Deterministic quantum computation with one qubit (DQC1) is of significant theoretical and practical interest due to its computational advantages in certain problems, despite its subuniversality with limited quantum resources. In this work, we introduce parametrized DQC1 as a quantum machine learning model. We demonstrate that the gradient of the measurement outcome of a DQC1 circuit with respect to its gate parameters can be computed directly using the DQC1 protocol. This allows for gradient-based optimization of DQC1 circuits, positioning DQC1 as a quantum protocol for both training and inference. We then analyze the expressivity of the parametrized DQC1 circuits characterizing the set of learnable functions, and show that DQC1-based machine learning (ML) is as powerful as quantum neural networks based on universal computation. Our findings highlight the potential of DQC1 as a practical and versatile platform for ML, capable of rivaling more complex quantum computing models while utilizing simpler quantum resources.
Deterministic quantum computation with one qubit (DQC1) is of significant theoretical and practical interest due to its computational advantages in certain problems, despite its subuniversality with limited quantum resources. In this work, we introduce parametrized DQC1 as a quantum machine learning model. We demonstrate that the gradient of the measurement outcome of a DQC1 circuit with respect to its gate parameters can be computed directly using the DQC1 protocol. This allows for gradient-based optimization of DQC1 circuits, positioning DQC1 as a quantum protocol for both training and inference. We then analyze the expressivity of the parametrized DQC1 circuits characterizing the set of learnable functions, and show that DQC1-based machine learning (ML) is as powerful as quantum neural networks based on universal computation. Our findings highlight the potential of DQC1 as a practical and versatile platform for ML, capable of rivaling more complex quantum computing models while utilizing simpler quantum resources.
Quantum machine learning (QML) has gained significant interest by combining quantum computing and artificial intelligence, two topics that are expected to revolutionize the way of data processing. While gate-based quantum computing uses precisely defined unitary operations on qubits, currently available noisy intermediate-scale quantum (NISQ) devices are not ready for implementations of high-depth circuits. However, machine learning is one of the promising applications to be used on NISQ hardware via parameterized quantum circuits (PQCs). An alternative QML paradigm comes from a different direction: Quantum reservoir computing (QRC) relies on using physical systems as quantum artificial neural networks. Instead of using controlled gate operations, here the system dynamics are controlled by the underlying Hamiltonian, and the machine learning layer is performed at the output weights. Despite their distinct origin, both ML approaches are connected and can formally be mapped onto each other. We discuss this analogy by realizing a transverse-field Ising model on a gate-based quantum computing architecture establishing a fundamental connection on an abstract level between these two very different QML paradigms. This enables us to connect the known expressivity measure of PQC-QML with the quantification of expressiveness of physical dynamical systems.
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.
Kernel methods play an important role in machine learning applications due to their conceptual simplicity and superior performance on numerous machine learning tasks. Expressivity of a machine learning model, referring to the ability of the model to approximate complex functions, has a significant influence on its performance in these tasks. One approach to enhancing the expressivity of kernel machines is to combine multiple individual kernels to arrive at a more expressive combined kernel. This approach is referred to as multiple kernel learning (MKL). In this work, we propose an MKL method we refer to as quantum MKL, which combines multiple quantum kernels. Our method leverages the power of deterministic quantum computing with one qubit (DQC1) to estimate the combined kernel for a set of classically intractable individual quantum kernels. The combined kernel estimation is achieved without explicitly computing each individual kernel, while still allowing for the tuning of individual kernels in order to achieve better expressivity. Our simulations on two binary classification problems---one performed on a synthetic dataset and the other on a German credit dataset---demonstrate the superiority of the quantum MKL method over single quantum kernel machines.
The rapid progress in quantum computing (QC) and machine learning (ML) has attracted growing attention, prompting extensive research into quantum machine learning (QML) algorithms to solve diverse and complex problems. Designing high-performance QML models demands expert-level proficiency, which remains a significant obstacle to the broader adoption of QML. A few major hurdles include crafting effective data encoding techniques and parameterized quantum circuits, both of which are crucial to the performance of QML models. Additionally, the measurement phase is frequently overlooked—most current QML models rely on pre-defined measurement protocols that often fail to account for the specific problem being addressed. We introduce a novel approach that makes the observable of the quantum system—specifically, the Hermitian matrix—learnable. Our method features an end-to-end differentiable learning framework, where the parameterized observable is trained alongside the ordinary quantum circuit parameters simultaneously. Using numerical simulations, we show that the proposed method can identify observables for variational quantum circuits that lead to improved outcomes, such as higher classification accuracy, thereby boosting the overall performance of QML models.
Quantum computing and machine learning (QML) have emerged as a revolutionary per approach to solve complex computational problems that classical systems are unable to. The use of superposition, entanglement, and quantum parallelism helps analyze data up to ten times faster than in a non-quantum manner, enhancing optimization, pattern identification, and computational efficiency. This paper studies the potential of quantum algorithms and machine learning in areas of categorization, grouping, and regression in banking, healthcare, cybersecurity, and scientific simulations. QML shines when it comes to generalizing low cost over high-dimensional data spaces. State-of-theart quantum-enhanced algorithms (QSVMs, VQCs, QBMs) yield better solutions to complex pattern recognition problems. Quantum-inspired neural networks accelerate deep learning architectures by optimizing gradient descent and decreasing training periods. The following research explores how QML enables a potentially computationally efficient solution to combinatorial optimization problems in the realms of logistics, cryptography, and artificial intelligence through quantum annealing and hybrid quantumclassical models. QML is still not able to deploy for the hardware limitations, noise sensitive nature, and quantum decoherence, despite promising results. The study underscores the importance of error correction procedures, as well as noise-resilient quantum circuits, and ultimately their scaling to full computers to reconcile theoretical promise with real-world application. It explores the ability of hybrid quantum-classical models to provide near-term developed applications as a bridge to realizable quantum computation. In this article, researchers present a thorough overview of quantum algorithms, reduced computational complexity, and practical applications, furthering the field of quantumenhanced machine learning. Industries might be revolutionized with quantum computers and AI-based decision-making systems working together with unprecedented computational power. In particular, quantum algorithms, hardware, and quantum cloud computing platforms must be a research focus area to ensure that quantum will deliver the most significant advances in AI.
Recent advances in Quantum Machine Learning (QML) bring together Quantum Computing and Machine Learning with the aim of enhancing the advantages of Machine Learning to solve problems efficiently. The properties of quantum systems (superposition, entanglement, etc.) to represent multiple states of information at once, QML can potentially offer significant advantages when solving complex high-dimensional (multidimensional) computational problems. This paper reviews the current state-of-art regarding QML in general through an organized compilation and assessment of selected studies recently published in scientific literature that were found via large electronic library catalogs based on peer-reviewed sources according to algorithms used, optimization approaches employed, and areas of applied study. This review provides comparative analyses of each selected studies for purposes of identifying major trends in QML research/practice as well as opportunities for methodological improvements and challenges still existing within QML. Finally, this review presents an overview of Quantum Computing and Quantum Data Encoding Principles utilized to translate Classical Data into Quantum States as a high-level evaluation of several popular Quantum Learning Algorithms (e.g., Quantum Neural Networks, Quantum Support Machines, and Variational Quantum Circuit). The survey describes the optimization strategies such as gradient based techniques, Bayesian Optimization and evolutionary techniques being used to improve the stability of the quantum machine learning (QML) training process. Then, it provides examples of application areas for such QML, where healthcare analytics, environmental modelling, manufacturing optimization and analysis of biologic data are included. The comparative review of the recent academic research has identified several limitations and challenges regarding the use of QML that researchers. Although QML is believed to be capable of solving complex computational problems, issues such as noise in hardware, limited numbers of qubits and scalability present significant challenges for researchers working with this type of machine learning application. Overall, it appears that this survey provides a broad overview of contemporary developments and future trends for developing high-performance quantum learning systems.