Quantum machine learning (QML) is often listed as a promising candidate for useful applications of quantum computers, in part due to numerous proofs of possible quantum advantages. A central question is how small a role quantum computers can play while still enabling provable learning advantages over classical methods. We study an especially restricted setting in which a quantum computer is used only as a feature extractor: it acts independently on individual data points, without access to labels or global dataset information, is available only to augment the training set, and is not available at deployment. Training and deployment are therefore carried out by fully classical learners on a dataset augmented with quantum-generated features. We formalize this model by adapting the classical framework of Learning Under Privileged Information (LUPI) to the quantum case, which we call Learning Under Quantum Privileged Information (LUQPI). Within this framework, we show that even such minimally involved quantum feature extraction, available only during training, can yield exponential quantum-classical separations for suitable concept classes and data distributions under reasonable computational assumptions. We further situate LUQPI within a taxonomy of related quantum and classical learning settings and show how standard classical machinery, most notably the SVM+ algorithm, can exploit quantum-augmented data. Finally, we present numerical experiments in a physically motivated many-body setting, where privileged quantum features are expectation values of observables on ground states, and observe consistent performance gains for LUQPI-style models over strong classical baselines.
Quantum machine learning (QML) is often listed as a promising candidate for useful applications of quantum computers, in part due to numerous proofs of possible quantum advantages. A central question is how small a role quantum computers can play while still enabling provable learning advantages over classical methods. We study an especially restricted setting in which a quantum computer is used only as a feature extractor: it acts independently on individual data points, without access to labels or global dataset information, is available only to augment the training set, and is not available at deployment. Training and deployment are therefore carried out by fully classical learners on a dataset augmented with quantum-generated features. We formalize this model by adapting the classical framework of Learning Under Privileged Information (LUPI) to the quantum case, which we call Learning Under Quantum Privileged Information (LUQPI). Within this framework, we show that even such minimally involved quantum feature extraction, available only during training, can yield exponential quantum-classical separations for suitable concept classes and data distributions under reasonable computational assumptions. We further situate LUQPI within a taxonomy of related quantum and classical learning settings and show how standard classical machinery, most notably the SVM+ algorithm, can exploit quantum-augmented data. Finally, we present numerical experiments in a physically motivated many-body setting, where privileged quantum features are expectation values of observables on ground states, and observe consistent performance gains for LUQPI-style models over strong classical baselines.
Quantum machine learning is often highlighted as one of the most promising practical applications for which quantum computers could provide a computational advantage. However, a major obstacle to the widespread use of quantum machine learning models in practice is that these models, even once trained, still require access to a quantum computer in order to be evaluated on new data. To solve this issue, we introduce a class of quantum models where quantum resources are only required during training, while the deployment of the trained model is classical. Specifically, the training phase of our models ends with the generation of a 'shadow model' from which the classical deployment becomes possible. We prove that: (i) this class of models is universal for classically-deployed quantum machine learning; (ii) it does have restricted learning capacities compared to 'fully quantum' models, but nonetheless (iii) it achieves a provable learning advantage over fully classical learners, contingent on widely believed assumptions in complexity theory. These results provide compelling evidence that quantum machine learning can confer learning advantages across a substantially broader range of scenarios, where quantum computers are exclusively employed during the training phase. By enabling classical deployment, our approach facilitates the implementation of quantum machine learning models in various practical contexts.
Quantum machine learning is often highlighted as one of the most promising practical applications for which quantum computers could provide a computational advantage. However, a major obstacle to the widespread use of quantum machine learning models in practice is that these models, even once trained, still require access to a quantum computer in order to be evaluated on new data. To solve this issue, we introduce a new class of quantum models where quantum resources are only required during training, while the deployment of the trained model is classical. Specifically, the training phase of our models ends with the generation of a 'shadow model' from which the classical deployment becomes possible. We prove that: i) this class of models is universal for classically-deployed quantum machine learning; ii) it does have restricted learning capacities compared to 'fully quantum' models, but nonetheless iii) it achieves a provable learning advantage over fully classical learners, contingent on widely-believed assumptions in complexity theory. These results provide compelling evidence that quantum machine learning can confer learning advantages across a substantially broader range of scenarios, where quantum computers are exclusively employed during the training phase. By enabling classical deployment, our approach facilitates the implementation of quantum machine learning models in various practical contexts.
Quantum machine learning, as an extension of classical machine learning that harnesses quantum mechanics, facilitates effiient learning from data encoded in quantum states. Training a quantum neural network typically demands a substantial labeled training set for supervised learning. Human annotators, often experts, provide labels for samples through additional experiments, adding to the training cost. To mitigate this expense, there is a quest for methods that maintain model performance over fully labeled datasets while requiring fewer labeled samples in practice, thereby extending few-shot learning to the quantum realm. Quantum active learning estimates the uncertainty of quantum data to select the most informative samples from a pool for labeling. Consequently, a QML model is supposed to accumulate maximal knowledge as the training set comprises labeled samples selected via sampling strategies. Notably, the QML models trained within the QAL framework are not restricted to specific types, enabling performance enhancement from the model architecture's perspective towards few-shot learning. Recognizing symmetry as a fundamental concept in physics ubiquitous across various domains, we leverage the symmetry inherent in quantum states induced by the embedding of classical data for model design. We employ an equivariant QNN capable of generalizing from fewer data with geometric priors. We benchmark the performance of QAL on two classification problems, observing both positive and negative results. QAL effectively trains the model, achieving performance comparable to that on fully labeled datasets by labeling less than 7\% of the samples in the pool with unbiased sampling behavior. Furthermore, we elucidate the negative result of QAL being overtaken by random sampling baseline through miscellaneous numerical experiments. (character count limit, see the main text)
Abstract - The exponential growth of large-scale data has created significant challenges in storage, processing, and optimization that classical computing systems struggle to address efficiently. Quantum Machine Learning (QML) has emerged as a promising paradigm that integrates quantum computing concepts with machine learning techniques to tackle complex big data optimization problems. By utilizing quantum features such as superposition, entanglement, and parallelism, QML algorithms can accelerate tasks like clustering, classification, and dimensionality reduction, which are traditionally computationally demanding. Recent advancements indicate strong potential for quantum-inspired optimization in fields including cybersecurity, financial portfolio management, Industry 4.0, and healthcare analytics. This paper provides a comprehensive survey of QML algorithms designed for big data optimization, examining their advantages, limitations, and application domains. Additionally, it discusses the performance trade-offs associated with hybrid quantum–classical frameworks and highlights future research directions aimed at creating secure, scalable, and resource-efficient quantum solutions for large-scale, data-driven decision-making. As data volumes continue to expand at extremely rapid rates, processing big data with traditional machine learning (ML) techniques has become increasingly challenging. ML models often struggle with issues related to computational power, efficient parameter tuning, accurate model selection, and maintaining high performance when dealing with massive datasets. Deep learning approaches—such as convolutional neural networks (CNNs)—demand substantial computational resources to train on large-scale supervised learning tasks. Moreover, the difficulty of training these networks grows significantly as the size and complexity of the datasets increase. In response to these limitations, Quantum Machine Learning (QML) has emerged as a promising research domain at the intersection of quantum computing and machine learning. Quantum computers operate fundamentally differently from classical systems, using the principles of quantum mechanics to encode and process information. As a result, quantum computational methods have the potential to address certain problems that are computationally intensive or infeasible for classical machines. Index Terms— Quantum Machine Learning (QML); Big Data Optimization; Quantum Algorithms; Hybrid Quantum-Classical Models; Quantum Computing; Data Analytics
Abstract Quantum computers are believed to bring computational advantages in simulating quantum many-body systems. However, recent works have shown that classical machine learning algorithms are able to predict numerous properties of quantum systems with classical data. Despite examples of learning tasks with provable quantum advantages being proposed, they all involve cryptographic functions and do not represent any physical scenarios encountered in laboratory settings. In this paper, we prove quantum advantages for the physically relevant task of learning quantum observables from classical (measured-out) data. We consider two types of observables: first, we prove a learning advantage for linear combinations of Pauli strings, then we extend our results to a broader case of unitarily parametrized observables. For each case, we delineate sharp boundaries separating physically relevant tasks that admit efficient classical learning from those for which a quantum computer remains necessary for data analysis. Unlike previous works, our classical hardness results rely only on the weaker assumption that BQP B Q P hard processes cannot be simulated by polynomial-size classical circuits, and we also provide a nontrivial quantum learning algorithm. Our results clarify when quantum resources are useful for learning problems in quantum many-body physics, and suggest practical directions in which quantum learning improvements may emerge.
Quantum machine learning (QML) is a promising early use case for quantum computing. There has been progress in the last five years from theoretical studies and numerical simulations to proof of concepts. Use cases demonstrated on contemporary quantum devices include classifying medical images and items from the Iris dataset, classifying and generating handwritten images, toxicity screening, and learning a probability distribution. Potential benefits of QML include faster training and identification of feature maps not found classically. Although, these examples lack the scale for commercial exploitation, and it may be several years before QML algorithms replace the classical solutions, QML is an exciting area. This article is written for those who already have a sound knowledge of quantum computing and now wish to gain a basic overview of the terminology and some applications of classical machine learning ready to study quantum machine learning. The reader will already understand the relevant relevant linear algebra, including Hilbert spaces, a vector space with an inner product.