Abstract Quantum machine learning is an approach that aims to improve the performance of machine learning methods by leveraging the properties of quantum computers. Quantum circuit learning (QCL) is a supervised learning framework that can be implemented using variational quantum algorithms. The parameterized quantum circuits are used as models that transform input data into predictions, and one can naturally represent a quantum model as a Fourier series of the data. The process of encoding input data into quantum states has been widely discussed for its important role in the learning models. In particular, the properties of the eigenvalues of the Hamiltonian used for encoding significantly influence the number of accessible Fourier components. Recent encoding methods have demonstrated that the number of accessible Fourier components can be enhanced by applying exponentially large magnetic fields proportional to the number of qubits. However, this approach poses a challenge as it requires exponentially increasing magnetic fields, which are impractical for implementation in large-scale systems. Here, we propose a QCL method that leverages a non-integrable Hamiltonian for encoding, aiming to achieve both practical feasibility and a large number of accessible Fourier components. We find that the thermalization properties of non-integrable systems over long timescales, implying that the energy difference has a low probability to be degenerate, lead to an exponentially large number of accessible Fourier components. Since the required magnetic field strength remains within a practical range, our approach to using the non-integrable system is suitable for intermediate-scale quantum computers. Our results bridge the dynamics of non-integrable systems and the field of quantum machine learning, suggesting the potential for significant interdisciplinary contributions.
Abstract Quantum machine learning is an approach that aims to improve the performance of machine learning methods by leveraging the properties of quantum computers. Quantum circuit learning (QCL) is a supervised learning framework that can be implemented using variational quantum algorithms. The parameterized quantum circuits are used as models that transform input data into predictions, and one can naturally represent a quantum model as a Fourier series of the data. The process of encoding input data into quantum states has been widely discussed for its important role in the learning models. In particular, the properties of the eigenvalues of the Hamiltonian used for encoding significantly influence the number of accessible Fourier components. Recent encoding methods have demonstrated that the number of accessible Fourier components can be enhanced by applying exponentially large magnetic fields proportional to the number of qubits. However, this approach poses a challenge as it requires exponentially increasing magnetic fields, which are impractical for implementation in large-scale systems. Here, we propose a QCL method that leverages a non-integrable Hamiltonian for encoding, aiming to achieve both practical feasibility and a large number of accessible Fourier components. We find that the thermalization properties of non-integrable systems over long timescales, implying that the energy difference has a low probability to be degenerate, lead to an exponentially large number of accessible Fourier components. Since the required magnetic field strength remains within a practical range, our approach to using the non-integrable system is suitable for intermediate-scale quantum computers. Our results bridge the dynamics of non-integrable systems and the field of quantum machine learning, suggesting the potential for significant interdisciplinary contributions.
Quantum machine learning is an approach that aims to improve the performance of machine learning methods by leveraging the properties of quantum computers. In quantum circuit learning (QCL), a supervised learning method that can be implemented using variational quantum algorithms (VQAs), the process of encoding input data into quantum states has been widely discussed for its important role on the expressive power of learning models. In particular, the properties of the eigenvalues of the Hamiltonian used for encoding significantly influence model performance. Recent encoding methods have demonstrated that the expressive power of learning models can be enhanced by applying exponentially large magnetic fields proportional to the number of qubits. However, this approach poses a challenge as it requires exponentially increasing magnetic fields, which are impractical for implementation in large-scale systems. Here, we propose a QCL method that leverages a non-integrable Hamiltonian for encoding, aiming to achieve both enhanced expressive power and practical feasibility. We find that the thermalization properties of non-integrable systems over long timescales, implying that the energy difference has a low probability to be degenerate, lead to an enhanced expressive power for QCL. Since the required magnetic field strength remains within a practical range, our approach to using the non-integrable system is suitable for large-scale quantum computers. Our results bridge the dynamics of non-integrable systems and the field of quantum machine learning, suggesting the potential for significant interdisciplinary contributions.
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.
When parametrized quantum circuits are viewed as models that translate data inputs into predictions, quantum computers can be utilized for supervised learning. Many crucial theoretical aspects of these models remain unknown, even though considerable work has been done to understand the practical consequences of this method. Quantum models can access richer and richer frequency spectra by repeatedly repeating straightforward data-encoding gates. Since simulation time increases exponentially, simulation-based training cannot be used to big QML models. Variational quantum algorithms and quantum GAN are expected to give the best results if applied for different health care applications in microseconds. The present work explains how QML can be applied for variational quantum eigen solving. This paper also explains quantum Fourier transform analysis.
Many applications of quantum computing in the near term rely on variational quantum circuits (VQCs). They have been showcased as a promising model for reaching a quantum advantage in machine learning with current noisy intermediate scale quantum computers (NISQ). It is often believed that the power of VQCs relies on their exponentially large feature space, and extensive works have explored the expressiveness and trainability of VQCs in that regard. In our work, we propose a classical sampling method that may closely approximate a VQC with Hamiltonian encoding, given only the description of its architecture. It uses the seminal proposal of Random Fourier Features (RFF) and the fact that VQCs can be seen as large Fourier series. We provide general theoretical bounds for classically approximating models built from exponentially large quantum feature space by sampling a few frequencies to build an equivalent low dimensional kernel, and we show experimentally that this approximation is efficient for several encoding strategies. Precisely, we show that the number of required samples grows favorably with the size of the quantum spectrum. This tool therefore questions the hope for quantum advantage from VQCs in many cases, but conversely helps to narrow the conditions for their potential success. We expect VQCs with various and complex encoding Hamiltonians, or with large input dimension, to become more robust to classical approximations.
The rapid advancements in quantum computing (QC) and machine learning (ML) have sparked significant interest, driving extensive exploration of quantum machine learning (QML) algorithms to address a wide range of complex challenges. The development of high-performance QML models requires expert-level expertise, presenting a key challenge to the widespread adoption of QML. Critical obstacles include the design of effective data encoding strategies and parameterized quantum circuits, both of which are vital for the performance of QML models. Furthermore, the measurement process is often neglected-most existing QML models employ predefined measurement schemes that may not align with the specific requirements of the targeted problem. We propose an innovative framework that renders the observable of a quantum system-specifically, the Hermitian matrix-trainable. This approach employs an end-to-end differentiable learning framework, enabling simultaneous optimization of the neural network used to program the parameterized observables and the standard quantum circuit parameters. Notably, the quantum observable parameters are dynamically programmed by the neural network, allowing the observables to adapt in real time based on the input data stream. Through numerical simulations, we demonstrate that the proposed method effectively programs observables dynamically within variational quantum circuits, achieving superior results compared to existing approaches. Notably, it delivers enhanced performance metrics, such as higher classification accuracy, thereby significantly improving the overall effectiveness of QML models.
Recent advancements in quantum computing (QC) and machine learning (ML) have garnered significant attention, leading to substantial efforts toward the development of quantum machine learning (QML) algorithms to address a variety of complex challenges. The design of high-performance QML models, however, requires expert-level knowledge, posing a significant barrier to the widespread adoption of QML. Key challenges include the design of data encoding mechanisms and parameterized quantum circuits, both of which critically impact the generalization capabilities of QML models. We propose a novel method that encodes quantum circuit architecture information to enable the evolution of quantum circuit designs. In this approach, the fitness function is based on the effective dimension, allowing for the optimization of quantum circuits towards higher model capacity. Through numerical simulations, we demonstrate that the proposed method is capable of discovering variational quantum circuit architectures that offer improved learning capabilities, thereby enhancing the overall performance of QML models for complex tasks.