Quantum Machine Learning Models Research Articles

Robust quantum federated learning with noise

Abstract Federated learning is a decentralized machine learning approach where multiple participants collaboratively train machine learning models. With the development of quantum computing, there has been significant potential in the integration of quantum computing and federated learning. However, existing research has demonstrated that, similar to classical federated learning models, quantum federated learning models also face various security threats and privacy leakage issues. This paper proposes a quantum federated learning model based on quantum noise. Adding quantum noise to the model not only addresses privacy leakage, but also enhances the model robustness, effectively resists adversarial attacks. Specifically, extensive numerical simulations are conducted using various datasets to evaluate the effectiveness of the proposed method. The results reveal a more pronounced variation in robust training in high-dimensional datasets compared to low-dimensional datasets. Furthermore, the impact of noise intensity on model robustness is explored. Experimental demonstrate that a small amount of quantum noise does not have a significant impact on accuracy, and as the noise increases, the robustness of the model also improves. Finally, three different types of quantum noise were used for robustness testing in the paper to analyze the impact of quantum noise on the robustness of quantum machine learning models. The abundant experimental results have verified that the noise can improve the security of distributed quantum machine learning.

Quantum support vector machines for classification and regression on a trapped-ion quantum computer

Quantum machine learning is a rapidly growing field at the intersection of quantum computing and machine learning. In this work, we examine our quantum machine learning models, which are based on quantum support vector classification (QSVC) and quantum support vector regression (QSVR). We investigate these models using a quantum circuit simulator, both with and without noise, as well as the IonQ Harmony quantum processor. For the QSVC tasks, we use a dataset containing fraudulent credit card transactions and image datasets (the MNIST and the Fashion-MNIST datasets); for the QSVR tasks, we use a financial dataset and a materials dataset. For the classification tasks, the performance of our QSVC models using 4 qubits of the trapped-ion quantum computer was comparable to that obtained from noiseless quantum circuit simulations. The result is consistent with the analysis of our device noise simulations with varying qubit gate error rates. For the regression tasks, applying a low-rank approximation to the noisy quantum kernel, in combination with hyperparameter tuning in ε-SVR, improved the performance of the QSVR models on the near-term quantum device. The alignment, as measured by the Frobenius inner product between the noiseless and noisy quantum kernels, can serve as an indicator of the relative prediction performance on noisy quantum devices in comparison with their ideal counterparts. Our results suggest that the quantum kernel, as described by our shallow quantum circuit, can be effectively used for both QSVC and QSVR tasks, indicating its resistance to noise and its adaptability to various datasets.

Automatic evolutionary design of quantum rule-based systems and applications to quantum reinforcement learning

Explainable artificial intelligence is a research topic whose relevance has increased in recent years, especially with the advent of large machine learning models. However, very few attempts have been proposed to improve interpretability in the case of quantum artificial intelligence, and many existing quantum machine learning models in the literature can be considered almost as black boxes. In this article, we argue that an appropriate semantic interpretation of a given quantum circuit that solves a problem can be of interest to the user not only to certify the correct behavior of the learned model, but also to obtain a deeper insight into the problem at hand and its solution. We focus on decision-making problems that can be formulated as classification tasks and propose a method for learning quantum rule-based systems to solve them using evolutionary optimization algorithms. The approach is tested to learn rules that solve control and decision-making tasks in reinforcement learning environments, to provide interpretable agent policies that help to understand the internal dynamics of an unknown environment. Our results conclude that the learned policies are not only highly explainable, but can also help detect non-relevant features of problems and produce a minimal set of rules.

A hybrid quantum ensemble learning model for malicious code detection

Quantum computing as a new computing model with parallel computing capability and high information carrying capacity, has attracted a lot of attention from researchers. Ensemble learning is an effective strategy often used in machine learning to improve the performance of weak classifiers. Currently, the classification performance of quantum classifiers is not satisfactory enough due to factors such as the depth of quantum circuit, quantum noise, and quantum coding method, etc. For this reason, this paper combined the ensemble learning idea and quantum classifiers to design a novel hybrid quantum machine learning model. Firstly, we run the Stacking method in classical machine learning to realize the dimensionality reduction of high-latitude data while ensuring the validity of data features. Secondly, we used the Bagging method and Bayesian hyperparameter optimization method applied to quantum support vector machine (QSVM), quantum K nearest neighbors (QKNN), variational quantum classifier (VQC). Thirdly, the voting method is used to ensemble the predict results of QSVM, QKNN, VQC as the final result. We applied the hybrid quantum ensemble machine learning model to malicious code detection. The experimental results show that the classification precision (accuracy, F1-score) of this model has been improved to 98.9% (94.5%, 94.24%). Combined with the acceleration of quantum computing and the higher precision rate, it can effectively deal with the growing trend of malicious codes, which is of great significance to cyberspace security.

Transition role of entangled data in quantum machine learning

Entanglement serves as the resource to empower quantum computing. Recent progress has highlighted its positive impact on learning quantum dynamics, wherein the integration of entanglement into quantum operations or measurements of quantum machine learning (QML) models leads to substantial reductions in training data size, surpassing a specified prediction error threshold. However, an analytical understanding of how the entanglement degree in data affects model performance remains elusive. In this study, we address this knowledge gap by establishing a quantum no-free-lunch (NFL) theorem for learning quantum dynamics using entangled data. Contrary to previous findings, we prove that the impact of entangled data on prediction error exhibits a dual effect, depending on the number of permitted measurements. With a sufficient number of measurements, increasing the entanglement of training data consistently reduces the prediction error or decreases the required size of the training data to achieve the same prediction error. Conversely, when few measurements are allowed, employing highly entangled data could lead to an increased prediction error. The achieved results provide critical guidance for designing advanced QML protocols, especially for those tailored for execution on early-stage quantum computers with limited access to quantum resources.

A variational quantum perceptron with Grover’s algorithm for efficient classification

This study introduces the Quantum Variational Perceptron with Grover’s algorithm (QVP-G), an innovative Quantum machine Learning (QML) model significantly enhancing binary classification tasks’ capabilities. The study goes beyond theoretical constructs, employing empirical evaluations of QVP-G on the well-established Iris and more complex breast cancer datasets. This dual-dataset approach highlights the model’s adaptability and effectiveness in varied contexts. Our experimental findings reveal the exceptional accuracy of QVP-G, achieving a remarkable 99% success rate. This superior performance is owed mainly to integrating Grover’s algorithm, a cornerstone in Quantum Computing (QC), which substantially increases the probability of accurately determining the correct classification hyperplane. Beyond academic interest, our research positions QVP-G as a powerful tool with substantial practical applications. Its utility ranges from enhancing fraud detection and improving spam filtering to expediting drug discovery and contributing to advances in physics research. This study marks a significant advancement in QML, reinforcing the bridge between QC and machine learning.

Predicting Brain Age and Gender from Brain Volume Data Using Variational Quantum Circuits.

The morphology of the brain undergoes changes throughout the aging process, and accurately predicting a person's brain age and gender using brain morphology features can aid in detecting atypical brain patterns. Neuroimaging-based estimation of brain age is commonly used to assess an individual's brain health relative to a typical aging trajectory, while accurately classifying gender from neuroimaging data offers valuable insights into the inherent neurological differences between males and females. In this study, we aimed to compare the efficacy of classical machine learning models with that of a quantum machine learning method called a variational quantum circuit in estimating brain age and predicting gender based on structural magnetic resonance imaging data. We evaluated six classical machine learning models alongside a quantum machine learning model using both combined and sub-datasets, which included data from both in-house collections and public sources. The total number of participants was 1157, ranging from ages 14 to 89, with a gender distribution of 607 males and 550 females. Performance evaluation was conducted within each dataset using training and testing sets. The variational quantum circuit model generally demonstrated superior performance in estimating brain age and gender classification compared to classical machine learning algorithms when using the combined dataset. Additionally, in benchmark sub-datasets, our approach exhibited better performance compared to previous studies that utilized the same dataset for brain age prediction. Thus, our results suggest that variational quantum algorithms demonstrate comparable effectiveness to classical machine learning algorithms for both brain age and gender prediction, potentially offering reduced error and improved accuracy.

Quantum machine learning for drowsiness detection with EEG signals

Human reliability is an increasingly important area in various fields for accident prevention. Monitoring human biological parameters, such as metabolic agents, through techniques like an electroencephalogram (EEG), data analysis can help detect patterns indicating drowsiness, a major cause of fatigue that may impact tasks in various industries, including oil and gas, aviation, naval, railway, and others that involve shift work. While traditional machine learning methods, such as Multilayer Perceptron (MLP), have been explored in the literature for EEG-based drowsiness detection, advancements in computing technology have brought quantum mechanics concepts into play, offering potential advantages in computational efficiency for problem-solving. This work explores drowsiness detection via Quantum Machine Learning (QML). EEG signals are preprocessed to extract features specific to this type of data, such as Higuchi Fractal Dimension, Complexity, and Mobility, as well as statistical features such as mean, variance, root mean square, peak-to-peak, and maximum amplitude. We employ different quantum circuit architectures involving operations such as rotation gates (Ry, Rz, Ry), and entangling gates (CNOT, CZ, and iSWAP). We also combine those configurations considering different numbers of layers (1, 5, and 10). The models are trained and compared with classical MLP, considering five subjects. The main findings indicate that one subject (10) showed better results with the classic MLP model. However, for two subjects (1 and 8), iSWAP gates with 1 and 10 layers were notable, whereas for the last two subjects (5 and 6), configurations of CZ gates with 1 and 10 layers displayed the best results. This proof-of-principle study shows that QML models are suitable for analyzing EEG data related to drowsiness and can be further improved as quantum computing continues to evolve.

Generating Universal Adversarial Perturbations for Quantum Classifiers

Quantum Machine Learning (QML) has emerged as a promising field of research, aiming to leverage the capabilities of quantum computing to enhance existing machine learning methodologies. Recent studies have revealed that, like their classical counterparts, QML models based on Parametrized Quantum Circuits (PQCs) are also vulnerable to adversarial attacks. Moreover, the existence of Universal Adversarial Perturbations (UAPs) in the quantum domain has been demonstrated theoretically in the context of quantum classifiers. In this work, we introduce QuGAP: a novel framework for generating UAPs for quantum classifiers. We conceptualize the notion of additive UAPs for PQC-based classifiers and theoretically demonstrate their existence. We then utilize generative models (QuGAP-A) to craft additive UAPs and experimentally show that quantum classifiers are susceptible to such attacks. Moreover, we formulate a new method for generating unitary UAPs (QuGAP-U) using quantum generative models and a novel loss function based on fidelity constraints. We evaluate the performance of the proposed framework and show that our method achieves state-of-the-art misclassification rates, while maintaining high fidelity between legitimate and adversarial samples.

Understanding quantum machine learning also requires rethinking generalization

Quantum machine learning models have shown successful generalization performance even when trained with few data. In this work, through systematic randomization experiments, we show that traditional approaches to understanding generalization fail to explain the behavior of such quantum models. Our experiments reveal that state-of-the-art quantum neural networks accurately fit random states and random labeling of training data. This ability to memorize random data defies current notions of small generalization error, problematizing approaches that build on complexity measures such as the VC dimension, the Rademacher complexity, and all their uniform relatives. We complement our empirical results with a theoretical construction showing that quantum neural networks can fit arbitrary labels to quantum states, hinting at their memorization ability. Our results do not preclude the possibility of good generalization with few training data but rather rule out any possible guarantees based only on the properties of the model family. These findings expose a fundamental challenge in the conventional understanding of generalization in quantum machine learning and highlight the need for a paradigm shift in the study of quantum models for machine learning tasks.

Expressive quantum supervised machine learning using Kerr-nonlinear parametric oscillators

Quantum machine learning with variational quantum algorithms (VQA) has been actively investigated as a practical algorithm in the noisy intermediate-scale quantum (NISQ) era. Recent researches reveal that the data reuploading, which repeatedly encode classical data into quantum circuit, is necessary for obtaining the expressive quantum machine learning model in the conventional quantum computing architecture. However, the data reuploading tends to require a large amount of quantum resources, which motivates us to find an alternative strategy for realizing the expressive quantum machine learning efficiently. In this paper, we propose quantum machine learning with Kerr-nonlinear parametric oscillators (KPOs), as another promising quantum computing device. We use not only the ground state and first excited state but also higher excited states, which allows us to use a large Hilbert space even if we have a single KPO. Our numerical simulations show that the expressibility of our method with only one mode of the KPO is much higher than that of the conventional method with six qubits. Our results pave the way towards resource-efficient quantum machine learning, which is essential for the practical applications in the NISQ era.

Quantum machine learning for image classification

Image classification, a pivotal task in multiple industries, faces computational challenges due to the burgeoning volume of visual data. This research addresses these challenges by introducing two quantum machine learning models that leverage the principles of quantum mechanics for effective computations. Our first model, a hybrid quantum neural network with parallel quantum circuits, enables the execution of computations even in the noisy intermediate-scale quantum era, where circuits with a large number of qubits are currently infeasible. This model demonstrated a record-breaking classification accuracy of 99.21% on the full MNIST dataset, surpassing the performance of known quantum–classical models, while having eight times fewer parameters than its classical counterpart. Also, the results of testing this hybrid model on a Medical MNIST (classification accuracy over 99%), and on CIFAR-10 (classification accuracy over 82%), can serve as evidence of the generalizability of the model and highlights the efficiency of quantum layers in distinguishing common features of input data. Our second model introduces a hybrid quantum neural network with a Quanvolutional layer, reducing image resolution via a convolution process. The model matches the performance of its classical counterpart, having four times fewer trainable parameters, and outperforms a classical model with equal weight parameters. These models represent advancements in quantum machine learning research and illuminate the path towards more accurate image classification systems.

The expressivity of classical and quantum neural networks on entanglement entropy

Analytically continuing the von Neumann entropy from Rényi entropies is a challenging task in quantum field theory. While the n-th Rényi entropy can be computed using the replica method in the path integral representation of quantum field theory, the analytic continuation can only be achieved for some simple systems on a case-by-case basis. In this work, we propose a general framework to tackle this problem using classical and quantum neural networks with supervised learning. We begin by studying several examples with known von Neumann entropy, where the input data is generated by representing TrρAn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext {Tr}}\\rho _A^n$$\\end{document} with a generating function. We adopt KerasTuner to determine the optimal network architecture and hyperparameters with limited data. In addition, we frame a similar problem in terms of quantum machine learning models, where the expressivity of the quantum models for the entanglement entropy as a partial Fourier series is established. Our proposed methods can accurately predict the von Neumann and Rényi entropies numerically, highlighting the potential of deep learning techniques for solving problems in quantum information theory.

Optical wearable sensor based dance motion detection in health monitoring system using quantum machine learning model

Optical wearable sensor based dance motion detection in health monitoring system using quantum machine learning model

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

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

Theoretical guarantees for permutation-equivariant quantum neural networks

AbstractDespite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential. For instance, models based on quantum neural networks (QNNs) can suffer from excessive local minima and barren plateaus in their training landscapes. Recently, the nascent field of geometric quantum machine learning (GQML) has emerged as a potential solution to some of those issues. The key insight of GQML is that one should design architectures, such as equivariant QNNs, encoding the symmetries of the problem at hand. Here, we focus on problems with permutation symmetry (i.e., symmetry group Sn), and show how to build Sn-equivariant QNNs We provide an analytical study of their performance, proving that they do not suffer from barren plateaus, quickly reach overparametrization, and generalize well from small amounts of data. To verify our results, we perform numerical simulations for a graph state classification task. Our work provides theoretical guarantees for equivariant QNNs, thus indicating the power and potential of GQML.

Quantum discriminator for binary classification

Quantum computers have the unique ability to operate relatively quickly in high-dimensional spaces—this is sought to give them a competitive advantage over classical computers. In this work, we propose a novel quantum machine learning model called the Quantum Discriminator, which leverages the ability of quantum computers to operate in the high-dimensional spaces. The quantum discriminator is trained using a quantum-classical hybrid algorithm in O(NlogN)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(N\\log N)$$\\end{document} time, and inferencing is performed on a universal quantum computer in O(N)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(N)$$\\end{document} time. The quantum discriminator takes as input the binary features extracted from a given datum along with a prediction qubit, and outputs the predicted label. We analyze its performance on the Iris and Bars and Stripes data sets, and show that it can attain 99% accuracy in simulation.

Fourier Series Weight in Quantum Machine Learning

In this work, we aim to confirm the impact of the Fourier series on the quantum machine learning model. We will propose models, tests, and demonstrations to achieve this objective. We designed a quantum machine learning leveraged on the Hamiltonian encoding. With a subtle change, we performed the trigonometric interpolation, binary and multiclass classifier, and a quantum signal processing application. We also proposed a block diagram of determining approximately the Fourier coefficient based on quantum machine learning. We performed and tested all the proposed models using the Pennylane framework.

Precise Quantum Angle Generator Designed for Noisy Quantum Devices

Precise Quantum Angle Generator Designed for Noisy Quantum Devices

Application of quantum computing in image processing for recognition of infectious diseases of wheat

This study is devoted to the development and application of quantum methods in the field of diagnostics of infectious diseases of wheat. Taking into account the relevance of the problem of agriculture and the need to improve the efficiency of plant disease control, the work proposes a new approach based on the combined use of quantum computing, image processing and machine learning. Quantum image processing techniques have been applied to improve contrast, filter noise, and analyze key features of infectious diseases in the early stages of their development. The developed quantum machine learning models demonstrate high ac-curacy in image classification, which contributes to earlier and more accurate detection of diseases. The study results highlight the effectiveness of quantum methods in agriculture and provide new tools for more accurate diagnosis of infectious plant diseases. The prospects for introducing this approach into agriculture mean the possibility of improving yields, reducing the use of chemicals and ensuring food security.