Replicating chaotic characteristics of non-linear dynamics by machine learning (ML) has recently drawn wide attentions. In this work, we propose that a ML model, trained to predict the state one-step-ahead from several latest historic states, can accurately replicate the bifurcation diagram and the Lyapunov exponents of discrete dynamic systems. The characteristics for different values of the hyper-parameters are captured universally by a single ML model, while the previous works considered training the ML model independently by fixing the hyper-parameters to be specific values. Our benchmarks on the one- and two-dimensional Logistic maps show that variational quantum circuit can reproduce the long-term characteristics with higher accuracy than the long short-term memory (a well-recognized classical ML model). Our work reveals an essential difference between the ML for the chaotic characteristics and that for standard tasks, from the perspective of the relation between performance and model complexity. Our results suggest that quantum circuit model exhibits potential advantages on mitigating over-fitting, achieving higher accuracy and stability.
The No-Free-Lunch (NFL) theorem, which quantifies problem- and data-independent generalization errors regardless of the optimization process, provides a foundational framework for comprehending diverse learning protocols' potential. Despite its significance, the establishment of the NFL theorem for quantum machine learning models remains largely unexplored, thereby overlooking broader insights into the fundamental relationship between quantum and classical learning protocols. To address this gap, we categorize a diverse array of quantum learning algorithms into three learning protocols designed for learning quantum dynamics under a specified observable and establish their NFL theorem. The exploited protocols, namely Classical Learning Protocols (CLC-LPs), Restricted Quantum Learning Protocols (ReQu-LPs), and Quantum Learning Protocols (Qu-LPs), offer varying levels of access to quantum resources. Our derived NFL theorems demonstrate quadratic reductions in sample complexity across CLC-LPs, ReQu-LPs, and Qu-LPs, contingent upon the orthogonality of quantum states and the diagonality of observables. We attribute this performance discrepancy to the unique capacity of quantum-related learning protocols to indirectly utilize information concerning the global phases of non-orthogonal quantum states, a distinctive physical feature inherent in quantum mechanics. Our findings not only deepen our understanding of quantum learning protocols' capabilities but also provide practical insights for the development of advanced quantum learning algorithms.
Following the recent development of quantum machine learning techniques, the literature has reported several quantum machine learning algorithms for disease detection. This study explores the application of a hybrid quantum-classical algorithm for classifying region-of-interest time-series data obtained from resting-state functional magnetic resonance imaging in patients with early-stage cognitive impairment based on the importance of cognitive decline for dementia or aging. Classical one-dimensional convolutional layers are used together with quantum convolutional neural networks in our hybrid algorithm. In the classical simulation, the proposed hybrid algorithms showed higher balanced accuracies than classical convolutional neural networks under the similar training conditions. Moreover, a total of nine brain regions (left precentral gyrus, right superior temporal gyrus, left rolandic operculum, right rolandic operculum, left parahippocampus, right hippocampus, left medial frontal gyrus, right cerebellum crus, and cerebellar vermis) among 116 brain regions were found to be relatively effective brain regions for the classification based on the model performances. The associations of the selected nine regions with cognitive decline, as found in previous studies, were additionally validated through seed-based functional connectivity analysis. We confirmed both the improvement of model performance with the quantum convolutional neural network and neuroscientific validities of brain regions from our hybrid quantum-classical model.
Diabetic Retinopathy (DR), a prevalent complication in diabetes patients, can lead to vision impairment due to lesions formed on the retina. Detecting DR at an advanced stage often results in irreversible blindness. The traditional process of diagnosing DR through retina fundus images by ophthalmologists is not only time-intensive but also expensive. While classical transfer learning models have been widely adopted for computer-aided detection of DR, their high maintenance costs can hinder their detection efficiency. In contrast, Quantum Transfer Learning offers a more effective solution to this challenge. This approach is notably advantageous because it operates on heuristic principles, making it highly optimized for the task. Our proposed methodology leverages this hybrid quantum transfer learning technique to detect DR. To construct our model, we utilize the APTOS 2019 Blindness Detection dataset, available on Kaggle. We employ the ResNet-18, ResNet34, ResNet50, ResNet101, ResNet152 and Inception V3, pre-trained classical neural networks, for the initial feature extraction. For the classification stage, we use a Variational Quantum Classifier. Our hybrid quantum model has shown remarkable results, achieving an accuracy of 97% for ResNet-18. This demonstrates that quantum computing, when integrated with quantum machine learning, can perform tasks with a level of power and efficiency unattainable by classical computers alone. By harnessing these advanced technologies, we can significantly improve the detection and diagnosis of Diabetic Retinopathy, potentially saving many from the risk of blindness. Keywords: Diabetic Retinopathy, Quantum Transfer Learning, Deep Learning
Quantum machine learning is a new research field combining quantum information science and machine learning. Quantum computing technologies appear to be particularly well-suited for addressing problems in the health sector efficiently. They have the potential to handle large datasets more effectively than classical models and offer greater transparency and interpretability for clinicians. Alzheimer's disease is a neurodegenerative brain disorder that mostly affects elderly people, causing important cognitive impairments. It is the most common cause of dementia and it has an effect on memory, thought, learning abilities and movement control. This type of disease has no cure, consequently an early diagnosis is fundamental for reducing its impact. The analysis of handwriting can be effective for diagnosing, as many researches have conjectured. The DARWIN (Diagnosis AlzheimeR WIth haNdwriting) dataset contains handwriting samples from people affected by Alzheimer's disease and a group of healthy people. Here we apply quantum AI to this use-case. In particular, we use this dataset to test classical methods for classification and compare their performances with the ones obtained via quantum machine learning methods. We find that quantum methods generally perform better than classical methods. Our results pave the way for future new quantum machine learning applications in early-screening diagnostics in the healthcare domain.
Quantum machine learning (QML) has the potential for improving the multi-label classification of rare, albeit critical, diseases in large-scale chest x-ray (CXR) datasets due to theoretical quantum advantages over classical machine learning (CML) in sample efficiency and generalizability. While prior literature has explored QML with CXRs, it has focused on binary classification tasks with small datasets due to limited access to quantum hardware and computationally expensive simulations. To that end, we implemented a Jax-based framework that enables the simulation of medium-sized qubit architectures with significant improvements in wall-clock time over current software offerings. We evaluated the performance of our Jax-based framework in terms of efficiency and performance for hybrid quantum transfer learning for long-tailed classification across 8, 14, and 19 disease labels using large-scale CXR datasets. The Jax-based framework resulted in up to a 58% and 95% speed-up compared to PyTorch and TensorFlow implementations, respectively. However, compared to CML, QML demonstrated slower convergence and an average AUROC of 0.70, 0.73, and 0.74 for the classification of 8, 14, and 19 CXR disease labels. In comparison, the CML models had an average AUROC of 0.77, 0.78, and 0.80 respectively. In conclusion, our work presents an accessible implementation of hybrid quantum transfer learning for long-tailed CXR classification with a computationally efficient Jax-based framework.
Quantum Machine Learning investigates the possibility of quantum computers enhancing Machine Learning algorithms. Anomaly segmentation is a fundamental task in various domains to identify irregularities at sample level and can be addressed with both supervised and unsupervised methods. Autoencoders are commonly used in unsupervised tasks, where models are trained to reconstruct normal instances efficiently, allowing anomaly identification through high reconstruction errors. While quantum autoencoders have been proposed in the literature, their application to anomaly segmentation tasks remains unexplored. In this paper, we introduce a patch-based quantum autoencoder (QPB-AE) for image anomaly segmentation, with a number of parameters scaling logarithmically with patch size. QPB-AE reconstructs the quantum state of the embedded input patches, computing an anomaly map directly from measurement through a SWAP test without reconstructing the input image. We evaluate its performance across multiple datasets and parameter configurations and compare it against a classical counterpart.
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.
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. The subgroups of $S_{n}$ arise, among many other contexts, to describe label symmetry of classical images with respect to spatial transformations, e.g. reflection or rotation. Equipped with the formalism of geometric quantum machine learning, in this work 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 Generative Adversarial Networks (qGANs) are at the forefront of image-generating quantum machine learning models. To accommodate the growing demand for Noisy Intermediate-Scale Quantum (NISQ) devices to train and infer quantum machine learning models, the number of third-party vendors offering quantum hardware as a service is expected to rise. This expansion introduces the risk of untrusted vendors potentially stealing proprietary information from the quantum machine learning models. To address this concern we propose a novel watermarking technique that exploits the noise signature embedded during the training phase of qGANs as a non-invasive watermark. The watermark is identifiable in the images generated by the qGAN allowing us to trace the specific quantum hardware used during training hence providing strong proof of ownership. To further enhance the security robustness, we propose the training of qGANs on a sequence of multiple quantum hardware, embedding a complex watermark comprising the noise signatures of all the training hardware that is difficult for adversaries to replicate. We also develop a machine learning classifier to extract this watermark robustly, thereby identifying the training hardware (or the suite of hardware) from the images generated by the qGAN validating the authenticity of the model. We note that the watermark signature is robust against inferencing on hardware different than the hardware that was used for training. We obtain watermark extraction accuracy of 100% and ~90% for training the qGAN on individual and multiple quantum hardware setups (and inferencing on different hardware), respectively. Since parameter evolution during training is strongly modulated by quantum noise, the proposed watermark can be extended to other quantum machine learning models as well.
Quantum machine learning (QML) continues to be an area of tremendous interest from research and industry. While QML models have been shown to be vulnerable to adversarial attacks much in the same manner as classical machine learning models, it is still largely unknown how to compare adversarial attacks on quantum versus classical models. In this paper, we show how to systematically investigate the similarities and differences in adversarial robustness of classical and quantum models using transfer attacks, perturbation patterns and Lipschitz bounds. More specifically, we focus on classification tasks on a handcrafted dataset that allows quantitative analysis for feature attribution. This enables us to get insight, both theoretically and experimentally, on the robustness of classification networks. We start by comparing typical QML model architectures such as amplitude and re-upload encoding circuits with variational parameters to a classical ConvNet architecture. Next, we introduce a classical approximation of QML circuits (originally obtained with Random Fourier Features sampling but adapted in this work to fit a trainable encoding) and evaluate this model, denoted Fourier network, in comparison to other architectures. Our findings show that this Fourier network can be seen as a "middle ground" on the quantum-classical boundary. While adversarial attacks successfully transfer across this boundary in both directions, we also show that regularization helps quantum networks to be more robust, which has direct impact on Lipschitz bounds and transfer attacks.
The study of variational quantum algorithms (VQCs) has received significant attention from the quantum computing community in recent years. These hybrid algorithms, utilizing both classical and quantum components, are well-suited for noisy intermediate-scale quantum devices. Though estimating exact gradients using the parameter-shift rule to optimize the VQCs is realizable in NISQ devices, they do not scale well for larger problem sizes. The computational complexity, in terms of the number of circuit evaluations required for gradient estimation by the parameter-shift rule, scales linearly with the number of parameters in VQCs. On the other hand, techniques that approximate the gradients of the VQCs, such as the simultaneous perturbation stochastic approximation (SPSA), do not scale with the number of parameters but struggle with instability and often attain suboptimal solutions. In this work, we introduce a novel gradient estimation approach called Guided-SPSA, which meaningfully combines the parameter-shift rule and SPSA-based gradient approximation. The Guided-SPSA results in a 15% to 25% reduction in the number of circuit evaluations required during training for a similar or better optimality of the solution found compared to the parameter-shift rule. The Guided-SPSA outperforms standard SPSA in all scenarios and outperforms the parameter-shift rule in scenarios such as suboptimal initialization of the parameters. We demonstrate numerically the performance of Guided-SPSA on different paradigms of quantum machine learning, such as regression, classification, and reinforcement learning.
With the rapid advancement of Quantum Machine Learning (QML), the critical need to enhance security measures against adversarial attacks and protect QML models becomes increasingly evident. In this work, we outline the connection between quantum noise channels and differential privacy (DP), by constructing a family of noise channels which are inherently $\epsilon$-DP: $(\alpha, \gamma)$-channels. Through this approach, we successfully replicate the $\epsilon$-DP bounds observed for depolarizing and random rotation channels, thereby affirming the broad generality of our framework. Additionally, we use a semi-definite program to construct an optimally robust channel. In a small-scale experimental evaluation, we demonstrate the benefits of using our optimal noise channel over depolarizing noise, particularly in enhancing adversarial accuracy. Moreover, we assess how the variables $\alpha$ and $\gamma$ affect the certifiable robustness and investigate how different encoding methods impact the classifier's robustness.
Underwater images taken from autonomous underwater vehicles (AUV's) often suffer from low light, high turbidity, poor contrast, motion-blur and excessive light scattering and hence require image enhancement techniques for object recognition. Machine learning methods are being increasingly used for object recognition under such adverse conditions. These enhanced object recognition methods of images taken from AUV's has potential applications in underwater pipeline and optical fibre surveillance, ocean bed resource extraction, ocean floor mapping, underwater species exploration, etc. While the classical machine learning methods are very efficient in terms of accuracy, they require large datasets and high computational time for image classification. In the current work, we use quantum-classical hybrid machine learning methods for real-time under-water object recognition on-board an AUV for the first time. We use real-time motion-blurred and low-light images taken from an on-board camera of AUV built in-house and apply existing hybrid machine learning methods for object recognition. Our hybrid methods consist of quantum encoding and flattening of classical images using quantum circuits and sending them to classical neural networks for image classification. The results of hybrid methods carried out using Pennylane based quantum simulators both on GPU and using pre-trained models on an on-board NVIDIA GPU chipset are compared with results from corresponding classical machine learning methods. We observe that the hybrid quantum machine learning methods show an efficiency greater than 65\% and reduction in run-time by one-thirds and require 50\% smaller dataset sizes for training the models compared to classical machine learning methods. We hope that our work opens up further possibilities in quantum enhanced real-time computer vision in autonomous vehicles.
Benefiting from cloud computing, today's early-stage quantum computers can be remotely accessed via the cloud services, known as Quantum-as-a-Service (QaaS). However, it poses a high risk of data leakage in quantum machine learning (QML). To run a QML model with QaaS, users need to locally compile their quantum circuits including the subcircuit of data encoding first and then send the compiled circuit to the QaaS provider for execution. If the QaaS provider is untrustworthy, the subcircuit to encode the raw data can be easily stolen. Therefore, we propose a co-design framework for preserving the data security of QML with the QaaS paradigm, namely PristiQ. By introducing an encryption subcircuit with extra secure qubits associated with a user-defined security key, the security of data can be greatly enhanced. And an automatic search algorithm is proposed to optimize the model to maintain its performance on the encrypted quantum data. Experimental results on simulation and the actual IBM quantum computer both prove the ability of PristiQ to provide high security for the quantum data while maintaining the model performance in QML.
Quantum Computing in the Noisy Intermediate-Scale Quantum (NISQ) era has shown promising applications in machine learning, optimization, and cryptography. Despite the progress, challenges persist due to system noise, errors, and decoherence that complicate the simulation of quantum systems. The depolarization channel is a standard tool for simulating a quantum system's noise. However, modeling such noise for practical applications is computationally expensive when we have limited hardware resources, as is the case in the NISQ era. We propose a modified representation for a single-qubit depolarization channel with two Kraus operators based only on X and Z Pauli matrices. Our approach reduces the computational complexity from six to four matrix multiplications per execution of a channel. Experiments on a Quantum Machine Learning (QML) model on the Iris dataset across various circuit depths and depolarization rates validate that our approach maintains the model's accuracy while improving efficiency. This simplified noise model enables more scalable simulations of quantum circuits under depolarization, advancing capabilities in the NISQ era.
In recent years, Quantum Machine Learning (QML) has increasingly captured the interest of researchers. Among the components in this domain, activation functions hold a fundamental and indispensable role. Our research focuses on the development of activation functions quantum circuits for integration into fault-tolerant quantum computing architectures, with an emphasis on minimizing $T$-depth. Specifically, we present novel implementations of ReLU and leaky ReLU activation functions, achieving constant $T$-depths of 4 and 8, respectively. Leveraging quantum lookup tables, we extend our exploration to other activation functions such as the sigmoid. This approach enables us to customize precision and $T$-depth by adjusting the number of qubits, making our results more adaptable to various application scenarios. This study represents a significant advancement towards enhancing the practicality and application of quantum machine learning.
This paper introduces quantum circuit $C^*$-algebra net, which provides a connection between $C^*$-algebra nets proposed in classical machine learning and quantum circuits. Using $C^*$-algebra, a generalization of the space of complex numbers, we can represent quantum gates as weight parameters of a neural network. By introducing additional parameters, we can induce interaction among multiple circuits constructed by quantum gates. This interaction enables the circuits to share information among them, which contributes to improved generalization performance in machine learning tasks. As an application, we propose to use the quantum circuit $C^*$-algebra net to encode classical data into quantum states, which enables us to integrate classical data into quantum algorithms. Numerical results demonstrate that the interaction among circuits improves performance significantly in image classification, and encoded data by the quantum circuit $C^*$-algebra net are useful for downstream quantum machine learning tasks.
This study introduces the Quantum Federated Neural Network for Financial Fraud Detection (QFNN-FFD), a cutting-edge framework merging Quantum Machine Learning (QML) and quantum computing with Federated Learning (FL) for financial fraud detection. Using quantum technologies' computational power and the robust data privacy protections offered by FL, QFNN-FFD emerges as a secure and efficient method for identifying fraudulent transactions within the financial sector. Implementing a dual-phase training model across distributed clients enhances data integrity and enables superior performance metrics, achieving precision rates consistently above 95%. Additionally, QFNN-FFD demonstrates exceptional resilience by maintaining an impressive 80% accuracy, highlighting its robustness and readiness for real-world applications. This combination of high performance, security, and robustness against noise positions QFNN-FFD as a transformative advancement in financial technology solutions and establishes it as a new benchmark for privacy-focused fraud detection systems. This framework facilitates the broader adoption of secure, quantum-enhanced financial services and inspires future innovations that could use QML to tackle complex challenges in other areas requiring high confidentiality and accuracy.
Quantum Kernels are projected to provide early-stage usefulness for quantum machine learning. However, highly sophisticated classical models are hard to surpass without losing interpretability, particularly when vast datasets can be exploited. Nonetheless, classical models struggle once data is scarce and skewed. Quantum feature spaces are projected to find better links between data features and the target class to be predicted even in such challenging scenarios and most importantly, enhanced generalization capabilities. In this work, we propose a novel approach called Systemic Quantum Score (SQS) and provide preliminary results indicating potential advantage over purely classical models in a production grade use case for the Finance sector. SQS shows in our specific study an increased capacity to extract patterns out of fewer data points as well as improved performance over data-hungry algorithms such as XGBoost, providing advantage in a competitive market as it is the FinTech and Neobank regime.