Given the rising popularity of quantum machine learning (QML), it is important to develop techniques that effectively simplify commonly adopted families of parameterised quantum circuits (commonly known as ansätze). This thesis pioneers the use of diagrammatic techniques to reason with QML ansätze. We take commonly used QML ansätze and convert them to diagrammatic form and give a full description of how these gates commute, making the circuits much easier to analyse and simplify. Furthermore, we leverage a combinatorial description of the interaction between CNOTs and phase gadgets to analyse a periodicity phenomenon in layered ansätze and also to simplify a class of circuits commonly used in QML.
Given the rising popularity of quantum machine learning (QML), it is important to develop techniques that effectively simplify commonly adopted families of parameterised quantum circuits (commonly known as ansätze). This thesis pioneers the use of diagrammatic techniques to reason with QML ansätze. We take commonly used QML ansätze and convert them to diagrammatic form and give a full description of how these gates commute, making the circuits much easier to analyse and simplify. Furthermore, we leverage a combinatorial description of the interaction between CNOTs and phase gadgets to analyse a periodicity phenomenon in layered ansätze and also to simplify a class of circuits commonly used in QML.
The field of quantum machine learning (QML) explores how quantum computers can be used to more efficiently solve machine learning problems. As an application of hybrid quantum-classical algorithms, it promises a potential quantum advantages in the near term. In this thesis, we use the ZXW-calculus to diagrammatically analyse two key problems that QML applications face. First, we discuss algorithms to compute gradients on quantum hardware that are needed to perform gradient-based optimisation for QML. Concretely, we give new diagrammatic proofs of the common 2- and 4-term parameter shift rules used in the literature. Additionally, we derive a novel, generalised parameter shift rule with 2n terms that is applicable to gates that can be represented with n parametrised spiders in the ZXW-calculus. Furthermore, to the best of our knowledge, we give the first proof of a conjecture by Anselmetti et al. by proving a no-go theorem ruling out more efficient alternatives to the 4-term shift rule. Secondly, we analyse the gradient landscape of quantum ansätze for barren plateaus using both empirical and analytical techniques. Concretely, we develop a tool that automatically calculates the variance of gradients and use it to detect likely barren plateaus in commonly used quantum ansätze. Furthermore, we formally prove the existence or absence of barren plateaus for a selection of ansätze using diagrammatic techniques from the ZXW-calculus.
Parameterized Quantum Circuits have emerged as a central framework for variational quantum algorithms in the NISQ regime, with major applications in quantum simulation, combinatorial optimization, and, more recently, quantum machine learning (QML). By developing a new approach for computing dynamical Lie algebras associated with quantum circuits combining parametrized gates and non-parametrized entangling gates, we aim to extend the applicability of recent algebraic results to architectures that are actually used in quantum machine learning.
Diagrammatic representations of quantum algorithms and circuits offer novel approaches to their design and analysis.In this work, we describe extensions of the ZX-calculus especially suitable for parameterized quantum circuits, in particular for computing observable expectation values as functions of or for fixed parameters, which are important algorithmic quantities in a variety of applications ranging from combinatorial optimization to quantum chemistry.We provide several new ZX-diagram rewrite rules and generalizations for this setting.In particular, we give formal rules for dealing with linear combinations of ZX-diagrams, where the relative complex-valued scale factors of each diagram must be kept track of, in contrast to most previously studied single-diagram realizations where these coefficients can be effectively ignored.This allows us to directly import a number useful relations from the operator analysis to ZX-calculus setting, including causal cone and quantum gate commutation rules.We demonstrate that the diagrammatic approach offers useful insights into algorithm structure and performance by considering several ansätze from the literature including realizations of hardware-efficient ansätze and QAOA.We find that by employing a diagrammatic representation, calculations across different ansätze can become more intuitive and potentially easier to approach systematically than by alternative means.Finally, we outline how diagrammatic approaches may aid in the design and study of new and more effective quantum circuit ansätze.
Machine Learning (ML) has been widely applied across numerous domains due to its ability to automatically identify informative patterns from data for various tasks. The availability of large-scale data and advanced computational power enables the development of sophisticated models and training strategies, leading to state-of-the-art performance, but it also introduces substantial challenges. Quantum Computing (QC), which exploits quantum mechanisms for computation, has attracted growing attention and significant global investment as it may address these challenges. Consequently, Quantum Machine Learning (QML), the integration of these two fields, has received increasing interest, with a notable rise in related studies in recent years. We are motivated to review these existing contributions regarding quantum circuit-based learning models for classical data analysis and highlight the identified potentials and challenges of this technique. Specifically, we focus not only on QML models, both kernel-based and neural network-based, but also on recent explorations of their integration with classical machine learning layers within hybrid frameworks. Moreover, we examine both theoretical analysis and empirical findings to better understand their capabilities, and we also discuss the efforts on noise-resilient and hardware-efficient QML that could enhance its practicality under current hardware limitations. In addition, we cover several emerging paradigms for advanced quantum circuit design and highlight the adaptability of QML across representative application domains. This study aims to provide an overview of the contributions made to bridge quantum computing and machine learning, offering insights and guidance to support its future development and pave the way for broader adoption in the coming years.
[EN] Quantum computing is widely regarded as one of the scientific fields with the greatest transformative potential. Its applications are already being explored in areas such as cybersecurity, chemistry, and machine learning. Within the domain of quantum machine learning, one emerging subfield is quantum natural language processing (QNLP), which seeks to leverage quantum algorithms to address complex language-related tasks more efficiently than classical counterparts. This thesis begins with a systematic literature review of the current landscape of quantum machine learning, focusing particularly on the design, development, and deployment of QNLP models on real quantum hardware. The SLR identifies 94 relevant articles that utilize quantum machine learning techniques and algorithms, highlighting their implementation via computational quantum circuits, or ansatzes. The main types of algorithms found include quantum adaptations of classical models such as support vector machines and k-nearest neighbors, as well as quantum neural networks, one of the most prominent applications being image classification. In addition, this work offers both quantitative and qualitative analyses, integrating a comprehensive set of experiments conducted on quantum simulators and real quantum devices. A significant contribution of this work lies in the design and evaluation of these new quantum circuit architectures, tailored to optimize expressibility, entanglement, and trainability. Empirical analysis shows that model accuracy tends to exhibit an inverse relationship with ansatz expressibility and a direct correlation with entanglement capability. In parallel, it contributes to the field by proposing novel ansatz architectures and applying circuit knitting techniques to overcome current hardware limitations. Ultimately, this thesis demonstrates the feasibility of hybrid quantum-classical approaches in QNLP and highlights their potential to be extended to support more complex and scalable real-world language applications.
Explainable ML algorithms are designed to provide transparency and insight into their decision-making process. Explaining how ML models come to their prediction is critical in fields such as healthcare and finance, as it provides insight into how models can help detect bias in predictions and help comply with GDPR compliance in these fields. QML leverages quantum phenomena such as entanglement and superposition, offering the potential for computational speedup and greater insights compared to classical ML. However, QML models also inherit the black-box nature of their classical counterparts, requiring the development of explainability techniques to be applied to these QML models to help understand why and how a particular output was generated. This paper will explore the idea of creating a modular, explainable QML framework that splits QML algorithms into their core components, such as feature maps, variational circuits (ansatz), optimizers, kernels, and quantum-classical loops. Each component will be analyzed using explainability techniques, such as ALE and SHAP, which have been adapted to analyse the different components of these QML algorithms. By combining insights from these parts, the paper aims to infer explainability to the overall QML model.