Optimizing Robust Quantum Gates in Open Quantum Systems

We are currently at the cusp of a revolution in quantum technology that relies not just on the passive use of quantum effects, but on their active control. At the forefront of this revolution is the implementation of a quantum computer. Encoding information in quantum states as “qubits” allows to use entanglement and quantum superposition to perform calculations that are infeasible on classical computers. The fundamental challenge in the realization of quantum computers is to avoid decoherence – the loss of quantum properties – due to unwanted interaction with the environment. This thesis addresses the problem of implementing entangling two-qubit quantum gates that are robust with respect to both decoherence and classical noise. It covers three aspects: the use of efficient numerical tools for the simulation and optimal control of open and closed quantum systems, the role of advanced optimization functionals in facilitating robustness, and the application of these techniques to two of the leading implementations of quantum computation, trapped atoms and superconducting circuits. After a review of the theoretical and numerical foundations, the central part of the thesis starts with the idea of using ensemble optimization to achieve robustness with respect to both classical fluctuations in the system parameters, and decoherence. For the example of a controlled phasegate implemented with trapped Rydberg atoms, this approach is demonstrated to yield a gate that is at least one order of magnitude more robust than the best known analytic scheme. Moreover this robustness is maintained even for gate durations significantly shorter than those obtained in the analytic scheme. Superconducting circuits are a particularly promising architecture for the implementation of a quantum computer. Their flexibility is demonstrated by performing optimizations for both diagonal and non-diagonal quantum gates. In order to achieve robustness with respect to decoherence, it is essential to implement quantum gates in the shortest possible amount of time. This may be facilitated by using an optimization functional that targets an arbitrary perfect entangler, based on a geometric theory of two-qubit gates. For the example of superconducting qubits, it is shown that this approach leads to significantly shorter gate durations, higher fidelities, and faster convergence than the optimization towards specific two-qubit gates. Performing optimization in Liouville space in order to properly take into account decoherence poses significant numerical challenges, as the dimension scales quadratically compared to Hilbert space. However, it can be shown that for a unitary target, the optimization only requires propagation of at most three states, instead of a full basis of Liouville space. Both for the example of trapped Rydberg atoms, and for superconducting qubits, the successful optimization of quantum gates is demonstrated, at a significantly reduced numerical cost than was previously thought possible. Together, the results of this thesis point towards a comprehensive framework for the optimization of robust quantum gates, paving the way for the future realization of quantum computers.

Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications

Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence. In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control - the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.

La edición electrónica y la gestión de trabajos académicos con Open Conference Systems (OCS).

Monográfico con el título: 'Nuevos desafíos en la formación del profesorado'

Memory effects and geometrical considerations in open quantum systems

This thesis discusses memory effects in open quantum systems with an emphasis on the Breuer, Laine, Piilo (BLP) measure of non-Markovianity. It is shown how the calculation of the measure can be simplifed and how quantum information protocols can bene t from memory e ects. The superdense coding protocol is used as an example of this. The quantum Zeno effect will also be studied from the point of view of memory e ects. Finally the geometric ideas used in simplifying the calculation of the BLP measure are applied in studying the amount of resources needed for detecting bipartite quantum correlations. It is shown that to decide without prior information if an unknown quantum state is entangled or not, an informationally complete measurement is required. The first part of the thesis contains an introduction to the theoretical ideas such as quantum states, closed and open quantum systems and necessary mathematical tools. The theory is then applied in the second part of the thesis as the results obtained in the original publications I-VI are presented and discussed.

Degenerate mixtures of rubidium and ytterbium for engineering open quantum systems

In the last two decades, experimental progress in controlling cold atoms and ions now allows us to manipulate fragile quantum systems with an unprecedented degree of precision. This has been made possible by the ability to isolate small ensembles of atoms and ions from noisy environments, creating truly closed quantum systems which decouple from dissipative channels. However in recent years, several proposals have considered the possibility of harnessing dissipation in open systems, not only to cool degenerate gases to currently unattainable temperatures, but also to engineer a variety of interesting many-body states. This thesis will describe progress made towards building a degenerate gas apparatus that will soon be capable of realizing these proposals. An ultracold gas of ytterbium atoms, trapped by a species-selective lattice will be immersed into a Bose-Einstein condensate (BEC) of rubidium atoms which will act as a bath. Here we describe the challenges encountered in making a degenerate mixture of rubidium and ytterbium atoms and present two experiments performed on the path to creating a controllable open quantum system. The first experiment will describe the measurement of a tune-out wavelength where the light shift of $\Rb{87}$ vanishes. This wavelength was used to create a species-selective trap for ytterbium atoms. Furthermore, the measurement of this wavelength allowed us to extract the dipole matrix element of the $5s \rightarrow 6p$ transition in $\Rb{87}$ with an extraordinary degree of precision. Our method to extract matrix elements has found use in atomic clocks where precise knowledge of transition strengths is necessary to account for minute blackbody radiation shifts. The second experiment will present the first realization of a degenerate Bose-Fermi mixture of rubidium and ytterbium atoms. Using a three-color optical dipole trap (ODT), we were able to create a highly-tunable, species-selective potential for rubidium and ytterbium atoms which allowed us to use $\Rb{87}$ to sympathetically cool $\Yb{171}$ to degeneracy with minimal loss. This mixture is the first milestone creating the lattice-bath system and will soon be used to implement novel cooling schemes and explore the rich physics of dissipation.

Linking electronic journals - Lessons from the Open Journal project

The Open Journal project has completed its three year period of funding by the UK Electronic Libraries (eLib) programme (Rusbridge 1998). During that time, the number of journals that are available electronically leapt from a few tens to a few thousand. Some of these journals are now developing the sort of features the project has been advocating, in particular the use of links within journals, between different primary journals, with secondary journals data, and to non-journal sources. Assessing the achievements of the project and considering some of the difficulties it faced, we report on the different approaches to linking that the project developed, and summarise the important user responses that indicate what works and what does not. Looking ahead, there are signs of change, not just to simple linking within journals but to schemes in which links are the basis of "distributed" journals, where information may be shared and documents built from different sources. The significance has yet to be appreciated, but this would be a major change from printed journals. If projects such as this and others have provided the initial impetus, the motivation for distributed journals comes, perhaps surprisingly, from within certain parts of the industry, as the paper shows.

Modern Computational Chemistry Methods for Prediction of Ground- and Excited-State Properties in Open-Shell Systems

The main goal of the research presented in this work is to provide some important insights about computational modeling of open-shell species. Such projects are: the investigation of the size-extensivity error in Equation-of-Motion Coupled Cluster methods, the analysis of the Long-Range corrected scheme in predicting UV-Vis spectra of Cu(II) complexes with the 4-imidazole acetate and its ethylated derivative, and the exploration of the importance of choosing a proper basis set for the description of systems such as the lithium monoxide anion. The most significant findings of this research are: (i) The contribution of the left operator to the size-extensivity error of the CR-EOMCC(2,3) approach, (ii) The cause of d-d shifts when varying the range-separation parameter and the amount of the exact exchange arising from the imbalanced treatment of localized vs. delocalized orbitals via the "tuned" CAM-B3LYP* functional, (iii) The proper acidity trend of the first-row hydrides and their lithiated analogs that may be reversed if the basis sets are not correctly selected.

Systems 1 and 2 thinking processes and cognitive reflection testing in medical students

Background: Diagnostic decision-making is made through a combination of Systems 1 (intuition or pattern-recognition) and Systems 2 (analytic) thinking. The purpose of this study was to use the Cognitive Reflection Test (CRT) to evaluate and compare the level of Systems 1 and 2 thinking among medical students in pre-clinical and clinical programs. Methods: The CRT is a three-question test designed to measure the ability of respondents to activate metacognitive processes and switch to System 2 (analytic) thinking where System 1 (intuitive) thinking would lead them astray. Each CRT question has a correct analytical (System 2) answer and an incorrect intuitive (System 1) answer. A group of medical students in Years 2 & 3 (pre-clinical) and Years 4 (in clinical practice) of a 5-year medical degree were studied. Results: Ten percent (13/128) of students had the intuitive answers to the three questions (suggesting they generally relied on System 1 thinking) while almost half (44%) answered all three correctly (indicating full analytical, System 2 thinking). Only 3-13% had incorrect answers (i.e. that were neither the analytical nor the intuitive responses). Non-native English speaking students (n = 11) had a lower mean number of correct answers compared to native English speakers (n = 117: 1.0 s 2.12 respectfully: p < 0.01). As students progressed through questions 1 to 3, the percentage of correct System 2 answers increased and the percentage of intuitive answers decreased in both the pre-clinical and clinical students. Conclusions: Up to half of the medical students demonstrated full or partial reliance on System 1 (intuitive) thinking in response to these analytical questions. While their CRT performance has no claims to make as to their future expertise as clinicians, the test may be used in helping students to understand the importance of awareness and regulation of their thinking processes in clinical practice.

Avaliação do estado nutricional dos idosos residentes em Fortaleza/CE: o uso de diferentes indicadores antropométricos

O objetivo deste estudo foi avaliar, utilizando diferentes indicadores antropométricos, o estado nutricional dos idosos de Fortaleza. Este estudo é de base populacional, do tipo transversal, com coleta de dados primários. As variáveis antropométricas analisadas foram: índice de massa corporal (IMC), dobra cutânea tricipital (DCT) e circunferência muscular do braço (CMB). O estado nutricional foi definido a partir dos diagnósticos obtidos com a análise das variáveis antropométricas: eutrófico (idoso, no qual as três variáveis antropométricas (IMC, DCT e CMB), simultaneamente, indicassem o estado de eutrofia, segundo os padrões adotados) e não eutrófico (demais idosos). Foram selecionados 385 domicílios para comporem a amostra deste estudo, nos quais foram entrevistados 483 idosos (68% mulheres). Quanto ao IMC, 47,3% do total de idosos foram considerados eutróficos. As mulheres apresentaram maior proporção de valores de IMC excessivo (21,9%), quando comparadas aos homens (13,5%). Foi verificada associação estatisticamente significativa entre adequação de IMC e sexo. Os valores de DCT mostraram que 54,4% do total de idosos eram eutróficos. Não houve associação estatisticamente significativa entre a adequação da DCT e sexo. Quanto à CMB, os homens apresentaram maior prevalência de desnutrição (66,5%), quando comparados às mulheres (40,6%). Foi verificada associação estatisticamente significativa entre adequação da CMB e sexo. Ao verificar o estado nutricional por meio das variáveis antropométricas, observou-se que 83,9% dos homens foram considerados não eutróficos, assim como maior parte das mulheres (74,2%). Foi observada associação estatisticamente significativa entre estado nutricional e sexo. Os idosos de Fortaleza apresentam estado nutricional vulnerável, visto as prevalências de não eutróficos

Local model predictive control experiences with differential driven wheeled mobile robots

This work extends a previously developed research concerning about the use of local model predictive control in differential driven mobile robots. Hence, experimental results are presented as a way to improve the methodology by considering aspects as trajectory accuracy and time performance. In this sense, the cost function and the prediction horizon are important aspects to be considered. The aim of the present work is to test the control method by measuring trajectory tracking accuracy and time performance. Moreover, strategies for the integration with perception system and path planning are briefly introduced. In this sense, monocular image data can be used to plan safety trajectories by using goal attraction potential fields

Mobile robot experimental modeling and control strategies using sensor fusion

This research work deals with the problem of modeling and design of low level speed controller for the mobile robot PRIM. The main objective is to develop an effective educational, and research tool. On one hand, the interests in using the open mobile platform PRIM consist in integrating several highly related subjects to the automatic control theory in an educational context, by embracing the subjects of communications, signal processing, sensor fusion and hardware design, amongst others. On the other hand, the idea is to implement useful navigation strategies such that the robot can be served as a mobile multimedia information point. It is in this context, when navigation strategies are oriented to goal achievement, that a local model predictive control is attained. Hence, such studies are presented as a very interesting control strategy in order to develop the future capabilities of the system. In this context the research developed includes the visual information as a meaningful source that allows detecting the obstacle position coordinates as well as planning the free obstacle trajectory that should be reached by the robot

Reconfigurable Architecture To Estimate The Motion Of An Underwater Vehicle

This work proposes a parallel architecture for a motion estimation algorithm. It is well known that image processing requires a huge amount of computation, mainly at low level processing where the algorithms are dealing with a great numbers of data-pixel. One of the solutions to estimate motions involves detection of the correspondences between two images. Due to its regular processing scheme, parallel implementation of correspondence problem can be an adequate approach to reduce the computation time. This work introduces parallel and real-time implementation of such low-level tasks to be carried out from the moment that the current image is acquired by the camera until the pairs of point-matchings are detected

Local model predictive control experiences with differential driven wheeled mobile robots

This work extends a previously developed research concerning about the use of local model predictive control in differential driven mobile robots. Hence, experimental results are presented as a way to improve the methodology by considering aspects as trajectory accuracy and time performance. In this sense, the cost function and the prediction horizon are important aspects to be considered. The aim of the present work is to test the control method by measuring trajectory tracking accuracy and time performance. Moreover, strategies for the integration with perception system and path planning are briefly introduced. In this sense, monocular image data can be used to plan safety trajectories by using goal attraction potential fields