In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then describe more precisely how to link them through linear algebra: we introduce quantum algorithms to efficiently solve tasks such as matrix product or distance estimation. These results are then used to develop new quantum algorithms for unsupervised machine learning, such as k-means and spectral clustering. This allows us to define many fundamental procedures, in particular in vector and graph analysis. We will also present new quantum algorithms for neural networks, or deep learning. For this, we introduce an algorithm to perform a quantum convolution product on images, as well as a new way to perform a fast tomography on quantum states. We prove that these quantum algorithms are faster versions of equivalent classical algorithms, but exhibit random effects due to the quantum nature of the computation. Many simulations have been carried out to study these effects and measure their learning accuracy on real data. Finally, we will present a quantum orthogonal neural network circuit adapted to the currently available small and imperfect quantum computers. This allows us to perform real experiments to test our theory.
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then describe more precisely how to link them through linear algebra: we introduce quantum algorithms to efficiently solve tasks such as matrix product or distance estimation. These results are then used to develop new quantum algorithms for unsupervised machine learning, such as k-means and spectral clustering. This allows us to define many fundamental procedures, in particular in vector and graph analysis. We will also present new quantum algorithms for neural networks, or deep learning. For this, we introduce an algorithm to perform a quantum convolution product on images, as well as a new way to perform a fast tomography on quantum states. We prove that these quantum algorithms are faster versions of equivalent classical algorithms, but exhibit random effects due to the quantum nature of the computation. Many simulations have been carried out to study these effects and measure their learning accuracy on real data. Finally, we will present a quantum orthogonal neural network circuit adapted to the currently available small and imperfect quantum computers. This allows us to perform real experiments to test our theory.
This thesis presents original contributions at the intersection of quantum computing and machine learning, investigating how these two fields can benefit from each other. The first part of the thesis presents two applications of machine learning techniques in quantum computing. The first contribution involves the use of artificial neural networks for the decoding of quantum error correction codes, resulting in faster decoding times while maintaining a high level of accuracy. The originality of this work lies in the application of explainable machine learning techniques to both improve the decoding performance and to provide insights into the decoding process. The second contribution introduces a novel technique based on reinforcement learning to characterize and simulate the noise affecting a quantum chip. This technique reduces the heuristic assumption on the noise model, making it more adaptable to the specific noise characteristics of the quantum device. In the second part of the thesis, we demonstrate, with two examples, how it is possible to implement machine learning algorithms on quantum devices by replacing artificial neural networks with parametrized quantum circuits. The first contribution in this section introduces a quantum anomaly detection algorithm, applied to the field of high-energy physics. This algorithm allows for the identification of anomalous patterns in quantum data, maintaining a level of accuracy comparable to classical algorithms. The novelty of this work lies in the first use of quantum circuits for the task of anomaly detection in a muon drift chamber trigger system, with possible future applications to quantum detector systems in high-energy physics experiments. The second contribution presents the quantum version of a generative diffusion model, able to sample quantum states from a well-defined distribution. This first implementation of a quantum diffusion model is not meant to outperform classical models, but rather to show potential advantages and limitations of these kinds of algorithms. The aim of the thesis is to show how quantum computing can benefit from machine learning, and how machine learning can be implemented on quantum devices, setting the stage for future advancements in both fields.
Quantum machine learning techniques have been proposed as a way to potentially enhance performance in machine learning applications. In this paper, we introduce two new quantum methods for neural networks. The first one is a quantum orthogonal neural network, which is based on a quantum pyramidal circuit as the building block for implementing orthogonal matrix multiplication. We provide an efficient way for training such orthogonal neural networks; novel algorithms are detailed for both classical and quantum hardware, where both are proven to scale asymptotically better than previously known training algorithms. The second method is quantum-assisted neural networks, where a quantum computer is used to perform inner product estimation for inference and training of classical neural networks. We then present extensive experiments applied to medical image classification tasks using current state of the art quantum hardware, where we compare different quantum methods with classical ones, on both real quantum hardware and simulators. Our results show that quantum and classical neural networks generates similar level of accuracy, supporting the promise that quantum methods can be useful in solving visual tasks, given the advent of better quantum hardware.
The convergence of machine learning (ML) and quantum computing is quickly becoming a game-changing new frontier in computational science. The most intriguing area of overlap may be quantum optimization, which seeks to reduce the exponentially increasing complexity and computational cost of ML algorithms. As they grow larger and more complicated, traditional optimization methods, particularly in high-dimensional and non-convex space, will inevitably hit performance limits. Quantum optimization is the whole new paradigm that leverages quantum mechanical effects like superposition, entanglement, and tunnelling to explore solution spaces more efficiently. The chapter outlines the theory, practice, and potential of hybrid quantum-classical optimization algorithms for machine learning. The most brilliant research direction in the current NISQ (noisy intermediate-scale quantum) era is mixed systems leveraging classical computing capability augmented by quantum capacity. In such designs, computationally intensive subroutines like optimization for global optima or escape from local minima are left to quantum processors and data preprocessing, iterative refinement, and model testing are performed by classical processors. We start by defining the fundamental principles of quantum computing and acquainting readers with the fundamentals like qubits, quantum gates, and quantum circuits. These are the building blocks for quantum algorithms, which hopefully can be utilized for optimization, for example, the QAOA (quantum approximate optimization algorithm), the VQE (variational quantum Eigensolver), and quantum annealing. They all build to optimize the problems in some way differently: QAOA through parameterized quantum circuits, VQE through approximations of ground states of the Hamiltonians, and quantum annealing through quantum evolution to low-energy solutions. We then form a loop between these quantum algorithms and regular machine learning tasks. Optimization impacts virtually all ML phases, from training neural networks, where one reduces loss functions; feature selection, where one aims to discover the most relevant subset of input variables; and hyperparameter optimization, which often involves expensive search procedures over extremely large combinatorial spaces. Quantum optimization techniques can therefore, in principle, accelerate such procedures through computational complexity reduction and enhancing solutions over challenging landscapes. Realistic simulations and case studies emphasize the degree to which hybrid quantum-classical algorithms have been employed in solving ML problems, that is, QSVMs, quantum-enhanced clustering, and quantum reinforcement learning. Despite their experimental nature, these applications already show encouraging results in terms of improved performance metrics as well as reduction in time-to-solution compared to classical-only solutions. Notwithstanding that, this new field is not bereft of real challenges. Quantum hardware suffers from hard limits on qubit fidelity, decoherence, and scalability in the current times. Furthermore, quantum circuit integration into broad ML pipelines requires novel architectures and software platforms. As a counter to those issues, this chapter surveys recent advances in quantum programming languages, simulators, and hybrid platforms like PennyLane, Qiskit, and TensorFlow Quantum. We conclude by looking to the future possibility that quantum optimization will revolutionize the machine learning landscape. As hardware improves and algorithmic complexity increases, the possibility of quantum-powered learning systems solving hard problems becomes increasingly accessible. From speeding up deep network training to enabling new types of unsupervised learning, quantum optimization holds the potential to recast computational tractability in machine learning. This chapter is an all-encompassing introduction and state-of-the-art work for students, researchers, and practitioners interested in using quantum optimization for practical ML applications. It sets the foundation for understanding how to pursue hybrid approaches (how they may be applied today in the real world and bracing oneself for disruption in the future).
In this thesis, I develop the theory required to use quantum computers to accelerate linear algebra and machine learning, in a manner akin to how GPUs are used today. I begin by analysing quantum random access memory (QRAM), the mechanism by which quantum algorithms can access classical (non-quantum) data. When used for linear algebra applications, I show that QRAM has substantial challenges making it harder to construct than an error-corrected quantum computer. Should QRAM prove to be unrealistic, I ask what types of classical data can be efficiently loaded into quantum computers, and prove that discretized continuous functions are one such option. Next, I introduce a framework for manipulating vectors with quantum computers. The primary result of this framework is a technique allowing for the non-linear transformations of vectors to be enacted efficiently for a broad class of functions, despite the underlying unitary (and thus linear) nature of quantum algorithms. In the final chapter, utilizing the preceding results and further developing the vector encoding framework, I demonstrate that quantum computers can accelerate inference for multilayer neural networks under a range of scenarios of QRAM feasibility. This chapter also notes a plausible path towards constructing a practically useful QRAM.
Quantum machine learning has the potential for broad industrial applications, and the development of quantum algorithms for improving the performance of neural networks is of particular interest given the central role they play in machine learning today. We present quantum algorithms for training and evaluating feedforward neural networks based on the canonical classical feedforward and backpropagation algorithms. Our algorithms rely on an efficient quantum subroutine for approximating inner products between vectors in a robust way, and on implicitly storing intermediate values in quantum random access memory for fast retrieval at later stages. The running times of our algorithms can be quadratically faster in the size of the network than their standard classical counterparts since they depend linearly on the number of neurons in the network, and not on the number of connections between neurons. Furthermore, networks trained by our quantum algorithm may have an intrinsic resilience to overfitting, as the algorithm naturally mimics the effects of classical techniques used to regularize networks. Our algorithms can also be used as the basis for new quantum-inspired classical algorithms with the same dependence on the network dimensions as their quantum counterparts but with quadratic overhead in other parameters that makes them relatively impractical.
Quantum machine learning (QML) provides a transformative approach to data analysis by integrating the principles of quantum computing with classical machine learning methods. With the exponential growth of data and the increasing complexity of computational tasks, quantum algorithms offer tremendous advantages in terms of processing speed, memory efficiency, and the ability to resolve issues intractable for classical systems. In this work, the use of QML techniques for both supervised and unsupervised learning problems is explored. Quantum-enhanced models such Quantum Support Vector Machines (QSVMs) and Quantum Neural Networks (QNNs) show outstanding performance in classification and regression tasks by using quantum kernels and entanglement in supervised learning. Moreover, hybrid quantum-classical solutions offer useful implementations on noisy intermediate-scale quantum (NISQ) devices, hence bridging the gap between present quantum technology and practical uses. By means of comparative analysis, this paper emphasizes the possible benefits and drawbacks of QML, thereby providing understanding of its future importance in sectors including material science, finance, and healthcare. In the end, QML opens the path for a new era of intelligent data processing and solves until unthinkable difficult challenges.