Quantum machine learning promises to deliver near-term practical quantum computation applications using machine learning tools to optimize quantum hardware for scientific applications. Studies in this direction often propose using variational quantum circuits as the underlying hardware. However, these so-called VQCs exhibit flat landscapes with narrow and concentrated local minima, making their optimization inefficient and thwarting their advantage. This dissertation proposes using quantum many-body systems' dynamics for computation instead of circuits. This Analog quantum machine learning approach (AQML) uses tools from optimal control to deliver more manageable optimization landscapes and helps explain what types of computation are suitable for different hardware. Concretely, I show that arrays of Rydberg atoms can be leveraged to implement reservoir computers with enhanced memory storage and retrieval. I also show that two atom-species Rydberg arrays can reproduce the dynamics of the basic building blocks of artificial neural networks and be used for quantum-enhanced sensing and entanglement detection. This study shows that AQML algorithms are theoretically more expressive than their classical counterparts. Lastly, I show that while AQML algorithms can still exhibit problematic optimization landscapes, flatness can be mitigated, and local minima can be circumvented by co-designing the underlying hardware with the desired task. We exemplify this co-design in the context of quantum chemistry calculations. This dissertation shows that AQML algorithms can be used for various scientific and small-scale applications such as sensing, chemical design, entanglement witnessing, and time-series prediction. However, we still have a way to go before seeing full-scale applications. Instead, this dissertation focuses on theoretical studies and answers the question of what we can compute with quantum hardware's analog dynamics.
Quantum machine learning promises to deliver near-term practical quantum computation applications using machine learning tools to optimize quantum hardware for scientific applications. Studies in this direction often propose using variational quantum circuits as the underlying hardware. However, these so-called VQCs exhibit flat landscapes with narrow and concentrated local minima, making their optimization inefficient and thwarting their advantage. This dissertation proposes using quantum many-body systems' dynamics for computation instead of circuits. This Analog quantum machine learning approach (AQML) uses tools from optimal control to deliver more manageable optimization landscapes and helps explain what types of computation are suitable for different hardware. Concretely, I show that arrays of Rydberg atoms can be leveraged to implement reservoir computers with enhanced memory storage and retrieval. I also show that two atom-species Rydberg arrays can reproduce the dynamics of the basic building blocks of artificial neural networks and be used for quantum-enhanced sensing and entanglement detection. This study shows that AQML algorithms are theoretically more expressive than their classical counterparts. Lastly, I show that while AQML algorithms can still exhibit problematic optimization landscapes, flatness can be mitigated, and local minima can be circumvented by co-designing the underlying hardware with the desired task. We exemplify this co-design in the context of quantum chemistry calculations. This dissertation shows that AQML algorithms can be used for various scientific and small-scale applications such as sensing, chemical design, entanglement witnessing, and time-series prediction. However, we still have a way to go before seeing full-scale applications. Instead, this dissertation focuses on theoretical studies and answers the question of what we can compute with quantum hardware's analog dynamics.
Quantum machine learning algorithms promise to deliver near-term, applicable quantum computation on noisy, intermediate-scale systems. While most of these algorithms leverage quantum circuits for generic applications, a recent set of proposals, called analog quantum machine learning (AQML) algorithms, breaks away from circuit-based abstractions and favors leveraging the natural dynamics of quantum systems for computation, promising to be noise-resilient and suited for specific applications such as quantum simulation. Recent AQML studies have called for determining best ansatz selection practices and whether AQML algorithms have trap-free landscapes based on theory from quantum optimal control (QOC). We address this call by systematically studying AQML landscapes on two models: those admitting black-boxed expressivity and those tailored to simulating a specific unitary evolution. Numerically, the first kind exhibits local traps in their landscapes, while the second kind is trap-free. However, both kinds violate QOC theory’s key assumptions for guaranteeing trap-free landscapes. We propose a methodology to co-design AQML algorithms for unitary evolution simulation using the ansatz’s Magnus expansion. Our methodology guarantees the algorithm has an amenable dynamical Lie algebra with independently tunable terms. We show favorable convergence in simulating dynamics with applications to metrology and quantum chemistry. We conclude that such co-design is necessary to ensure the applicability of AQML algorithms.
Quantum machine learning sits at the intersection of two paradigm-shifting technologies: quantum computing and deep learning. By exploiting quantum mechanical phenomena – superposition, entanglement, and interference – QML promises exponential or quadratic speedups over classical algorithms for certain learning tasks, as well as the ability to model quantum data natively. However, the path to practical quantum advantage remains contested, constrained by noisy intermediate-scale quantum (NISQ) hardware, limited qubit counts (50–1,000), coherence times (50–500 μs), and high gate error rates (10⁻³–10⁻⁴). This paper provides a rigorous, technically deep survey of QML: mathematical foundations (Hilbert spaces, unitary evolution, measurement, quantum circuits), canonical algorithms (quantum kernel methods, variational quantum circuits (VQCs), quantum neural networks (QNNs), QSVMs, quantum generative adversarial networks (QGANs), encoding strategies (angle, amplitude, basis, and Hamiltonian encoding), optimization landscapes (barren plateaus, parameter shift rules, ansatz design), hardware aware implementation on superconducting (IBM, Google), trapped ion (IonQ), and neutral atom (Pasqal) platforms, empirical benchmarks on near term devices for classification, generative modeling, and quantum chemistry, and pathways to fault tolerant quantum machine learning (FTQML) with error correction (surface codes, logical qubits). Researchers critically assess claims of quantum advantage, identify scenarios where QML may outperform classical ML (small data, high-dimensional feature spaces from quantum systems, kernel estimation), and propose concrete evaluation metrics (quantum-classical cross-validation, resource estimation).
Recent advances in Machine Learning have transformed numerous industrial sectors, yet classical paradigms face fundamental limitations: rapidly growing data volumes, rising computational costs, significant energy consumption, and the physical scaling limits of conventional hardware architectures. Quantum computing has emerged as a promising computational paradigm to address these challenges, giving rise to the field of Quantum Machine Learning (QML). In this thesis, the theoretical foundations of QML are investigated, with a focus on near-term and future practical applications. Three central challenges are addressed: the trainability of variational quantum circuits, their expressivity, and their resistance to efficient classical simulation. The trainability of Hamming-weight preserving variational quantum circuits is first studied, and theoretical guarantees are established that resolve an open conjecture on the absence of barren plateaus for this circuit family. Subspace-preserving QML algorithms are then introduced, including photonic circuits and quantum convolutional neural networks, and are designed to mimic classical ML subroutines while offering polynomial quantum advantage. Finally, variational quantum circuits are analyzed as quantum Fourier models, and a framework is derived to jointly characterize expressivity and trainability, from which conditions are obtained under which quantum models provably separate from their classical counterparts. These contributions are intended to advance the theoretical roadmap for harnessing near-term and future quantum technologies in real-world applications.
Quantum computation is a form of computation utilizing quantum mechanical phenomena.A formal formulation of quantum computer was proposed in 1985, leading to novel quantum algorithms whose computation time scales better, with respect to the problem size, than the classical counterparts.However, running these quantum algorithms requires fault-tolerant implementations, and hence, such engineering in quantum systems can be an overhead in utilizing quantum systems for information processing.This suggests, in addition to seeking faster quantum algorithms, the necessity of exploring how to harness quantum systems more naturally without extensive engineering, leading to another form of quantum information processing.Quantum machine learning (QML) is expected to be a promising approach for harnessing quantum systems for information processing.This is motivated by the fact that the success of neural networks has led to the possibility of solving ML tasks more efficiently with non-digital computer designs.Several QML algorithms that resemble neural networks utilize quantum systems in a manner distinct from digital quantum algorithms.However, training quantum systems is fundamentally challenging, suggesting that it still remains necessary to explore an alternative way of harnessing quantum systems for ML.Along with this direction, the quantum reservoir model harnesses quantum systems in a unique way: nontrivial outputs from an untrained quantum system are leveraged by a linear classical machine learning model to solve various tasks.Hence, the quantum part does not need to be programmable and can be analog quantum dynamics.Without extensive engineering in the quantum part, a quantum reservoir model was shown to be capable of performing nontrivial ML tasks using physical dynamics, which had already been realized experimentally.Therefore, the quantum reservoir model should be one of the promising directions for pursuing another form of quantum information processing.In this thesis, I will investigate the computational capability of natural quantum dynamics in the quantum reservoir model.I will tackle the following critical open questions in this context: (i) how well natural dynamics perform nontrivial ML tasks compared to engineered systems, and (ii) what kind of engineering in quantum dynamics is essential and appropriate for a given task.To tackle the first question (i), I will benchmark the learning performance of various natural quantum dynamics against random circuits that require complicated engineering, thereby revealing the computational power of natural dynamics.For the second question (ii), I will present a characterization method of quantum dynamics that has the potential to bridge quantum properties and their machine learning roles, providing concrete insights into essential and appropriate engineering to design quantum systems for ML.v
Quantum computing has shown theoretical promise for accelerating machine learning, including both generative and discriminative tasks. Recent advances in analog Rydberg atom quantum computers have opened new opportunities for near-term quantum machine learning applications, due to uniquely reconfigurable qubit positions and global multi-qubit operations. In this work, we present two complementary contributions that leverage the unique properties of this technology. First, we propose ReCon, the first implementation of quantum generative adversarialnetworks (GANs) on analog Rydberg atom quantum computers, achieving a 33% improvement in image generation quality (measured via Frechet Inception Distance) compared to state-of-the-art superconducting-qubit techniques. Second, we introduce ResQ, a novel framework that optimizes the dynamics of Rydberg atom quantum computers for discriminative tasks, specifically neural ordinary differential equation (neural ODE) based residual neural network (ResNets) classifiers. ResQ demonstrates how analog quantum computing can be tailored to solve classification problems in machine learning, achieving a 36% improvement over classical neural ODE classifiers. Together, these works highlight the versatility and scalability of analog Rydberg atom quantum computing for both generative and discriminative quantum machine learning, advancing the feasibility and versatility of near-term hardware implementations for QML tasks.
The rapid advancement of quantum computing hardware and software has ushered in a new era for computational science, promising to tackle problems that are intractable for classical computers. Parallelly, machine learning (ML) has revolutionized data analysis and artificial intelligence. The confluence of these two fields, known as Quantum Machine Learning (QML), aims to harness the principles of quantum mechanics-such as superposition, entanglement, and interference-to enhance and redefine classical machine learning algorithms. This survey provides a comprehensive overview of the burgeoning field of QML. We begin by elucidating the fundamental quantum concepts that underpin QML approaches. We then present a detailed taxonomy and analysis of prominent QML algorithms, categorizing them into quantum-enhanced classical models and fully quantum models. Key families of algorithms discussed include Quantum Support Vector Machines (QSVM), Quantum Neural Networks (QNNs), and Quantum Generative Adversarial Networks (QGANs). For each, we explain the theoretical quantum advantage, the circuit implementation, and the current limitations. Furthermore, we delve into the critical challenges facing the practical realization of QML, including the pervasive issue of noise in Noisy Intermediate-Scale Quantum (NISQ) devices, the problem of barren plateaus in training quantum circuits, and the complexities of efficient data encoding (quantum feature maps). We also present a small-scale experimental simulation of a variational quantum classifier on a standardized dataset, demonstrating its principle and comparing its performance with a classical counterpart. Finally, the paper discusses the future trajectory of QML, highlighting the importance of error mitigation, hybrid quantum-classical architectures, and the development of quantum-specific learning inductive biases. We conclude that while fault-tolerant quantum computers remain on the horizon, QML represents a paradigm shift with the potential to deliver profound computational advantages in the coming decades.