The last forty years have seen an astounding level of progress in the field of quantum computing. Rapidly-improving techniques for fabricating and controlling devices, increasingly refined theoretical models, and innovative quantum computing algorithms have allowed us to pass a number of important milestones on the path towards fault-tolerant general purpose quantum computing. There remains, however, uncertainty regarding the feasibility and logistics of scaling quantum computing platforms to useful sizes. A great deal of work remains to be done in developing sophisticated control techniques, designing scalable quantum information processing architectures, and creating resource-efficient algorithms. This dissertation is a collection of seven manuscripts organized into three sections which aim to contribute to these efforts. In the first section, we explore quantum control techniques for exchange-coupled solid-state electronic spin qubits in arrays of gate-defined quantum dots. We start by demonstrating theoretically the existence of a discrete time crystal phase in finite Heisenberg spin chains. We present driving pulses that can be used to induce time crystalline behavior and probe the conditions under which this behavior can exist, finding that it should be realizable with current experimental capabilities. Next, we use a correspondence between quantum time evolution geometric space curves to design fast, high-fidelity entangling gates in two-spin double quantum dots. In the second section, we study systems of quantum dot spin qubits coupled to one another via mutual coupling to superconducting microwave resonators. We start with two qubits, developing and refining an effective model of resonator-mediated entangling interactions, and then use that model to ultimately design fast, long-distance, high-fidelity entangling gates which are robust to environmental noise. We then take the model further, extending our model to a system of three qubits coupled by a combination of short-range exchange interactions and long-range resonator-mediated interactions, and numerically demonstrate that previously-developed protocols can be used to realize both short- and long-range entangling operations. The final section investigates adaptive variational algorithms for efficient preparation of thermal Gibbs states on a quantum computer, a difficult task with a number of important applications. We suggest a novel objective function which can be used for variational Gibbs state preparation, but which requires fewer resources to measure than the often-used Gibbs free energy. We then introduce and characterize two variational algorithms using this objective function which adaptively construct variational ansätze for Gibbs state preparation. / Doctor of Philosophy / The computers we have now are able to perform computations by storing information in bits (units of memory which can take on either of two values e.g. 0 or 1) and then comparing and modifying the values of these bits according to a simple set of logical rules. The logic these computers use is suited to a universe that obeys the laws of classical mechanics, which was our best theory of physics prior to the 20th century, but the last 120 years have seen a radical shift in our understanding of nature. We now know that nature is much better described by the laws of quantum mechanics, which includes a great deal of surprising and unintuitive non-classical phenomena. The aim of quantum computing is to use our improved understanding of nature to design and build a new kind of computer which stores information in the states of quantum bits ("qubits") and then compares and modifies the combined state of these qubits using a logic adapted to the laws of quantum mechanics. By leveraging the quantum nature of reality, these quantum computers are capable of performing certain computations faster and more efficiently than is possible using classical computers. The prospect of faster computing has inspired a massive effort to develop useful quantum computers, and the last forty years have seen impressive progress towards this goal, but there is a great deal left to do. Current quantum computing devices are too sensitive to their surroundings and far too error-prone to do useful computations. To reach tolerable error rates, we need to develop better devices and better methods for controlling those devices. Meanwhile, although several different device platforms are being continually developed, none of them currently operates with a collection of qubits anywhere near as large as the billions of bits our classical computers are able to use. It is not yet clear that practical scaling of these platforms up to that level is even possible, let alone how we can do so. Furthermore, only a handful of promising quantum algorithms have been discovered, and the efficiency of many is questionable at best. We have much that we still need to learn about what quantum computers can do and how best to use them. This dissertation is a collection of seven papers arranged into three sections, all attempting to help address some of these issues. In the first two sections, we focus on one promising type of quantum computing platform -- solid-state electronic spin qubits. We introduce new methods for quickly performing quantum logic operations in these platforms, we suggest protocols for making these systems exhibit novel and potentially useful behavior, and we characterize and design control methods for a device design which might facilitate scaling up to large numbers of qubits. In the final section, we turn our attention to quantum software, and present two algorithms for using quantum computers to efficiently simulate physical systems at a fixed temperature.

Doctor of Philosophy / Electrical and Computer Engineering / Sanjoy Das / Quantum circuit synthesis is one of the major areas of current research in the field of quantum computing. Analogous to its Boolean counterpart, the task involves constructing arbitrary quantum gates using only those available within a small set of universal gates that can be realized physically. However, unlike the latter, there are an infinite number of single qubit quantum gates, all of which constitute the special unitary group SU(2). Realizing any given single qubit gate using a given universal gate family is a complex task. Although gates can be synthesized to arbitrary degree of precision as long as the set of finite strings of the gate family is a dense subset of SU(2), it is desirable to accomplish the highest level of precision using only the minimum number of universal gates within the string approximation. Almost all algorithms that have been proposed for this purpose are based on the Solovay-Kitaev algorithm. The crux of the Solovay-Kitaev algorithm is the use of a procedure to decompose a given quantum gate into a pair of group commutators with the pair being synthesized separately. The Solovay-Kitaev algorithm involves group commutator decomposition in a recursive manner, with a direct approximation of a gate into a string of universal gates being performed only at the last level, i.e. in the leaf nodes of the search tree representing the execution of the Solovay-Kitaev algorithm. The main contribution of this research is in integrating conventional optimization procedures within the Solovay-Kitaev algorithm. Two specific directions of research have been studied. Firstly, optimization is incorporated within the group commutator decomposition, so that a more optimal pair of group commutators are obtained. As the degree of precision of the synthesized gate is explicitly minimized by means of this optimization procedure, the enhanced algorithm allows for more accurate quantum gates to be synthesized than what the original Solovay-Kitaev algorithm achieves. Simulation results with random gates indicate that the obtained accuracy is an order of magnitude better than before. Two versions of the new algorithm are examined, with the optimization in the first version being invoked only at the bottom level of Solovay-Kitaev algorithm and when carried out across all levels of the search tree in the next. Extensive simulations show that the second version yields better results despite equivalent computation times. Theoretical analysis of the proposed algorithm is able to provide a more formal, quantitative explanation underlying the experimentally observed phenomena. The other direction of investigation of this research involves formulating the group commutator decomposition in the form of bi-criteria optimization. This phase of research relaxed the equality constraint in the previous approach and with relaxation, a bi-criteria optimization is proposed. This optimization algorithm is new and has been devised primarily when the objective needs to be relaxed in different stages. This bi-criteria approach is able to provide comparably accurate synthesis as the previous approach.

L'un des principaux obstacles pour construire un ordinateur quantique est la décohérence, laquelle limite grandement le temps alloué pour un calcul ainsi que la taille du système. Pour combattre la décohérence dans un système quantique, des protocoles de correction d'erreurs ont été proposés et semblent apporter une bonne solution à ce problème. Ces protocoles consistent à confiner l'information que contiennent les qubits dans un sous-espace nommé espace code. Après un certain temps d'évolution, on pose un diagnostic sur l'erreur qui s'est produite sur le système en effectuant des mesures indiquant s'il est toujours dans l'espace code où s'il a évolué vers un autre sous-espace. Pour que de tels protocoles soient efficaces, les mesures effectuées doivent en principe être rapides et projectives. Cependant, pour plusieurs architectures de qubits existantes, les mesures sont faibles et se font de façon continue. De plus, elles peuvent introduire elles-mêmes des erreurs dans le système. Ces caractéristiques de mesure rendent difficile le diagnostic de l'erreur tel qu'il est effectué traditionnellement. Aussi comme les mesures peuvent introduire des erreurs, il n'est pas certain que les protocoles de diagnostic d'erreur traditionnels soient utiles. Dans ce travail, on étudie l'utilité d'une mesure faible et continue dans un processus de correction d'erreurs. Cette étude s'est réalisée en deux volets. D'abord, on présente un protocole de correction d'erreur adapté aux architectures de qubits dont la mesure est faible et se fait de façon continue. On montre que ce protocole permet d'évaluer sous quelles conditions une mesure présentant ces caractéristiques peut aider à corriger des erreurs. Ensuite, on teste ce protocole de correction dans le cas particulier des qubits supraconducteurs. On établit sous quelles conditions la mesure sur ces qubits peut aider à diagnostiquer les erreurs et on étudie l'effet de différents paramètres expérimentaux dans ce contexte.

L'électrodynamique quantique en cavité et en circuit étudie l'interaction lumière-matière à son stade le plus fondamental, dans lequel un atome unique, qu'il soit naturel ou artificiel, interagit avec un seul mode du champ électromagnétique. Dans ce système, le confinement du champ augmente l'intensité de l'interaction jusqu'à permettre d'observer l'échange cohérent de quanta entre lumière et matière [1, 2, 3]. Récemment, des expériences réalisées à l'aide de qubits supraconducteurs ont démontré des couplages record caractéristiques d'un nouveau régime, dit ultra-fort, dans lequel l'état fondamental n'est plus le vide, mais un état fortement intriqué entre l'atome et le champ [4, 5]. Malgré cet accroissement gigantesque du couplage lumière-matière, ce dernier est le plus souvent négligé lorsqu'on considère l'interaction de ce système avec son environnement. En effet, la plupart des travaux théoriques publiés récemment décrivent la dynamique dissipative du système atome-cavité en se basant sur l'équation maîtresse de l'optique quantique, un modèle valide seulement dans le cas de l'atome ou du résonateur séparés [6, 7, 8, 9]. Dans ce travail, on démontre qu'employer l'équation maîtresse de l'optique quantique en couplage ultra-fort mène des prédictions qui violent la conservation de l'énergie. Pour pallier ce problème, on établit un modèle de la dissipation qui inclut le couplage atome-champ. On montre en particulier que des fluctuations aléatoires dans la fréquence de l'atome artificiel peuvent générer des excitations dans le système des fréquences précises. On indique aussi que des oscillations cohérentes à ces fréquences dans l'espacement des niveaux de l'atome pourraient être utiles pour accélérer le contrôle cohérent du système quantique. Notre modèle prédit finalement une asymétrie dans les raies de spectroscopie du système atome-cavité qui pourrait être exploitée pour sonder la densité spectrale de bruit de l'environnement des fréquences jusqu'à ce jour inexplorées.

Un ordinateur quantique est un ordinateur formé de bits quantiques (qubits) qui tire profit des propriétés quantiques de la matière. Un grand intérêt est porté au développement d’un tel ordinateur depuis qu’il a été montré que le calcul quantique permettrait d’effectuer certains types de calculs exponentiellement plus rapidement qu’avec les meilleurs algorithmes connus sur un ordinateur classique. D’ailleurs, plusieurs algorithmes ont déjà été suggérés pour résoudre efficacement des problèmes tels que la factorisation de grands nombres premiers et la recherche dans des listes désordonnées. Avant d’en arriver à un ordinateur quantique fonctionnel, certains grands défis doivent être surmontés. Un de ces défis consiste à fabriquer des qubits ayant un temps d’opération nettement inférieur au temps de cohérence (temps durant lequel l’état du qubit est conservé). Cette condition est nécessaire pour parvenir à un calcul quantique fiable. Pour atteindre cet objectif, de nombreuses recherches visent à augmenter le temps de cohérence en choisissant judicieusement les matériaux utilisés dans la fabrication des qubits en plus d’imaginer de nouvelles méthodes d’utiliser ces dispositifs pour diminuer la durée des opérations. Une manière simple d’implémenter un qubit est de piéger quelques électrons dans l’espace et d’utiliser l’état de spin de cet ensemble d’électrons pour encoder les états du qubit. Ce type de dispositif porte le nom de qubit de spin. Les boîtes quantiques (BQs) latérales fabriquées sur des substrats de GaAs/AlGaAs sont un exemple de qubit de spin et sont les dispositifs étudiés dans ce mémoire. En 2007, Pioro-Ladrière et al. ont suggéré de placer un microaimant à proximité d’une BQ pour créer un gradient de champ magnétique non-uniforme et permettre d’effectuer des rotations de spin à l’aide d’impulsions électriques rapides. Ce mémoire présente comment modifier la géométrie de ces microaimants pour obtenir un plus grand gradient de champ magnétique dans la BQ. Une nouvelle technique de contrôle de spin menant à des rotations de spin et de phase plus rapides sera aussi détaillée. Enfin, il sera montré que le département de physique de l’Université de Sherbrooke possède tous les outils nécessaires pour implémenter cette méthode.

A great deal of theoretical activity has resulted from blending the fields of computer science and quantum mechanics. Out of this work has come the concept of a quantum computer, which promises to solve problems currently intractable for classical computers. This promise has, in turn, generated a large amount of effort directed toward investigating quantum computing experimentally. ¶ Quantum computing is difficult because fragile quantum superposition states of the computer’s register must be protected from the environment. This is made more difficult by the need to manipulate and measure these states. ¶ This thesis describes work that was carried out both to investigate and to demonstrate the utility of rare earth ion dopants for quantum computation. Dopants in solids are seen by many as a potential means of achieving scalable quantum computing. Rare earth ion dopants are an obvious choice for investigating such quantum computation. Long coherence times for both optical and nuclear spin transitions have been observed as well as optical manipulation of the spin states. The advantage that the scheme developed here has over nearly all of its competitors is that no complex nanofabrication is required. The advantages of avoiding nano-fabrication are two fold. Firstly, coherence times are likely to be adversely effected by the “damage” to the crystal structure that this manufacture represents. Secondly, the nano-fabrication presents a very serious difficulty in itself. ¶ Because of these advantages it was possible to perform two-qubit operations between independent qubits. This is the first time that such operations have been performed and presents a milestone in quantum computation using dopants in solids. It is only the second time two-qubit operations have been demonstrated in a solid. ¶ The experiments performed in this thesis were in two main areas: The first was the characterisation of hyperfine interactions in rare earth ion dopants; the second, simple demonstrations directly related to quantum computation. ¶ The first experiments that were carried out were to characterise the hyperfine interactions in Pr[superscript 3]+:Y[subscript 2]SiO[subscript 5]. The characterisation was the first carried out for the dopants in a site of such low symmetry. The resulting information about oscillator strengths and transition frequencies should prove indispensable when using such a system for quantum computation. It has already enabled an increase in the coherence times of nuclear spin transitions by two orders of magnitudes. ¶ The experiments directly related to the demonstration of quantum computation were all carried out using ensembles. The presence of a significant distribution of resonant frequencies, or inhomogeneous broadening, meant that many different sub-ensembles could be addressed, based on their resonant frequencies. Furthermore, the properties of the sub-ensembles could be engineered by optically pumping unwanted members to different hyperfine states away from resonance with the laser. ¶ A previously demonstrated technique for realising ensembles that could be used as single qubits was investigated and improved. Also, experiments were carried out to demonstrate the resulting ensembles’ utility as qubits. Further to this, ions from one of the ensembles were selected out, based on their interaction with the ions of another. Elementary two qubit operations were then demonstrated using these ensembles.

On commence dans le chapitre d'introduction par rappeler les résultats majeurs sur l'intrication et les systèmes quantiques ouverts. Puis en particulier on prouve la désintrication en temps fini pour deux qubits (systèmes quantiques à deux niveaux d'énergie) en interaction avec des bains thermiques distincts à température positive. On propose dans le premier chapitre de cette thèse une méthode pour empêcher la désintrication en temps fini basée sur des mesures continues sur les bains et utilisant la théorie des sauts quantiques et celle des équations différentielles stochastiques. Dans le deuxième chapitre on étudie un sous-ensemble des états de deux qubits : celui des états qu'on peut représenter dans la base canonique pour une matrice ayant une forme de X. Cela nous permet d'obtenir des formules explicites pour la décomposition d'un état X séparable en au plus cinq états purs produits. On généralise ensuite cette étude à l'ensemble des états obtenus à partir d'états X par conjugaison avec des unitaires locaux. Puis on donne un algorithme pour décomposer tout état séparable de cet ensemble en une combinaison convexe de cinq états purs produits. Le troisième chapitre de cette thèse propose l'étude de l'évolution de l'intrication de deux qubits dans un modèle d'interactions répétées avec la même chaîne de spins dans les limites de van Hove et de couplage singulier. En particulier on observe une intrication asymptotique non nulle quand la chaîne est à température infinie et des phénomènes de création d'intrication quand la chaîne est à température nulle.

Un ordinateur quantique est un ordinateur formé de bits quantiques (qubits) qui tire profit des propriétés quantiques de la matière. Un grand intérêt est porté au développement d’un tel ordinateur depuis qu’il a été montré que le calcul quantique permettrait d’effectuer certains types de calculs exponentiellement plus rapidement qu’avec les meilleurs algorithmes connus sur un ordinateur classique. D’ailleurs, plusieurs algorithmes ont déjà été suggérés pour résoudre efficacement des problèmes tels que la factorisation de grands nombres premiers et la recherche dans des listes désordonnées. Avant d’en arriver à un ordinateur quantique fonctionnel, certains grands défis doivent être surmontés. Un de ces défis consiste à fabriquer des qubits ayant un temps d’opération nettement inférieur au temps de cohérence (temps durant lequel l’état du qubit est conservé). Cette condition est nécessaire pour parvenir à un calcul quantique fiable. Pour atteindre cet objectif, de nombreuses recherches visent à augmenter le temps de cohérence en choisissant judicieusement les matériaux utilisés dans la fabrication des qubits en plus d’imaginer de nouvelles méthodes d’utiliser ces dispositifs pour diminuer la durée des opérations. Une manière simple d’implémenter un qubit est de piéger quelques électrons dans l’espace et d’utiliser l’état de spin de cet ensemble d’électrons pour encoder les états du qubit. Ce type de dispositif porte le nom de qubit de spin. Les boîtes quantiques (BQs) latérales fabriquées sur des substrats de GaAs/AlGaAs sont un exemple de qubit de spin et sont les dispositifs étudiés dans ce mémoire. En 2007, Pioro-Ladrière et al. ont suggéré de placer un microaimant à proximité d’une BQ pour créer un gradient de champ magnétique non-uniforme et permettre d’effectuer des rotations de spin à l’aide d’impulsions électriques rapides. Ce mémoire présente comment modifier la géométrie de ces microaimants pour obtenir un plus grand gradient de champ magnétique dans la BQ. Une nouvelle technique de contrôle de spin menant à des rotations de spin et de phase plus rapides sera aussi détaillée. Enfin, il sera montré que le département de physique de l’Université de Sherbrooke possède tous les outils nécessaires pour implémenter cette méthode.

A highly successful architecture for the exchange of single quanta between coupled quantum systems is circuit quantum electrodynamics (QED), in which the electrical interaction between a qubit and a high-quality microwave resonator offers the possibility to reliably control, store, and read out quantum bits of information on a chip. This architecture has also been implemented with mechanical resonators, showing that a vibrational mode can in principle be manipulated via a coupled qubit. The work presented in this thesis consists of realising an acoustic version of circuit QED that we call circuit quantum acoustodynamics (QAD), in which a superconducting qubit is piezoelectrically coupled to an acoustic cavity based on surface acoustic waves (SAWs). Designing and building this novel platform involved the following main accomplishments: a systematic characterisation of SAW resonators at low temperatures; successfully developing a recipe for the fabrication of Josephson junction on quartz and diamond; measuring the coherence time of superconducting 3D transmon qubits on these substrates and demonstrating the dispersive coupling between a SAW cavity and a qubit on a planar geometry. This thesis presents evidence of the coherent interaction between a SAW cavity and a superconducting qubit in several ways. First of all, a frequency shift of the mechanical mode as a function of qubit frequency is observed. We also measure the acoustic Stark shift of the qubit due to the population of the SAW cavity. The extracted coupling is in agreement with theoretical expectations. A time delayed acoustic Stark shift serves to further demonstrate that the Stark shifts that we observe are indeed due to the acoustic field of the SAW mode. The dispersive coupling between these two quantum systems offers the possibility to perform qubit spectroscopy using the SAW resonator as readout component, indicating that these acoustic resonators can, in principle, be adopted as an alternative qubit readout scheme in quantum information processors. We finally present preliminary measurements of the direct coupling between a SAW resonator and a transmon on diamond, suggesting that strong coupling can in principle be obtained.

Orientador: Prof. Dr. Fernando Luis Semião Da Silva / Tese (doutorado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2014. / Nessa tese, foram utilizadas ferramentas da Informação Quântica para estudar a dinâmica e efeitos de memória induzidos de maneira controlada em um qubit supercondutor. Propomos dois sistemas ou arquiteturas em Eletrodinâmica Quântica de Circuitos para realizar tal tipo de controle. A característica comum as duas arquiteturas é a presença de modos, ou linhas de transmissão, acopladas. Porém, em cada caso, o acoplamento se dá por mecanismos e formas diferentes. Um dos objetivos da tese foi justamente mostrar em que regimes as previsões físicas de cada modelo começam a divergir. Nesses estudos, analisamos a chamada não-Markovianidade em sistemas quânticos abertos, característica relacionada a memória ou tempo de correlação finito nas variáveis do ambiente. Também nos interessou o estudo de correlações quânticas como emaranhamento, e seu uso em aplicações como o teletransporte quântico. Nossos resultados encontram aplicações no controle coerente de sistemas quânticos abertos e, principalmente, constituem a primeira proposta na literatura para a indução, controle e medida de não-Markovianidade em qubits supercondutores. / In this thesis, tools from Quantum Optics were used to study the dynamics and memory effects controllably induced on a superconducting qubit. We proposed two different systems or architectures in the context of circuit quantum electrodynamics to achieve that level of control. The common feature shared by both architectures is the presence of modes or transmission lines that are coupled together. However, in each case the coupling is given by different mechanisms and forms. One of the main objectives of the thesis was precisely to show the regimes in which the physical predictions employing each model start to diverge. In these studies, we analysed the so called Non-Markovianity in open quantum systems, a feature related to memory or finite correlation time in the environmental variables. In addition, we were interested in the study of quantum correlations such as entanglement, and its use for quantum teleportation. Our results find applications in the problem of coherent control of open quantum systems, and most importantly, they constitute the first proposal in the literature for the induction, control and measurement of Non-Markovianity in superconducting qubits.