Quantum Machine Learning Research Articles

Comparison of the performance of classical and quantum machine‐learning methods on the detection of sugar beet Cercospora leaf disease

AbstractImage processing and machine‐learning (ML) techniques are essential for the detection of diseases and pests in plants. This study explored the application of quantum ML (QML) algorithms for the early detection of Cercospora beticola leaf disease in sugar beet, which causes significant impact on global sugar production. Using a dataset of 1065 images (739 diseased and 326 healthy), we extracted 70 ML statistical features, including 10 from the grey‐level co‐occurrence matrix (GLCM) and 60 colour‐related features. Performance evaluations of classical ML algorithms, such as random forest (RF; 91.95% accuracy) and extreme gradient boosting (91.95% accuracy), demonstrated strong results compared to quantum approaches. Notably, the quantum support vector classifier (QSVC) achieved an accuracy of 85% with perfect recall of 1.00, while the variational quantum classifier (VQC) recorded an accuracy of 88.73%. Dimensionality reduction via principal component analysis reduced features from 70 to 5, enabling effective classification with competitive results: ML (RF) 91.41%, VQC with limited‐memory Broyden–Fletcher–Goldfarb–Shanno with box constraints (L_BFGS_B) 88.73% and QSVC 85%. These findings highlight the potential of QML algorithms in improving agricultural disease identification and aiding in the advancement of more efficient, sustainable farming techniques.

The role of data embedding in equivariant quantum convolutional neural networks

AbstractGeometric deep learning refers to the scenario in which the symmetries of a dataset are used to constrain the parameter space of a neural network and thus, improve their trainability and generalization. Recently, this idea has been incorporated into the field of quantum machine learning, which has given rise to equivariant quantum neural networks (EQNNs). In this work, we investigate the role of classical-to-quantum embedding on the performance of equivariant quantum convolutional neural networks (EQCNNs) for the classification of images. We discuss the connection between the data embedding method and the resulting representation of a symmetry group and analyze how changing representation affects the expressibility of an EQCNN. We numerically compare the classification accuracy of EQCNNs with three different basis-permuted amplitude embeddings to the one obtained from a non-equivariant quantum convolutional neural network (QCNN). Our results show a clear dependence of classification accuracy on the underlying embedding, especially for initial training iterations. The improvement in classification accuracy of EQCNN over non-equivariant QCNN may be present or absent depending on the particular embedding and dataset used. The noisy simulation using simple noise models shows that certain EQCNNs are more robust to noise than non-equivariant QCNNs. It is expected that the results of this work can be useful to the community for a better understanding of the importance of data embedding choice in the context of geometric quantum machine learning.

Sarcopenia risk prediction and feature selection by using quantum machine learning algorithms

Sarcopenia risk prediction and feature selection by using quantum machine learning algorithms

Retraction Note: E-healthcare application cyber security analysis using quantum machine learning in malicious user detection

Retraction Note: E-healthcare application cyber security analysis using quantum machine learning in malicious user detection

Retraction Note: Early steroid detection in athlete players using quantum photonics and machine learning model based analysis

Retraction Note: Early steroid detection in athlete players using quantum photonics and machine learning model based analysis

What we can do with one qubit in quantum machine learning: ten classical machine learning problems that can be solved with a single qubit

What we can do with one qubit in quantum machine learning: ten classical machine learning problems that can be solved with a single qubit

Quantum machine learning enhanced laser speckle analysis for precise speed prediction.

Laser speckle contrast imaging (LSCI) is an optical technique used to assess blood flow perfusion by modeling changes in speckle intensity, but it is generally limited to qualitative analysis due to difficulties in absolute quantification. Three-dimensional convolutional neural networks (3D CNNs) enhance the quantitative performance of LSCI by excelling at extracting spatiotemporal features from speckle data. However, excessive downsampling techniques can lead to significant information loss. To address this, we propose a hybrid quantum-classical 3D CNN framework that leverages variational quantum algorithms (VQAs) to enhance the performance of classical models. The proposed framework employs variational quantum circuits (VQCs) to replace the 3D global pooling layer, enabling the model to utilize the complete 3D information extracted by the convolutional layers for feature integration, thereby enhancing velocity prediction performance. We perform cross-validation on experimental LSCI speckle data and demonstrate the superiority of the hybrid models over their classical counterparts in terms of prediction accuracy and learning stability. Furthermore, we evaluate the models on an unseen test set and observe that the hybrid models outperform the classical models with up to 14.8% improvement in mean squared error (MSE) and up to 26.1% improvement in mean absolute percentage error (MAPE) evaluation metrics. Finally, our qualitative analysis shows that the hybrid models offer substantial improvements over classical models in predicting blood flow at both low and high velocities. These results indicate that the hybrid models possess more powerful learning and generalization capabilities.

Near-optimal quantum kernel principal component analysis

Abstract Kernel principal component analysis (kernel PCA) is a nonlinear dimensionality reduction technique that employs kernel functions to map data into a high-dimensional feature space, thereby extending the applicability of linear PCA to nonlinear data and facilitating the extraction of informative principal components. However, kernel PCA necessitates the manipulation of large-scale matrices, leading to high computational complexity and posing challenges for efficient implementation in big data environments. Quantum computing has recently been integrated with kernel methods in machine learning, enabling effective analysis of input data within intractable feature spaces. Although existing quantum kernel PCA proposals promise exponential speedups, they impose stringent requirements on quantum hardware that are challenging to fulfill. In this work, we propose a quantum algorithm for kernel PCA by establishing a connection between quantum kernel methods and block encoding, thereby diagonalizing the centralized kernel matrix on a quantum computer. The query complexity is logarithmic with respect to the size of the data vector, $D$, and linear with respect to the size of the dataset. An exponential speedup could be achieved when the dataset consists of a few high-dimensional vectors, wherein the dataset size is polynomial in $\log(D)$, with $D$ being significantly large. In contrast to existing work, our algorithm enhances the efficiency of quantum kernel PCA and reduces the requirements for quantum hardware. Furthermore, we have also demonstrated that the algorithm based on block encoding matches the lower bound of query complexity, indicating that our algorithm is nearly optimal. Our research has laid down new pathways for developing quantum machine learning algorithms aimed at addressing tangible real-world problems and demonstrating quantum advantages within machine learning.

Machine Learning and AI Innovations with Python: Trends and Future Directions

This comprehensive article examines the current state and future directions of machine learning and artificial intelligence innovations using Python. It provides an in-depth analysis of recent advancements in popular Python-based libraries such as TensorFlow, PyTorch, and scikit-learn, highlighting key features and performance improvements. The article explores emerging machine learning techniques, including federated learning, few-shot learning, and explainable AI, discussing their principles, Python implementations, and real-world applications. Furthermore, the article investigates future trends in AI development with Python, considering potential technological advancements, new libraries and frameworks, and emerging research areas such as quantum machine learning and neurosymbolic AI. It also addresses the challenges and opportunities facing Python in the evolving landscape of AI, including performance optimization, ethical considerations, and the increasing demand for production-ready AI solutions. By synthesizing current developments and future prospects, this article offers valuable insights for researchers, developers, and organizations seeking to leverage Python's capabilities in the rapidly advancing field of artificial intelligence and machine learning.

Quantum intrusion detection system using outlier analysis

In the field of cybersecurity, hackers often enter computer systems despite current security measures, owing to the huge amount of network traffic that makes intruder identification difficult. Differentiating between authorized traffic and abnormal data produced by Distributed Denial of Service (DDoS) attackers is still a major difficulty. This research provides a unique technique that uses Quantum Machine Learning (QML) to improve security protocols for secure communication between two parties. Our strategy enhances detection accuracy and speed by using the characteristics of quantum neural networks. The approach includes creating a dataset from network traffic patterns, preprocessing it, and then turning it into quantum bits via angle embedding. The research uses outlier analysis, min-entropy, and quantum state fidelity to distinguish between normal and abnormal data patterns. The dispersed randomness of network header data is measured using entropy, which aids in identifying security concerns. The suggested QML-based methodology outperforms conventional approaches and current models, including AMM-CNN and ANN models, with a detection accuracy of 99.87% for DDoS attacks. This advancement leads to more effective and secure communication networks.

Benchmarking Digital Quantum Simulations Above Hundreds of Qubits Using Quantum Critical Dynamics

The real-time simulation of large many-body quantum systems is a formidable task, that may only be achievable with a genuine quantum computational platform. Currently, quantum hardware with a number of qubits sufficient to make classical emulation challenging is available. This condition is necessary for the pursuit of a so-called quantum advantage, but it also makes verifying the results very difficult. In this paper, we flip the perspective and utilize known theoretical results about many-body quantum critical dynamics to qualitatively benchmark digital quantum hardware and various error mitigation techniques. In particular, we benchmark against known universal scaling laws in the Hamiltonian simulation of a time-dependent transverse-field Ising Hamiltonian of up to 133 qubits. Incorporating only basic error mitigation and suppression methods, our study shows reliable control up to a two-qubit gate depth of 28, featuring a maximum of 1396 two-qubit gates, before noise becomes prevalent. These results are transferable to applications such as Hamiltonian simulation, variational algorithms, optimization, or quantum machine learning. We demonstrate this on the example of digitized quantum annealing for optimization and identify an optimal working point in terms of both circuit depth and time step on a 133-site optimization problem. Published by the American Physical Society 2024

Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologies

Much is understood about 1-dimensional spin chains in terms of entanglement properties, physical phases, and integrability. However, the Lie algebraic properties of the Hamiltonians describing these systems remain largely unexplored. In this work, we provide a classification of all Lie algebras generated by the terms of 2-local spin chain Hamiltonians, or so-called dynamical Lie algebras, on 1-dimensional linear and circular lattice structures. We find 17 unique dynamical Lie algebras. Our classification includes some well-known models such as the transverse-field Ising model and the Heisenberg chain, and we also find more exotic classes of Hamiltonians that appear new. In addition to the closed and open spin chains, we consider systems with a fully connected topology, which may be relevant for quantum machine learning approaches. We discuss the practical implications of our work in the context of variational quantum computing, quantum control and the spin chain literature.

Quantum machine learning with indefinite causal order

Quantum machine learning with indefinite causal order

Permutation-equivariant quantum convolutional neural networks

Abstract The Symmetric group $S_{n}$ manifests itself in large classes of quantum systems as the invariance of certain characteristics of a quantum state with respect to permuting the qubits. Subgroups of $S_{n}$ arise, among many other contexts, to describe label symmetry of classical images with respect to spatial transformations, such as reflection or rotation. Equipped with the formalism of geometric quantum machine learning, in this study we propose the architectures of equivariant quantum convolutional neural networks (EQCNNs) adherent to $S_{n}$ and its subgroups. We demonstrate that a careful choice of pixel-to-qubit embedding order can facilitate easy construction of EQCNNs for small subgroups of $S_{n}$. Our novel EQCNN architecture corresponding to the full permutation group $S_{n}$ is built by applying all possible QCNNs with equal probability, which can also be conceptualized as a dropout strategy in quantum neural networks. For subgroups of $S_{n}$, our numerical results using MNIST datasets show better classification accuracy than non-equivariant QCNNs. The $S_{n}$-equivariant QCNN architecture shows significantly improved training and test performance than non-equivariant QCNN for classification of connected and non-connected graphs. When trained with sufficiently large number of data, the $S_{n}$-equivariant QCNN shows better average performance compared to $S_{n}$-equivariant QNN . These results contribute towards building powerful quantum machine learning architectures in permutation-symmetric systems.

Quantum machine learning: Classifications, challenges, and solutions

Quantum machine learning: Classifications, challenges, and solutions

Prediction of chaotic dynamics and extreme events: A recurrence-free quantum reservoir computing approach

In chaotic dynamical systems, extreme events manifest in time series as unpredictable large-amplitude peaks. Although deterministic, extreme events appear seemingly randomly, which makes their forecasting difficult. By learning the dynamics from observables (data), reservoir computers can time accurately predict extreme events and chaotic dynamics, but they may require many degrees of freedom (large reservoirs). In this paper, by exploiting quantum-computer ansätze and entanglement, we design reservoir computers with compact reservoirs and accurate prediction capabilities. First, we propose the recurrence-free quantum reservoir computer (RF-QRC) architecture. By developing quantum feature maps and removing recurrent connections, the RF-QRC has quantum circuits with smaller depths. This allows the RF-QRC to scale well with higher-dimensional chaotic systems, which makes it suitable for hardware implementation. Second, we forecast the temporal chaotic dynamics and their long-term statistics of low- and higher-dimensional dynamical systems. We find that RF-QRC requires smaller reservoirs than classical reservoir computers for higher-dimensional systems and the same predictability. Third, we apply the RF-QRC to the time prediction of extreme events in a model of a turbulent shear flow with turbulent bursts. We find that the RF-QRC has longer predictability than the classical reservoir computer for extreme events forecasting. The results and analyses indicate that quantum-computer ansätze offers nonlinear expressivity and computational scalability, which are useful for forecasting chaotic dynamics and extreme events. This work opens new opportunities for using quantum machine learning on near-term quantum computers. Published by the American Physical Society 2024

Computation and Applications of Gaussian Integrals in Mathematics and Applied Sciences

Gaussian integrals, particularly those involving the function e−x2 , play a central role in various fields, ranging from physics to finance. This paper explores the computation of Gaussian integrals, beginning with the fundamental integral in the interval −∞ to ∞, which yields π . The author extends this analysis to integrals involving powers of x multiplied by e−x2 , showing their relevance in calculating moments in quantum mechanics and probability theory. Additionally, the author discusses the applications of multivariate Gaussian integrals in machine learning and statistical mechanics, where they are key to solving problems in high-dimensional spaces. Practical examples are provided from quantum mechanics (path integrals), statistical mechanics (partition functions), finance (option pricing models), and machine learning (Gaussian processes). Through these examples, the paper highlights the versatility and universality of Gaussian integrals as essential tools in both theoretical and applied contexts. The integral’s widespread applicability reflects its importance in connecting mathematical theory with real-world phenomena. This work highlights the role played by the Gaussian integral.

Quantum Machine Learning—Quo Vadis?

The book Quantum Machine Learning: What Quantum Computing Means to Data Mining, by Peter Wittek, made quantum machine learning popular to a wider audience. The promise of quantum machine learning for big data is that it will lead to new applications due to the exponential speed-up and the possibility of compressed data representation. However, can we really apply quantum machine learning for real-world applications? What are the advantages of quantum machine learning algorithms in addition to some proposed artificial problems? Is the promised exponential or quadratic speed-up realistic, assuming that real quantum computers exist? Quantum machine learning is based on statistical machine learning. We cannot port the classical algorithms directly into quantum algorithms due to quantum physical constraints, like the input–output problem or the normalized representation of vectors. Theoretical speed-ups of quantum machine learning are usually analyzed in the literature by ignoring the input destruction problem, which is the main bottleneck for data encoding. The dilemma results from the following question: should we ignore or marginalize those constraints or not?

Quantum Machine Learning: Exploring the Role of Data Encoding Techniques, Challenges, and Future Directions

Quantum computing and machine learning (ML) have received significant developments which have set the stage for the next frontier of creative work and usefulness. This paper aims at reviewing various data-encoding techniques in Quantum Machine Learning (QML) while highlighting their significance in transforming classical data into quantum systems. We analyze basis, amplitude, angle, and other high-level encodings in depth to demonstrate how various strategies affect encoding improvements in quantum algorithms. However, they identify major problems with encoding in the framework of QML, including scalability, computational burden, and noise. Future directions for research outline these challenges, aiming to enhance the excellence of encoding techniques in the constantly evolving quantum technology setting. This review shall enable the researcher to gain an enhanced understanding of data encoding in QML, and it also suggests solutions to the current limitations in this area.

A novel image classification framework based on variational quantum algorithms

Image classification is a crucial task in machine learning with widespread practical applications. The existing classical framework for image classification typically utilizes a global pooling operation at the end of the network to reduce computational complexity and mitigate overfitting. However, this operation often results in a significant loss of information, which can affect the performance of classification models. To overcome this limitation, we introduce a novel image classification framework that leverages variational quantum algorithms (VQAs) hybrid approaches combining quantum and classical computing paradigms within quantum machine learning. The major advantage of our framework is the elimination of the need for the global pooling operation at the end of the network. In this way, our approach preserves more discriminative features and fine-grained details in the images, which enhances classification performance. Additionally, employing VQAs enables our framework to have fewer parameters than the classical framework, even in the absence of global pooling, which makes it more advantageous in preventing overfitting. We apply our method to different state-of-the-art image classification models and demonstrate the superiority of the proposed quantum architecture over its classical counterpart through a series of state vector simulation experiments on public datasets. Our experiments show that the proposed quantum framework achieves up to a 9.21% increase in accuracy and up to a 15.79% improvement in F1 score, compared to the classical framework. Additionally, we explore the impact of shot noise on our method through shot-based simulation and find that increasing the number of measurements does not always lead to better results. Selecting an appropriate number of measurements can yield optimal results, even surpassing those obtained from state vector simulation.