Quantum machine learning (QML) aims to leverage the principles of quantum mechanics to speed up the process of solving machine learning problems or improve the quality of solutions. In supervised learning, training samples that are entangled with an auxiliary system were shown to reduce the approximation error of the trained model. However, also the training process is affected by various properties of the supervised learning task, including the model's circuit structure, the used cost function, and noise on the quantum computer. To evaluate the applicability of entanglement in supervised learning, the effect of highly entangled training data on the trainability is investigated in this work. This study shows that for highly expressive models, i.e., models capable of expressing a large number of candidate solutions, the possible improvement of loss function values in constrained neighborhoods during optimization is severely limited when maximally entangled states are used. Furthermore, this finding is experimentally supported by simulating training with Parameterized Quantum Circuits (PQCs). As the expressivity of the PQC increases, this training process becomes more susceptible to loss concentration induced by entangled training data. Lastly, for non‐maximally entangled states, the experiments highlight the fundamental role of entanglement entropy as a predictor for the trainability.
Quantum machine learning (QML) aims to leverage the principles of quantum mechanics to speed up the process of solving machine learning problems or improve the quality of solutions. In supervised learning, training samples that are entangled with an auxiliary system were shown to reduce the approximation error of the trained model. However, also the training process is affected by various properties of the supervised learning task, including the model's circuit structure, the used cost function, and noise on the quantum computer. To evaluate the applicability of entanglement in supervised learning, the effect of highly entangled training data on the trainability is investigated in this work. This study shows that for highly expressive models, i.e., models capable of expressing a large number of candidate solutions, the possible improvement of loss function values in constrained neighborhoods during optimization is severely limited when maximally entangled states are used. Furthermore, this finding is experimentally supported by simulating training with Parameterized Quantum Circuits (PQCs). As the expressivity of the PQC increases, this training process becomes more susceptible to loss concentration induced by entangled training data. Lastly, for non‐maximally entangled states, the experiments highlight the fundamental role of entanglement entropy as a predictor for the trainability.
ABSTRACT Quantum machine learning (QML) aims to leverage the principles of quantum mechanics to speed up the process of solving machine learning problems or improve the quality of solutions. In supervised learning, training samples that are entangled with an auxiliary system were shown to reduce the approximation error of the trained model. However, also the training process is affected by various properties of the supervised learning task, including the model's circuit structure, the used cost function, and noise on the quantum computer. To evaluate the applicability of entanglement in supervised learning, the effect of highly entangled training data on the trainability is investigated in this work. This study shows that for highly expressive models, i.e., models capable of expressing a large number of candidate solutions, the possible improvement of loss function values in constrained neighborhoods during optimization is severely limited when maximally entangled states are used. Furthermore, this finding is experimentally supported by simulating training with Parameterized Quantum Circuits (PQCs). As the expressivity of the PQC increases, this training process becomes more susceptible to loss concentration induced by entangled training data. Lastly, for non‐maximally entangled states, the experiments highlight the fundamental role of entanglement entropy as a predictor for the trainability.
Quantum Machine Learning (QML) is an emerging interdisciplinary field that combines the principles of quantum mechanics and machine learning to develop algorithms that can potentially outperform classical algorithms in certain tasks. QML leverages the unique properties of quantum systems, such as superposition and entanglement, to process information in ways that are not possible with classical computers. This paper provides a comprehensive overview of QML, including its principles, algorithms, and applications. We focus particularly on supervised learning methods, which involve training a quantum model on labeled data to make predictions on new, unseen data. We discuss the potential of QML to revolutionize various domains, such as finance, chemistry, and materials science, and highlight the challenges associated with the development and implementation of QML algorithms, including the need for more advanced quantum hardware and software. This paper aims to provide a clear understanding of the current state of QML research and its potential impact on future computational capabilities.
Quantum Machine Learning (QML) is an emerging interdisciplinary field that combines the principles of quantum mechanics and machine learning to develop algorithms that can potentially outperform classical algorithms in certain tasks. QML leverages the unique properties of quantum systems, such as superposition and entanglement, to process information in ways that are not possible with classical computers. This paper provides a comprehensive overview of QML, including its principles, algorithms, and applications. We focus particularly on supervised learning methods, which involve training a quantum model on labeled data to make predictions on new, unseen data. We discuss the potential of QML to revolutionize various domains, such as finance, chemistry, and materials science, and highlight the challenges associated with the development and implementation of QML algorithms, including the need for more advanced quantum hardware and software. This paper aims to provide a clear understanding of the current state of QML research and its potential impact on future computational capabilities.
Quantum Machine Learning (QML) is an emerging field that explores the potential of quantum computing to revolutionize various computational tasks. This paper introduces a novel quantum machine learning framework leveraging adaptive loss functions to optimize quantum model parameters, ultimately aiming to improve model performance and reduce computational costs. The core mechanism involves dynamically adjusting the loss weight based on the model's error during training, providing a more sophisticated and adaptable approach compared to traditional, fixed loss functions. We analyze the benefits of this approach across different quantum model architectures and demonstrate its effectiveness through simulations and preliminary experiments. The paper concludes with a discussion of future research directions, focusing on expanding the applicability of this adaptive loss function to diverse quantum machine learning applications.
Quantum entanglement is a key resource for achieving superiority of quantum computing.Currently, scientists are extensively focusing on how to integrate quantum entanglement into various components of quantum machine learning (QML) models, aiming to surpass the performance of traditional machine learning models.Notable successes include the use of entangled measurements [1][2][3] and entangled channels [4] , which have been shown to reduce query complexity or improve the prediction precision for specified QML tasks.Quantum entangled data, capable of encoding more information compared to classical data of the same size, is recognized for its potential to achieve quantum advantages.Nevertheless, the impact of the entanglement degree in quantum data on model performance remains a challenging and unresolved research question.Recently, Wang and collaborators [5] (Nat Commun 2024, 15, 3716) rigorously analyzed the impact of the entanglement degree of quantum data, the number and type of measurements, and the size of training dataset on the prediction error of QML models by establishing the quantum no-free-lunch (NFL) theorem.They consider tasks of quantum dynamics learning with entangled data, which is fundamental to many advanced quantum algorithms, as illustrated in Fig. 1.While conventional understanding suggests that entanglement mainly confers benefits to QML in terms of sample complexity [6,7] , this study demonstrates that the effect of the degree of entanglement on prediction error exhibits a dual effect, that is, whether quantum entanglement improves performance depends on the number of measurements allowed.With a sufficient number of measurements, increasing the entanglement degree in quan-
Machine learning is widely regarded as a promising application in which quantum computing could offer a computational advantage. However, general quantum machine learning models with provable guarantees on performance, trainability, and efficient inference remain limited. In this work, we introduce quantum Hamiltonian embeddings, a supervised learning framework in which a classical training dataset is encoded into a single effective, parameterized Hamiltonian. Training optimizes the parameters of this data-dependent Hamiltonian, whose approximate ground state defines the classification rule. Once the ground state has been approximated using a quantum algorithm, inference can be performed either classically using a classical representation of the learned state, or with a quantum representation of the state. We establish efficient methods for gradient estimation and prove favorable generalization guarantees. Furthermore, under standard cryptographic assumptions, we show that Hamiltonian embeddings can realize hypothesis functions beyond the reach of efficient classical algorithms. We then demonstrate the framework at scale on IBM Heron processors using a standard benchmark dataset. Together, these results establish Hamiltonian embeddings as a new framework for quantum machine learning, combining theoretical guarantees with a path for experimental investigations at scale on quantum hardware.