Parametrized quantum evolution is the main ingredient in variational quantum algorithms for near-term quantum devices.In digital quantum computing, it has been shown that random parametrized quantum circuits are able to express complex distributions intractable by a classical computer, leading to the demonstration of quantum supremacy.However, their chaotic nature makes parameter optimization challenging in variational approaches.Evidence of similar classically intractable expressibility has been recently demonstrated in analog quantum computing with driven many-body systems.A thorough investigation of trainability of such analog systems is yet to be performed.In this work we investigate how the interplay between external driving and disorder in the system dictates the trainability and expressibility of interacting quantum systems.We show that if the system thermalizes, the training fails at the expense of the large expressibility, while the opposite happens when the system enters the many-body localized (MBL) phase.From this observation we devise a protocol using quenched MBL dynamics which allows accurate trainability while keeping the overall dynamics in the quantum supremacy regime.Our work shows the fundamental connection between quantum many-body physics and its application in machine learning.We conclude our work with an example application in generative modeling employing a well studied analog many-body model of a driven Ising spin chain.Our approach can be implemented with a variety of available quantum platforms including cold ions, atoms, and superconducting circuits.
Parametrized quantum evolution is the main ingredient in variational quantum algorithms for near-term quantum devices.In digital quantum computing, it has been shown that random parametrized quantum circuits are able to express complex distributions intractable by a classical computer, leading to the demonstration of quantum supremacy.However, their chaotic nature makes parameter optimization challenging in variational approaches.Evidence of similar classically intractable expressibility has been recently demonstrated in analog quantum computing with driven many-body systems.A thorough investigation of trainability of such analog systems is yet to be performed.In this work we investigate how the interplay between external driving and disorder in the system dictates the trainability and expressibility of interacting quantum systems.We show that if the system thermalizes, the training fails at the expense of the large expressibility, while the opposite happens when the system enters the many-body localized (MBL) phase.From this observation we devise a protocol using quenched MBL dynamics which allows accurate trainability while keeping the overall dynamics in the quantum supremacy regime.Our work shows the fundamental connection between quantum many-body physics and its application in machine learning.We conclude our work with an example application in generative modeling employing a well studied analog many-body model of a driven Ising spin chain.Our approach can be implemented with a variety of available quantum platforms including cold ions, atoms, and superconducting circuits.
Quantum supremacy is the ability of quantum processors to outperform classical computers at certain tasks. In digital random quantum circuit approaches for supremacy, the output distribution produced is described by the Porter-Thomas (PT) distribution. In this regime, the system uniformly explores its entire Hilbert space, which makes simulating such quantum dynamics with classical computational resources impossible for large systems. However, the latter has no direct application so far in solving a specific problem. In this work, we show that the same sampling complexity can be achieved from driven analog quantum processors, with less stringent requirements for coherence and control. More importantly, we discuss how to apply this approach to solve problems in quantum simulations of phases of matter and machine learning. Specifically, we consider a simple quantum spin chain with nearest-neighbor interactions driven by a global magnetic field. We show how quantum supremacy is achieved as a consequence of the thermalization due to the interplay between the disorder and the driven many-body dynamics. We analyze how the achieved PT distribution can be used as an accessible reference distribution to probe the many-body localization (MBL) phase transition. In the second part of our work, we show how our setup can be used for generative modeling machine learning tasks. We propose a novel variational hybrid quantum-classical approach, exploiting the system's inherent tunable MBL dynamics, to train the device to learn distributions of complex classical data. The performance of our training protocol depends solely on the phase that the quantum system is in, which makes fine-tuning of local parameters not necessary. The protocol is implementable in a range of driven quantum many-body systems, compatible with noisy intermediate-scale quantum devices.
Variational quantum algorithms (VQAs) have emerged as the leading strategy to obtain quantum advantages on the current noisy intermediate-scale devices. However, their entanglement-trainability correlation indicates that deep circuits are generally untrainable due to the barren plateau phenomenon, which challenges their applications. In this work, we suggest a gate-to-tensor encoding method for parametrized quantum circuits (PQCs), with which two long short-term memory networks are trained to predict both entangling capability and trainability. We call these LG networks. The remarkable capabilities of LG networks afford a statistical way to investigate the entanglement-trainability correlation of PQCs within a data set encompassing millions of generated circuits. This machine-learning-driven method first confirms the negative correlation between entanglement and trainability. Then, we observe that circuits with any values of entangling capability and trainability exist. These circuits with high entanglement and high trainability possess an appropriate high portion of nearest-neighbor nonlocal gates. Furthermore, the trained LG networks can be employed to construct PQCs with specific entanglement and trainability, demonstrating their practical applications in VQAs.
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 generative models hold the promise of accelerating or improving machine learning tasks by leveraging the probabilistic nature of quantum states, but the successful optimization of these models remains a difficult challenge. To tackle this challenge, we present a new architecture for quantum generative modeling that combines insights from classical machine learning and quantum phases of matter. In particular, our model utilizes both many-body localized (MBL) dynamics and hidden units to improve the optimization of the model. We demonstrate the applicability of our model on a diverse set of classical and quantum tasks, including a toy version of MNIST handwritten digits, quantum data obtained from quantum many-body states, and nonlocal parity data. Our architecture and algorithm provide novel strategies of utilizing quantum many-body systems as learning resources and reveal a powerful connection between disorder, interaction, and learning in quantum many-body systems. Published by the American Physical Society 2024
Abstract A new paradigm for data science has emerged, with quantum data, quantum models, and quantum computational devices. This field, called quantum machine learning (QML), aims to achieve a speedup over traditional machine learning for data analysis. However, its success usually hinges on efficiently training the parameters in quantum neural networks, and the field of QML is still lacking theoretical scaling results for their trainability. Some trainability results have been proven for a closely related field called variational quantum algorithms (VQAs). While both fields involve training a parametrized quantum circuit, there are crucial differences that make the results for one setting not readily applicable to the other. In this work, we bridge the two frameworks and show that gradient scaling results for VQAs can also be applied to study the gradient scaling of QML models. Our results indicate that features deemed detrimental for VQA trainability can also lead to issues such as barren plateaus in QML. Consequently, our work has implications for several QML proposals in the literature. In addition, we provide theoretical and numerical evidence that QML models exhibit further trainability issues not present in VQAs, arising from the use of a training dataset. We refer to these as dataset-induced barren plateaus. These results are most relevant when dealing with classical data, as here the choice of embedding scheme (i.e., the map between classical data and quantum states) can greatly affect the gradient scaling.
Quantum machine learning (QML) is rapidly transitioning from theoretical promise to practical relevance across data-intensive scientific domains. In this Review, we provide a structured overview of recent advances that bridge foundational quantum learning principles with real-world applications. We survey foundational QML paradigms, including variational quantum algorithms, quantum kernel methods, and neural-network quantum states, with emphasis on their applicability to complex quantum systems. We examine neural-network quantum states as expressive variational models for correlated matter, non-equilibrium dynamics, and open quantum systems, and discuss fundamental challenges associated with training and sampling. Recent advances in quantum-enhanced sampling and diagnostics of learning dynamics, including information-theoretic tools, are reviewed as mechanisms for improving scalability and trainability. The Review further highlights application-driven QML frameworks in drug discovery, cancer biology, and agro-climate modeling, where data complexity and constraints motivate hybrid quantum-classical approaches. We conclude with a discussion of federated quantum machine learning as a route to distributed, privacy-preserving quantum intelligence. Overall, this Review presents a unified perspective on the opportunities and limitations of QML for complex systems.