAllel FACtors2). Dabei ist die CP-Zerlegung am weitesten verbreitet und wird findet in zahlreichen Gebieten Anwendung. Daher ist die Entwicklung von Algorithmen zur effizienten Berechnung der CP-Zerlegung von besonderer Bedeutung. Das SECSI (Semi-Algebraic Framework for approximate CP decomposition via Simultaneaous matrix diagonalization) Framework ist ein effizientes und robustes Werkzeug zur Berechnung der approximierten Low-Rank CP-Zerlegung durch simultane Matrixdiagonalisierung. In dieser Arbeit stellen wir fĂŒnf Erweiterungen des SECSI-Frameworks vor, welche die RechenkomplexitĂ€t des ursprĂŒnglichen Frameworks reduzieren bzw. EinschrĂ€nkungen fĂŒr die Faktormatrizen einfĂŒhren. DarĂŒber hinaus werden die PARAFAC2- und die PARATUCK2-Zerlegung in der Regel mit einer ebenenweisen Notation beschrieben, die sich in Form der allgemeinen Tensor-Kontraktion, wie sie in dieser Arbeit vorgeschlagen wird, ausdrĂŒcken lĂ€sst. Wir nutzen diese neuartige Darstellung, um explizite Tensormodelle fĂŒr diese beiden Zerlegungen abzuleiten. DarĂŒber hinaus verwenden wir das PARAFAC2-Modell, um einen ALS-Algorithmus (Alternating Least-Squares) fĂŒr die Berechnung der PARAFAC2-Zerlegungen abzuleiten. Weiterhin nutzen wir die neuartigen Kontraktionseigenschaften fĂŒr elementweise und ebenenweise Multiplikationen, um MIMO Multi-Carrier-Mobilfunksysteme zu modellieren. Wir zeigen, dass dieses sehr allgemeine Modell verwendet werden kann, um das Tensor-Modell des empfangenen Signals fĂŒr MIMO-OFDM- (Multiple- Input Multiple-Output - Orthogonal Frequency Division Multiplexing), Khatri-Rao codierte MIMO-OFDM- und zufĂ€llig codierte MIMO-OFDM-Systeme abzuleiten. Wir schlagen die Übertragungstechniken der Khatri-Rao-Kodierung und zufĂ€llige Kodierung vor, um eine zusĂ€tzliche Tensor-Struktur des Sendesignal-Tensors einzufĂŒhren, welcher gewöhnlich keine bestimmte Struktur aufweist. DarĂŒber hinaus zeigen wir, dass dieses Modell auf andere Multi-Carrier-Techniken wie GFDM (Generalized Frequency Division Multiplexing) erweitert werden kann. Unter Verwendung dieser Modelle auf der EmpfĂ€ngerseite entwerfen wir verschiedene Typen von EmpfĂ€ngern fĂŒr diese Systeme, die die traditionellen matrixbasierten Lösungen in Bezug auf die Symbolfehlerrate ĂŒbertreffen. Im letzten Teil dieser Arbeit zeigen wir die Vorteile der Verwendung von Tensor-Algebra in der biomedizinischen Signalverarbeitung durch die gemeinsame Zerlegung von EEG-(ElectroEncephaloGraphy) und MEG- (MagnetoEncephaloGraphy) Signalen. Diese werden in der Regel gleichzeitig erfasst, wobei sie gemeinsame Aspekte derselben GehirnaktivitĂ€t beschreiben. Daher können EEG- und MEG-Signale mit gekoppelten Tensor-Zerlegungen wie der gekoppelten CP Zerlegung analysiert werden. Wir nutzen das vorgeschlagene gekoppelte SECSI-Framework (eine der vorgeschlagenen Erweiterungen des SECSI-Frameworks) fĂŒr die Berechnung der gekoppelten CP Zerlegung, um zunĂ€chst den photic driving effect zu validieren und zu analysieren. DarĂŒber hinaus validieren wir die Auswirkungen von SchĂ€deldefekten auf die Messsignale von EEG und MEG durch eine gemeinsame EEG-MEG-Zerlegung mit dem gekoppelten SECSI-Framework. Beide Anwendungen zeigen, dass wir von gekoppelten Tensor-Zerlegungen profitieren, wobei die Methoden des gekoppelten SECSI-Frameworks erfolgreich zur Analyse biomedizinischer Daten genutzt werden können

    The application of a high-order discontinuous Galerkin time-domain method for the computation of electromagnetic resonant modes

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    This work presents a highly accurate and efficient methodology for the computation of electromagnetic resonant frequencies and their associated modes in cavities. The proposed technique consists of a high–order discontinuous Galerkin time–domain solver combined with a signal processing algorithm for extracting the frequency content. The methodology is capable of incorporating the CAD boundary representation of the domain. The numerical results demonstrate that incorporating the exact boundary representation results in a improved convergence rate, a phenomenon that has not been previously reported. Several numerical examples in two and three dimensions show the potential of the proposed technique for cavities filled with non–dispersive or dispersive media

    With Vibrationally Excited Thiophosgene Molecule and Double-Well Ion Traps

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    For practical realization of quantum information processing we need a quantum system that provides reliable preparation of the initial state, high-fidelity quantum gate operations, error tolerance, readout of the result of quantum computation and scalability of the system to increase the number of qubits. In this dissertation we show how these requirements can be addressed for molecular quantum computer. For computational study of quantum information processing with molecules we employ thiophosgene (SCCl2) molecule that has been used as a test system for quantum control experiments [Mol. Phys. 105, 1999 (2007)]. We investigate the gateway scheme of control in which transitions between the vibrational states that encode qubits are only allowed through the intermediate “gateway” state in the B electronic state. This scheme of control provides reliable preparation of the initial qubit state and allows using UV/vis laser pulses. We demonstrate that high-fidelity quantum gates are possible to achieve in molecular quantum computer. The optimal control theory is employed to obtain a shape of laser pulse that performs CNOT gate with ~0.9999 fidelity. Analysis of frequency profile of the optimal pulse shows that preparation of the high-fidelity computational pulse requires only 64 frequency channels. Error tolerance of the computational pulse is studied by modifying amplitudes and phases of frequency components. It is shown that gate fidelity remains high after small modifications are introduced to the optimal pulse. The scheme of readout of quantum information using quantum beat spectroscopy is proposed. The quantum beat signal is obtained from excitation of the final superposition of the qubit states to a readout state in the B electronic state with a time-delayed pulse. We find that fitting the quantum beat signal with a standard fitting expression produces a phase error and propose a new accurate expression that includes phase correction term. The system of two atomic ions trapped in a double-well potential is also studied as a first step towards scalable quantum computation with trapped molecular ions. The rigorous computational treatment of the system provides explanation of the vibrational energy transfer between the ions in terms of wave packet dynamics in the accurate asymmetric potential

    Simulation et optimisation du contrĂŽle et de la mesure du qubit supraconducteur

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    Abstract: The field of superconducting circuits has grown dramatically in the last decade and is a leading architecture for quantum computation. Part of this architecture’s success is the simple control, scalability, and increasingly long lifetime of the transmon qubit, which became dominant in most processors. Nevertheless, there will need to be significant improvements in their performance to reach fault-tolerant computation. A major limitation of these qubit operations today is from ‘leakage’, or from populating the higher energy states of the qubit. This process is generally incurred from off-resonant processes, which are hard to capture from both a numerical and theoretical viewpoint, and our understanding of such processes must be improved to continue enhancing these devices. In this thesis, I investigate how we can understand, accurately simulate, and suppress error-causing processes resulting from strong measurement and control drives on transmon qubits. As part of my research, I present a method of efficiently simulating systems in the presence of fast-oscillating drives, and how this allows us to optimize the controls to improve the fidelity of operations. I additionally demonstrate how sufficiently strong measurement drives during readout can not only result in leakage but also in the population of states outside of the transmon's confining potential, which we refer to as `ionization'. I conclude with my work in collaboration with ETH Zurich on state-of-the-art readout results using flux-tunable transmons and Purcell Filters.Le domaine des circuits supraconducteurs a connu une croissance spectaculaire au cours de la derniĂšre dĂ©cennie et constitue une architecture de premier plan pour l’informatique quantique. Le succĂšs de cette architecture tient en partie Ă  la simplicitĂ© du contrĂŽle, Ă  l’évolutivitĂ© et Ă  la durĂ©e de vie de plus en plus longue du qubit transmon, qui est devenu dominant dans la plupart des processeurs. Bien que la fidĂ©litĂ© de la plupart des opĂ©rations quantiques sur ces dispositifs dĂ©passe gĂ©nĂ©ralement 98− 99%, des amĂ©liorations significatives des performances seront nĂ©cessaires pour parvenir Ă  un calcul tolĂ©rant aux fautes. L’une des principales limites actuelles de ces opĂ©rations sur les qubits est due aux “fuites”, c’est-Ă -dire au peuplement des Ă©tats d’énergie supĂ©rieure du qubit. Ces effets sont difficiles Ă  apprĂ©hender d’un point de vue numĂ©rique et thĂ©orique, car de nombreuses transitions rĂ©sultent de processus hors rĂ©sonance qui sont gĂ©nĂ©ralement ignorĂ©s afin de rendre le problĂšme traitable. En outre, beaucoup de ces effets sont causĂ©s par les niveaux d’énergie plus Ă©levĂ©s du transmon, prĂ©sents hors de son potentiel de confinement. Ceux-ci sont Ă©galement nĂ©gligĂ©s dans les simulations et les Ă©tudes thĂ©oriques pour des raisons de simplicitĂ©, ce qui entraĂźne une mauvaise caractĂ©risation de la dynamique. Dans cette thĂšse, j’étudie comment nous pouvons comprendre, simuler avec prĂ©cision et supprimer les processus Ă  l’origine d’erreurs rĂ©sultant de mesures et de contrĂŽles forts sur les qubits transmon. Dans le cadre de ma recherche, je prĂ©sente une mĂ©thode permettant de simuler efficacement des systĂšmes en prĂ©sence de commandes Ă  oscillation rapide, et comment celle-ci nous permet d’optimiser les commandes afin d’amĂ©liorer la fidĂ©litĂ© des opĂ©rations. Cette mĂ©thode permet une accĂ©lĂ©ration significative par rapport aux intĂ©grateurs numĂ©riques traditionnels, et une version de ce solveur est maintenant incluse dans Qiskit Dynamics, un logiciel d’IBM. Je dĂ©montre en outre comment un pilote de mesure suffisamment forts pendant la lecture peut non seulement entraĂźner des fuites, mais aussi la population d’états en dehors du potentiel de confinement du transmon, ce que nous appelons l’“ionisation”. La comprĂ©hension de l’impact de ces effets parasites - et de la maniĂšre dont ils peuvent ĂȘtre Ă©vitĂ©s - sera cruciale pour l’optimisation et le fonctionnement de la lecture dans les futurs dispositifs. Je conclurai par mes travaux en collaboration avec l’ETH Zurich sur les rĂ©sultats de lecture de pointe utilisant des transmons et des filtres de Purcell rĂ©glables en fonction du flux, et j’expliquerai comment le rĂ©glage de la frĂ©quence du transmon peut amĂ©liorer la fidĂ©litĂ© de la lecture. Cela ouvre une autre voie pour amĂ©liorer la lecture des qubits supraconducteurs et nous rapproche potentiellement des applications utiles de ces dispositifs

    Relativistic Real-Time Methods

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    Recent advances in laser technology enable to follow electronic motion at its natural time-scale with ultrafast pulses, leading the way towards atto- and femtosecond spectroscopic experiments of unprecedented resolution. Understanding of these laser-driven processes, which almost inevitably involve non-linear light-matter interactions and non-equilibrium electron dynamics, is challenging and requires a common effort of theory and experiment. Real-time electronic structure methods provide the most straightforward way to simulate experiments and to gain insights into non-equilibrium electronic processes. In this Chapter, we summarize the fundamental theory underlying the relativistic particle-field interaction Hamiltonian as well as equation-of-motion for exact-state wave function in terms of the one- and two-electron reduced density matrix. Further, we discuss the relativistic real-time electron dynamics mean-field methods with an emphasis on Density-Functional Theory and Gaussian basis, starting from the four-component (Dirac) picture and continue to the two-component (Pauli) picture, where we introduce various flavours of modern exact two-component (X2C) Hamiltonians for real-time electron dynamics. We also overview several numerical techniques for real-time propagation and signal processing in quantum electron dynamics. We close this Chapter by listing selected applications of real-time electron dynamics to frequency-resolved and time-resolved spectroscopies
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