The future quantum Internet (QI) will transform today's communication networks and user experiences by providing unparalleled security levels, superior quantum computational powers, along with enhanced sensing accuracy and data processing capabilities. These features will be enabled through applications like quantum key distribution (QKD) and quantum machine learning (QML). Towards enabling these applications, the QI requires the development of global quantum communication networks (QCNs) that enable the distribution of entangled resources between distant nodes. This dissertation addresses two major challenges facing QCNs, which are the scalability and coverage of their architectures, and the efficiency of their operations. Additionally, the dissertation studies the near-term deployment of QML applications over today's noisy quantum devices, essential for realizing the future QI. In doing so, the scalability and efficiency challenges facing the different QCN elements are explored, and practical noise-aware and physics-informed approaches are developed to optimize the QCN performance given heterogeneous quantum application-specific quality of service (QoS) user requirements on entanglement rate and fidelity. Towards achieving this goal, this dissertation makes a number of key contributions. First, the scaling limits of quantum repeaters is investigated, and a holistic optimization framework is proposed to optimize the geographical coverage of quantum repeater networks (QRNs), including the number of quantum repeaters, their placement and separating distances, quantum memory management, and quantum operations scheduling. Then, a novel framework is proposed to address the scalability challenge of free-space optical (FSO) quantum channels in the presence of blockages and environmental effects. Particularly, the utilization of a reconfigurable intelligent surface (RIS) in QCNs is proposed to maintain a line-of-sight (LoS) connection between quantum nodes separated by blockages, and a novel analytical model of quantum noise and end-to-end (e2e) fidelity in such QCNs is developed. The results show enhanced entangled state fidelity and entanglement distribution rates, improving user fairness by around 40% compared to benchmark approaches. The dissertation then investigates the efficiency challenges in a practical use-case of QCNs with a single quantum switch (QS). Particularly, the average quantum memory noise effects are analytically analyzed and their impacts on the allocation of entanglement generation sources and minimization of entanglement distribution delay while optimizing QS entanglement distillation operations are investigated. The results show an enhanced e2e fidelity and a minimized e2e entanglement distribution delay compared to existing approaches, and a unique capability of satisfying all users QoS requirements. This QCN architecture is scaled up with multiple QSs serving heterogeneous user requests, necessary for scalable quantum applications over the QI. Here, a novel efficient matching theory-based framework for optimizing the request-QS association in such QCNs while managing quantum memories and optimizing QS operations is proposed. Finally, after scaling QCNs and ensuring their efficient operations, the dissertation proposes novel distributed QML frameworks that can leverage both classical networks and QCNs to enable collaborative learning between today's noisy quantum devices. In particular, the first quantum federated learning (QFL) frameworks incorporating different quantum neural networks and leveraging quantum and classical data are developed, and the first publicly available federated quantum dataset is introduced. The results show enhanced performance and reductions in the communication overhead and number of training epochs needed until convergence, compared to classical counterpart frameworks. Overall, this dissertation develops robust frameworks and algorithms that advance the theoretical understanding of QCNs and offers practical insights for the future development of the QI and its applications. The dissertation concludes by analyzing some open challenges facing QCNs and proposing a vision for physics-informed QCNs, along with important future directions. / Doctor of Philosophy / In today's digital age, we are generating vast amounts of data through videos, live streams, and various online activities. This explosion of data brings not only incredible opportunities for innovation but also heightened security concerns. The current Internet infrastructure struggles to keep up with the demand for speed and security. In this regard, the quantum Internet (QI) emerges as a revolutionary technology poised to make the communication and data sharing processes faster and more secure than ever before. The QI requires the development of quantum communication networks (QCNs) that will be seamlessly integrated with today's existing communication systems that form today's Internet. This way, the QI enables ultra-secure communication and advanced computing applications that can transform various sectors, from finance to healthcare. However, building such global QCNs, requires overcoming significant challenges, including the sensitive nature and limitations of quantum devices. In this regard, the goal of this dissertation is to develop scalable and efficient QCNs that overcome the different challenges facing different QCN elements and enable a wide coverage and robust performance towards realizing the QI at a global scale. Simultaneously, machine learning (ML), which is driving significant advancements and transforming industries in today's world. Here, quantum technologies are anticipated to make a breakthrough in ML through quantum machine learning (QML) models that can handle today's large and complex data. However, quantum computers are still limited in scale and efficiency, often being noisy and unreliable. Throughout this dissertation, these limitations of QML are addressed by developing frameworks that allow multiple quantum computers to work together collaboratively in a distributed manner over classical networks and QCNs. By leveraging distributed QML, it is possible to achieve remarkable advancements in privacy and data utilization. For instance, distributed QML can enhance navigation systems by providing more accurate and secure route planning or revolutionize healthcare by enabling secure and efficient analysis of medical data. In summary, this dissertation addresses the critical challenges of building scalable and efficient QCNs to support the QI and develops distributed QML frameworks to enable near-term utilization of QML in transformative applications. By doing so, it paves the way for a future where quantum technology is integral to our daily lives, enhancing security, efficiency, and innovation across various domains.

The development of quantum machine learning is bridging the way to fault tolerant quantum computation by providing algorithms running on the current noisy intermediate scale quantum devices.However, it is difficult to find use-cases where quantum computers exceed their classical counterpart.The high energy physics community is experiencing a rapid growth in the amount of data physicists need to collect, store, and analyze within the more complex experiments are being conceived.Our work approaches the study of a particle physics event involving the Higgs boson from a quantum machine learning perspective.We compare quantum support vector machine with the best classical kernel method grounding our study in a new theoretical framework based on metrics observing at three different aspects: the geometry between the classical and quantum learning spaces, the dimensionality of the feature space, and the complexity of the ML models.We exploit these metrics as a compass in the parameter space because of their predictive power. Hence, we can exclude those areas where we do not expect any advantage in using quantum models and guide our study through the best parameter configurations.Indeed, how to select the number of qubits in a quantum circuits and the number of datapoints in a dataset were so far left to trial and error attempts.We observe, in a vast parameter region, that the used classical rbf kernel model overtakes the performances of the devised quantum kernels.We include in this study the projected quantum kernel - a kernel able to reduce the expressivity of the traditional fidelity quantum kernel by projecting its quantum state back to an approximate classical representation through the measurement of local quantum systems.The Higgs dataset has been proved to be low dimensional in the quantum feature space meaning that the quantum encoding selected is not enough expressive for the dataset under study.Nonetheless, the optimization of the parameters on all the kernels proposed, classical and quantum, revealed a quantum advantage for the projected kernel which well classify the Higgs boson events and surpass the classical ML model. / Utvecklingen inom kvantmaskininlärning banar vägen för nya algoritmer att lösa krävande kvantberäkningar på dagens brusfyllda kvantkomponenter. Däremot är det en utmaning att finna användningsområden för vilka algoritmer som dessa visar sig mer effektiva än sina klassiska motsvarigheter. Forskningen inom högenergifysik upplever för tillfället en drastisk ökning i mängden data att samla, lagra och analysera inom mer komplexa experiment. Detta arbete undersöker Higgsbosonen ur ett kvantmaskinsinlärningsperspektiv. Vi jämför "quantum support vector machine" med den främsta klassiska metoden med avseende på tre olika metriker: geometrin av inlärningsrummen, dimensionaliteten av egenskapsrummen, och tidskomplexiteten av maskininlärningsmetoderna. Dessa tre metriker används för att förutsäga hur problemet manifesterar sig i parameterrummet. På så vis kan vi utesluta regioner i rummet där kvantalgoritmer inte förväntas överprestera klassiska algoritmer. Det finns en godtycklighet i hur antalet qubits och antalet datapunkter bestämms, och resultatet beror på dessa parametrar.I en utbredd region av parameterrummet observerar vi dock att den klassiska rbf-kärnmodellen överpresterar de studerade kvantkärnorna. I denna studie inkluderar vi en projicerad kvantkärna - en kärna som reducerar det totala kvanttillståndet till en ungefärlig klassisk representation genom att mäta en lokal del av kvantsystemet.Den studerade Higgs-datamängden har visat sig vara av låg dimension i kvantegenskapsrummet. Men optimering av parametrarna för alla kärnor som undersökts, klassiska såväl som kvantmekaniska, visade på ett visst kvantövertag för den projicerade kärnan som klassifierar de undersöka Higgs-händelserna som överstiger de klassiska maskininlärningsmodellerna.

Quantum computing has emerged as a new field that may have the potential to revolutionize the landscape of information processing and computational power, although physically constructing quantum hardware has proven difficult,and quantum computers in the current Noisy Intermediate Scale Quantum (NISQ) era are error prone and limited in the number of qubits they contain.A sub-field within quantum algorithms research which holds potential for the NISQ era, and which has seen increasing activity in recent years, is quantum machine learning, where researchers apply approaches from classical machine learning to quantum computing algorithms and explore the interplay between the two. This master thesis investigates feature selection and autoencoding algorithms for quantum computers. Our review of the prior art led us to focus on contributing to three sub-problems: A) Embedded feature selection on quantum annealers, B) short depth quantum autoencoder circuits, and C)embedded compressed feature representation for quantum classifier circuits.For problem A, we demonstrate a working example by converting ridge regression to the Quadratic Unconstrained Binary Optimization (QUBO) problem formalism native to quantum annealers, and solving it on a simulated backend. For problem B we develop a novel quantum convolutional autoencoder architecture and successfully run simulation experiments to study its performance.For problem C, we choose a classifier quantum circuit ansatz based on theoretical considerations from the prior art, and experimentally study it in parallel with a classical benchmark method for the same classification task,then show a method from embedding compressed feature representation onto that quantum circuit. / Kvantberäkning är ett framväxande område som potentiellt kan revolutionera informationsbehandling och beräkningskraft. Dock är praktisk konstruktion av kvantdatorer svårt, och nuvarande kvantdatorer i den s.k. NISQ-eran lider av fel och begränsningar i antal kvantbitar de kan hantera. Ett lovande delområde inom kvantalgoritmer är kvantmaskininlärning, där forskare tillämpar klassiska maskininlärningsmetoder på kvantalgoritmer och utforskar samspelet mellande två områdena.. Denna avhandling fokuserar på kvantalgoritmer för funktionsval,och datakompression (i form av s.k. “autoencoders”). Vi undersöker tre delproblem: A) Inbäddat funktionsval på en kvantannealer, B) autoencoder-kvantkretsar för datakompression, och C) inbyggt funktionsval för kvantkretsar för klassificering. För problem A demonstrerar vi ett fungerande exempel genom att omvandla ridge regression till problemformuleringen "Quadratic Unconstrained Binary Optimization"(QUBO) som är nativ för kvantannealers,och löser det på en simulerad backend. För problem B utvecklar vi en ny konvolutionerande autoencoder-kvantkrets-arkitektur och utför simuleringsexperimentför att studera dess prestanda. För problem C väljer vi en kvantkrets-ansats för klassificering baserad på teoretiska överväganden från tidigare forskning och studerar den experimentellt parallellt med en klassisk benchmark-metod församma klassificeringsuppgift, samt visar en metod för inbyggt funktionsval (i form av datakompression) i denna kvantkrets.

Today, a modern and interesting research area is machine learning. Another new and exciting research area is quantum computation, which is the study of the information processing tasks accomplished by practising quantum mechanical systems. This master thesis will combine both areas, and investigate quantum machine learning. Kerenidis’ and Prakash’s quantum algorithm for recommendation systems, that offered exponential speedup over the best known classical algorithms at the time, will be examined together with Tang’s classical algorithm regarding recommendation systems, which operates in time only polynomial slower than the previously mentioned algorithm. The speedup in the quantum algorithm was achieved by assuming that the algorithm had quantum access to the data structure and that the mapping to the quantum state was performed in polylog(mn). The speedup in the classical algorithm was attained by assuming that the sampling could be performed in O(logn) and O(logmn) for vectors and matrices, respectively.

L'informatique quantique exploite les phénomènes de la théorie quantique pour le traitement de l'information, tandis que l'apprentissage automatique s'intéresse aux algorithmes qui peuvent s'améliorer en fonction des expériences passées. L'informatique quantique a produit des algorithmes qui dépassent de loin les capacités des ordinateurs classiques que nous utilisons tous les jours. Cependant, l'identification de nouveaux algorithmes quantiques fut moins prolifique que dans le cas classique. Ces dernières années, on a cherché à combiner l'informatique quantique et l'apprentissage automatique. Le cadre de l'apprentissage automatique a servi à apprendre les paramètres de circuits quantiques paramétrés dans l'espoir d'apprendre à résoudre des problèmes où les phénomènes quantiques peuvent aider grâce au traitement de l'information quantique. L'objectif principal de ce mémoire est de pousser plus loin cette idée d'apprentissage de circuits quantiques et de fonder solidement ses capacités en développant une architecture universelle de circuit quantique paramétré. La première contribution est une évaluation d'algorithmes d'optimisation itératifs actuels pour les circuits quantiques paramétrés en tant que modèles d'apprentissage automatique, ainsi que la présentation d'un algorithme d'optimisation itératif simple, mais robuste. La deuxième contribution est une architecture de circuit quantique dans laquelle une famille de petits circuits avec des connexions arbitraires peut être intégrée. / Quantum information processing leverages the phenomena of quantum theory for information processing, while machine learning concerns itself with algorithms that can improve based on past experiences. Quantum information processing has produced algorithms that go far past the capabilities of the classical computers we use every day. However, the identification of new quantum algorithms has been much slower than during the early days of classical computing. In recent years, there has been a push to combine quantum information processing and machine learning. The framework of machine learning has been used to learn quantum circuits in the hopes of learning to solve problems where quantum phenomena can help through the use of quantum information processing. The main goal of this thesis is to further push this idea of learning quantum circuits and to solidly ground its capabilities by developing a learnable parametrized universal quantum circuit. The first contribution is an assessment of current optimization methods for parametrized quantum circuits as machine learning models. The second contribution is a quantum circuit architecture in which a family of smaller circuits with arbitrary connections can be embedded.

Random walks on graphs are an essential base for crucial algorithms for solving problems, like the boolean satisfiability problem. A speedup of random walks could improve these algorithms. The quantum version of the random walk, quantum walk, is faster than random walks in specific cases, e.g., on some linear graphs. An analysis of when the quantum walk is faster than the random walk can be accomplished analytically or by simulating both the walks on the graph. The problem arises when the graphs grow in size and connectivity. There are no known general rules for what an arbitrary graph not having explicit symmetries should exhibit to promote the quantum walk. Simulations will only answer the question for one single case, and will not provide any general rules for properties the graph should have. Using artificial neural networks (ANNs) as an aid for detecting when the quantum walk is faster on average than random walk on graphs, going from an initial node to a target node, has been done before. The quantum speedup may not be more than polynomial if the initial state of the quantum walk is purely in the initial node of the graph. We investigate starting the quantum walk in various superposition states, with an additional auxiliary node, to maybe achieve a larger quantum speedup. We suggest different ways to add the auxiliary node and select one of these schemes for use in this thesis. The superposition states examined are two stabiliser states and two magic states, inspired by the Gottesman-Knill theorem. According to this theorem, starting a quantum algorithm in a magic state may give an exponential speedup, but starting in a stabilizer state cannot give an exponential speedup, given that only gates from the Clifford group are used in the algorithm, as well as measurements are performed in the Pauli basis. We show that it is possible to train an ANN to classify graphs into what quantum walk was the fastest for various initial states of the quantum walk. The ANN classifies linear graphs and random graphs better than a random guess. We also show that a convolutional neural network (CNN) with a deeper architecture than earlier proposed for the task, is better at classifying the graphs than before. Our findings pave the way for automated research in novel quantum walk-based algorithms. / Slumpvandringar på grafer är essensiella i viktiga algoritmer för att lösa olika problem, till exempel SAT, booleska uppfyllningsproblem (the satisfiability problem). Genom att göra slumpvandringar snabbare går det att förbättra dessa algoritmer. Kvantversionen av slumpvandringar, kvantvandringar, har visats vara snabbare än klassiska slumpvandringar i specifika fall, till exempel på vissa linjära grafer. Det går att analysera, analytiskt eller genom att simulera vandringarna på grafer, när kvantvandringen är snabbare än slumpvandingen. Problem uppstår dock när graferna blir större, har fler noder samt fler kanter. Det finns inga kända generella regler för vad en godtycklig graf, som inte har några explicita symmetrier, borde uppfylla för att främja kvantvandringen. Simuleringar kommer bara besvara frågan för ett enda fall. De kommer inte att ge några generella regler för vilka egenskaper grafer borde ha. Artificiella neuronnät (ANN) har tidigare används som hjälpmedel för att upptäcka när kvantvandringen är snabbare än slumpvandingen på grafer. Då jämförs tiden det tar i genomsnitt att ta sig från startnoden till slutnoden. Dock är det inte säkert att få kvantacceleration för vandringen om initialtillståndet för kvantvandringen är helt i startnoden. I det här projektet undersöker vi om det går att få en större kvantacceleration hos kvantvandringen genom att starta den i superposition med en extra nod. Vi föreslår olika sätt att lägga till den extra noden till grafen och sen väljer vi en för att använda i resen av projektet. De superpositionstillstånd som undersöks är två av stabilisatortillstånden och två magiska tillstång. Valen av dessa tillstånd är inspirerat av Gottesmann- Knill satsen. Enligt satsen så kan en algoritm som startar i ett magiskt tillstånd ha en exponetiell uppsnabbning, men att starta i någon stabilisatortillstånden inte kan ha det. Detta givet att grindarna som används i algoritmen är från Cliffordgruppen samt att alla mätningar är i Paulibasen. I projektet visar vi att det är möjligt att träna en ANN så att den kan klassificera grafer utifrån vilken kvantvandring, med olika initialtillstånd, som var snabbast. Artificiella neuronnätet kan klassificera linjära grafer och slumpmässiga grafer bättre än slumpen. Vi visar också att faltningsnätverk med en djupare arkitektur än tidigare föreslaget för uppgiften är bättre på att klassificera grafer än innan. Våra resultat banar vägen för en automatiserad forskning i nya kvantvandringsbaserade algoritmer.

Quantum computing is a form of computation that exploits quantum mechanical phenomena for information processing, with promising applications (among others) in optimization and machine learning. Indeed, quantum machine learning is currently one of the most popular directions of research in quantum computing, offering solutions with an at-least-theoretical advantage compared to the classical counterparts. Nevertheless, the quantum devices available in the current Noisy Intermediate-Scale Quantum (NISQ) era are limited in the number of qubits and significantly affected by noise. An interesting alternative to the current prototypes of general-purpose quantum devices is represented by quantum annealers, specific-purpose quantum machines implementing the heuristic search for solving optimization problems known as quantum annealing. However, despite the higher number of qubits, the current quantum annealers are characterised by very sparse topologies. These practical issues have led to the development of hybrid classical-quantum schemes, aiming at leveraging the strengths of both paradigms while circumventing some of the limitations of the available devices. In this thesis, several hybrid classical-quantum algorithms for optimization and machine learning are introduced and/or empirically assessed, as the empirical evaluation is a fundamental part of algorithmic research. The quantum computing models taken into account are both quantum annealing and circuit-based universal quantum computing. The results obtained have shown the effectiveness of most of the proposed approaches.

Nous présentons un nouvel algorithme d’apprentissage de circuits quantiques basé sur la descente de gradient classique. Comme ce sujet unifie deux disciplines, nous expliquons les deux domaines aux gens de l’autre discipline. Conséquemment, nous débutons par une présentation du calcul quantique et des circuits quantiques pour les gens en apprentissage automatique suivi d’une présentation des algorithmes d’apprentissage automatique pour les gens en informatique quantique. Puis, pour motiver et mettre en contexte nos résultats, nous passons à une légère revue de littérature en apprentissage automatique quantique. Ensuite, nous présentons notre modèle, son algorithme, ses variantes et quelques résultats empiriques. Finalement, nous critiquons notre implémentation en montrant des extensions et des nouvelles approches possibles. Les résultats principaux se situent dans ces deux dernières parties, qui sont respectivement les chapitres 4 et 5 de ce mémoire. Le code de l’algorithme et des expériences que nous avons créé pour ce mémoire se trouve sur notre github à l’adresse suivante : https://github.com/AldoLamarre/quantumcircuitlearning. / We present a new learning algorithm for quantum circuits based on gradient descent. Since this subject unifies two areas of research, we explain each field for people working in the other domain. Consequently, we begin by introducing quantum computing and quantum circuits to machine learning specialists, followed by an introduction of machine learning to quantum computing specialists. To give context and motivate our results we then give a light literature review on quantum machine learning. After this, we present our model, its algorithms and its variants, then discuss our currently achieved empirical results. Finally, we criticize our models by giving extensions and future work directions. These last two parts are our main results. They can be found in chapter 4 and 5 respectively. Our code which helped obtain these results can be found on github at this link : https://github.com/ AldoLamarre/quantumcircuitlearning.