The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of relevant information from a large system. The advent of the age of quantum computing calls for efficient methods that work on information regarding quantum systems. Here we address this by proposing a new and general algorithm for the quantum generalisation of information bottleneck. Our algorithm excels in the speed and the definiteness of convergence compared with prior results. It also works for a much broader range of problems, including the quantum extension of deterministic information bottleneck, an important variant of the original information bottleneck problem. Notably, we discover that a quantum system can achieve strictly better performance than a classical system of the same size regarding quantum information bottleneck, providing new vision on justifying the advantage of quantum machine learning.
The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of relevant information from a large system. The advent of the age of quantum computing calls for efficient methods that work on information regarding quantum systems. Here we address this by proposing a new and general algorithm for the quantum generalisation of information bottleneck. Our algorithm excels in the speed and the definiteness of convergence compared with prior results. It also works for a much broader range of problems, including the quantum extension of deterministic information bottleneck, an important variant of the original information bottleneck problem. Notably, we discover that a quantum system can achieve strictly better performance than a classical system of the same size regarding quantum information bottleneck, providing new vision on justifying the advantage of quantum machine learning.
All the data stored and processed by our computers is encoded as sequences of zeros and ones, called bits. Quantum computers offer an alternative to this traditional way of encoding and manipulating information. The information in a collection of qubits can be a combination, also called a superposition, over many possible sequences of zeros and ones. Where classical computation consists of flipping zeros and ones, quantum computation consists of manipulating high-dimensional vectors called quantum states. Researchers have found ways to use this to engineer quantum algorithms that solve some tasks much faster than any classical computer would. These are called quantum advantages, and are proven for specific tasks, such as breaking some encryption schemes and solving certain large linear systems. The goal of this thesis was to find new tasks for which quantum computers provably have an advantage over classical computers. In this thesis, I present two such advantages and associated results. The first one revolves around a physically relevant learning task. In other words, I explore how quantum computers can be used to help solve specialized machine learning tasks. The second one addresses the simulation of classical systems. One of the first high-potential and natural uses of quantum computers was the simulation of quantum systems. A lot of real-world problems, however, are ruled by classical physics. It turns out that quantum computers are well suited for the simulation of some exponentially large classical systems. In this thesis, I add a new problem to this list.
Quantum-enhanced optimization aims to accelerate the solution of complex optimization problems by utilizing quantum mechanics to improve the efficiency of algorithms. This paper investigates a novel quantum optimization algorithm specifically designed to handle sparse matrices, a common challenge in many real-world applications. We demonstrate the potential of quantum properties – particularly entanglement and superposition – to significantly reduce computational complexity and improve solution speed compared to classical approaches. The core mechanism centers around exploiting quantum algorithms to efficiently navigate and process sparse data structures, leading to substantial performance gains. This work offers a promising pathway to address a critical bottleneck in optimization, with implications for diverse fields including machine learning, finance, and logistics.
Quantum machine learning (QML) models operating on classical data require an encoding step to map information into the Hilbert space. However, this imposes a computational bottleneck absent in classical frameworks, necessitating rigorous theoretical complexity analysis and algorithmic mitigations. We provide theoretical foundations of different encoding methods that prepare quantum states for both simulators and hardware, analyzing normal and sparse high energy physics data. In addition, we propose a quantum data augmentation method based on randomly sampled circuits to improve sample efficiency and mitigate the data scarcity bottleneck. We demonstrate the effectiveness of this method on a generative quantum diffusionlike model to produce synthetic samples of classical images. Our results demonstrate that choosing domain optimal encoding and applying the novel quantum data augmentation leads to faster convergence and improved model performance, offering a highly sample-efficient and scalable approach to encoding and augmenting sparse classical data for QML.
Quantum computing offers a fundamentally new paradigm for solving complex optimisation and learning tasks by exploiting superposition, entanglement, and other quantum phenomena. Over the past decade, research has increasingly focused on quantum-enhanced approaches to optimisation and machine learning (ML), showing the potential to outperform classical methods in specific settings (Zaman, 2023; Peral-García, 2024). This paper presents a comprehensive review of quantum algorithms for optimisation (e.g., the Quantum Approximate Optimization Algorithm and quantum annealing) and quantum machine learning frameworks (such as quantum support vector machines and quantum neural networks), analysing their theoretical underpinnings, implementation status, and applicability to real-world tasks. Key challenges including hardware noise, limited qubit counts, and algorithmic scalability are examined (Chen, 2024). We also explore hybrid quantum-classical architectures as a near-term route to quantum advantage and propose future research directions aimed at bridging the current gap between quantum algorithm theory and large-scale deployment. Through this synthesis, we aim to provide both academic and practitioner audiences with a clear roadmap for leveraging quantum algorithms in optimisation and ML workflows
The training of large-scale machine learning models presents significant computational challenges, primarily due to the inherent complexity of optimization algorithms like stochastic gradient descent (SGD) and its variants. These algorithms often struggle with convergence speed, getting trapped in local minima, and the ability to effectively explore the vast solution space. This paper investigates the potential of quantum-inspired optimization techniques to address these limitations. Specifically, we explore the application of quantum annealing and variational quantum eigensolver (VQE) approaches to accelerate the training and optimization process of large-scale machine learning models. Our core claim is that by mapping the optimization problem to a quantum system, we can leverage quantum computation to overcome the computational bottlenecks associated with classical optimization methods. We propose a framework where the objective function of the machine learning model is translated into a Hamiltonian for a quantum annealer or the cost function for a VQE, enabling a quantum-inspired solution. The results, while theoretical in this initial exploration, demonstrate a potential pathway for significantly reducing training times and improving the overall performance of large-scale machine learning models. Further research is needed to develop efficient hybrid quantum-classical algorithms and explore the practical limitations of this approach.
This study focuses on the integration of quantum computing and artificial intelligence, proposing a multi-task optimisation framework based on the quantum annealing algorithm to address the bottlenecks in computational efficiency and model optimisation in traditional machine learning. The study converts problems such as time series prediction, Support Vector Machine (SVM) classification, and Convolutional Neural Network (CNN) training into Quadratic Unconstrained Binary Optimisation (QUBO) models and achieves parameter optimisation through the simulated annealing algorithm. In time series prediction, an autoregressive model is constructed based on historical data. The problem of minimising prediction error is mapped to a binary optimisation problem through QUBO transformation, and the model parameters are solved using the simulated annealing algorithm to achieve trend prediction of the target variable, validating the effectiveness of quantum optimisation in time series analysis. For classification tasks, the hinge loss and regularisation terms of SVM are converted into a QUBO matrix to optimise the classification hyperplane parameters, thereby enhancing the model's classification performance in the feature space. The results demonstrate that this method exhibits strong geometric interpretability and generalisation capabilities in binary classification problems. In the field of deep learning, L2 regularisation is introduced into the weight optimisation of CNNs, and a QUBO model is constructed to explore the application of quantum optimisation in image feature extraction and network training. Although limited by the scale of variables, this demonstrates the potential value of combining quantum computing with deep learning. The study shows that the quantum optimisation framework can effectively improve solution efficiency in small- to medium-scale problems, providing new technical pathways for time series analysis, classification tasks, and deep learning optimisation.