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Quantum machine learning holds the potential to revolutionize cancer treatment and diagnostic imaging by uncovering complex patterns beyond the reach of classical methods. This study explores the effectiveness of quantum convolutional layers in classifying ultrasound breast images for cancer detection. By encoding classical data into quantum states through angle embedding and employing a robustly entangled 9-qubit circuit design with an SU(4) gate, we developed a Quantum Convolutional Neural Network (QCNN) and compared it to a classical CNN of similar architecture. Our QCNN model, leveraging two quantum circuits as convolutional layers, achieved an impressive peak training accuracy of 76.66% and a validation accuracy of 87.17% at a learning rate of 1 × 10-2. In contrast, the classical CNN model attained a training accuracy of 77.52% and a validation accuracy of 83.33%. These compelling results highlight the potential of quantum circuits to serve as effective convolutional layers for feature extraction in image classification, especially with small datasets.

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In this study, the PennyLane quantum device simulator was used to investigate quantum and hybrid, quantum/classical physics-informed neural networks (PINNs) for solutions to both transient and steady-state, 1D and 2D partial differential equations. The comparative expressibility of the purely quantum, hybrid and classical neural networks is discussed, and hybrid configurations are explored. The results show that (1) for some applications, quantum PINNs can obtain comparable accuracy with less neural network parameters than classical PINNs, and (2) adding quantum nodes in classical PINNs can increase model accuracy with less total network parameters for noiseless models.

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Quantum machine learning has made remarkable progress in many important tasks. However, the gate complexity of the initial state preparation is seldom considered in lots of quantum machine learning algorithms, making them non-end-to-end. Herein, we propose a quantum algorithm for the node embedding problem that maps a node graph's topological structure to embedding vectors. The resulting quantum embedding state can be used as an input for other quantum machine learning algorithms. With O ( log ( N ) ) qubits to store the information of N nodes, our algorithm will not lose quantum advantage for the subsequent quantum information processing. Moreover, owing to the use of a parameterized quantum circuit with O ( poly ( log ( N ) ) ) depth, the resulting state can serve as an efficient quantum database. In addition, we explored the measurement complexity of the quantum node embedding algorithm, which is the main issue in training parameters, and extended the algorithm to capture high-order neighborhood information between nodes. Finally, we experimentally demonstrated our algorithm on an nuclear magnetic resonance quantum processor to solve a graph model.

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Tensor networks are emerging architectures for implementing quantum classification models. The branching multi-scale entanglement renormalization ansatz (BMERA) is a tensor network known for its enhanced entanglement properties. This paper introduces a hybrid quantum-classical classification model based on BMERA and explores the correlation between circuit layout, expressiveness, and classification accuracy. Additionally, we present an autodifferentiation method for computing the cost function gradient, which serves as a viable option for other hybrid quantum-classical models. Through numerical experiments, we demonstrate the accuracy and robustness of our classification model in tasks such as image recognition and cluster excitation discrimination, offering a novel approach for designing quantum classification models.

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This work introduces a quantum subroutine for computing the distance between two patterns and integrates it into two quantum versions of the kNN classifier algorithm: one proposed by Schuld et al. and the other proposed by Quezada et al. Notably, our proposed subroutine is tailored to be memory-efficient, requiring fewer qubits for data encoding, while maintaining the overall complexity for both QkNN versions. This research focuses on comparing the performance of the two quantum kNN algorithms using the original Hamming distance with qubit-encoded features and our proposed subroutine, which computes the distance using amplitude-encoded features. Results obtained from analyzing thirteen different datasets (Iris, Seeds, Raisin, Mine, Cryotherapy, Data Bank Authentication, Caesarian, Wine, Haberman, Transfusion, Immunotherapy, Balance Scale, and Glass) show that both algorithms benefit from the proposed subroutine, achieving at least a 50% reduction in the number of required qubits, while maintaining a similar overall performance. For Shuld's algorithm, the performance improved in Cryotherapy (68.89% accuracy compared to 64.44%) and Balance Scale (85.33% F1 score compared to 78.89%), was worse in Iris (86.0% accuracy compared to 95.33%) and Raisin (77.67% accuracy compared to 81.56%), and remained similar in the remaining nine datasets. While for Quezada's algorithm, the performance improved in Caesarian (68.89% F1 score compared to 58.22%), Haberman (69.94% F1 score compared to 62.31%) and Immunotherapy (76.88% F1 score compared to 69.67%), was worse in Iris (82.67% accuracy compared to 95.33%), Balance Scale (77.97% F1 score compared to 69.21%) and Glass (40.04% F1 score compared to 28.79%), and remained similar in the remaining seven datasets.

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Quantum Architecture Search (QAS) has shown significant promise in designing quantum circuits for Variational Quantum Algorithms (VQAs). However, existing QAS algorithms primarily explore circuit architectures within a discrete space, which is inherently inefficient. In this paper, we propose a Gradient-based Optimization for Quantum Architecture Search (GQAS), which leverages a circuit encoder, decoder, and predictor. Initially, the encoder embeds circuit architectures into a continuous latent representation. Subsequently, a predictor utilizes this continuous latent representation as input and outputs an estimated performance for the given architecture. The latent representation is then optimized through gradient descent within the continuous latent space based on the predicted performance. The optimized latent representation is finally mapped back to a discrete architecture via the decoder. To enhance the quality of the latent representation, we pre-train the encoder on a substantial dataset of circuit architectures using Self-Supervised Learning (SSL). Our simulation results on the Variational Quantum Eigensolver (VQE) indicate that our method outperforms the current Differentiable Quantum Architecture Search (DQAS).

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The depletion of fossil energy reserves and the environmental pollution caused by these sources highlight the need to harness renewable energy sources from the oceans, such as waves and tides, due to their high potential. On the other hand, the large-scale deployment of ocean energy converters to meet future energy needs requires the use of large farms of these converters, which may have negative environmental impacts on the ocean ecosystem. In the meantime, a very important point is the volume of data produced by different methods of collecting data from the ocean for their analysis, which makes the use of advanced tools such as different machine learning algorithms even more colorful. In this article, some environmental impacts of ocean energy devices have been analyzed using machine learning and quantum machine learning. The results show that quantum machine learning performs better than its classical counterpart in terms of calculation accuracy. This approach offers a promising new method for environmental impact assessment, especially in a complex environment such as the ocean.

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Alzheimer disease (AD) is among the most chronic neurodegenerative diseases that threaten global public health. The prevalence of Alzheimer disease and consequently the increased risk of spread all over the world pose a vital threat to human safekeeping. Early diagnosis of AD is a suitable action for timely intervention and medication, which may increase the prognosis and quality of life for affected individuals. Quantum computing provides a more efficient model for different disease classification tasks than classical machine learning approaches. The full potential of quantum computing is not applied to Alzheimer's disease classification tasks as expected. In this study, we proposed an ensemble deep learning model based on quantum machine learning classifiers to classify Alzheimer's disease. The Alzheimer's disease Neuroimaging Initiative I and Alzheimer's disease Neuroimaging Initiative II datasets are merged for the AD disease classification. We combined important features extracted based on the customized version of VGG16 and ResNet50 models from the merged images then feed these features to the Quantum Machine Learning classifier to classify them as non-demented, mild demented, moderate demented, and very mild demented. We evaluate the performance of our model by using six metrics; accuracy, the area under the curve, F1-score, precision, and recall. The result validates that the proposed model outperforms several state-of-the-art methods for detecting Alzheimer's disease by registering an accuracy of 99.89 and 98.37 F1-score.

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Quantum computing (QC) has opened the door to advancements in machine learning (ML) tasks that are currently implemented in the classical domain. Convolutional neural networks (CNNs) are classical ML architectures that exploit data locality and possess a simpler structure than a fully connected multi-layer perceptrons (MLPs) without compromising the accuracy of classification. However, the concept of preserving data locality is usually overlooked in the existing quantum counterparts of CNNs, particularly for extracting multifeatures in multidimensional data. In this paper, we present an multidimensional quantum convolutional classifier (MQCC) that performs multidimensional and multifeature quantum convolution with average and Euclidean pooling, thus adapting the CNN structure to a variational quantum algorithm (VQA). The experimental work was conducted using multidimensional data to validate the correctness and demonstrate the scalability of the proposed method utilizing both noisy and noise-free quantum simulations. We evaluated the MQCC model with reference to reported work on state-of-the-art quantum simulators from IBM Quantum and Xanadu using a variety of standard ML datasets. The experimental results show the favorable characteristics of our proposed techniques compared with existing work with respect to a number of quantitative metrics, such as the number of training parameters, cross-entropy loss, classification accuracy, circuit depth, and quantum gate count.

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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.

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In the realm of liver transplantation, accurately determining hepatic steatosis levels is crucial. Recognizing the essential need for improved diagnostic precision, particularly for optimizing diagnosis time by swiftly handling easy-to-solve cases and allowing the expert time to focus on more complex cases, this study aims to develop cutting-edge algorithms that enhance the classification of liver biopsy images. Additionally, the challenge of maintaining data privacy arises when creating automated algorithmic solutions, as sharing patient data between hospitals is restricted, further complicating the development and validation process. This research tackles diagnostic accuracy by leveraging novel techniques from the rapidly evolving field of quantum machine learning, known for their superior generalization abilities. Concurrently, it addresses privacy concerns through the implementation of privacy-conscious collaborative machine learning with federated learning. We introduce a hybrid quantum neural network model that leverages real-world clinical data to assess non-alcoholic liver steatosis accurately. This model achieves an image classification accuracy of 97%, surpassing traditional methods by 1.8%. Moreover, by employing a federated learning approach that allows data from different clients to be shared while ensuring privacy, we maintain an accuracy rate exceeding 90%. This initiative marks a significant step towards a scalable, collaborative, efficient, and dependable computational framework that aids clinical pathologists in their daily diagnostic tasks.

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Background Quantum computing and quantum machine learning (QML) are promising experimental technologies that can improve precision medicine applications by reducing the computational complexity of algorithms driven by big, unstructured, real-world data. The clinical problem of knee osteoarthritis is that, although some novel therapies are safe and effective, the response is variable, and defining the characteristics of an individual who will respond remains a challenge. In this study, we tested a quantum neural network (QNN) application to support precision data-driven clinical decisions to select personalized treatments for advanced knee osteoarthritis. Methodology After obtaining patients' consent and Research Ethics Committee approval, we collected the clinicodemographic data before and after the treatment from 170 patients eligible for knee arthroplasty (Kellgren-Lawrence grade ≥3, Oxford Knee Score (OKS) ≤27, age ≥64 years, and idiopathic aetiology of arthritis) treated over a two-year period with a single injection of microfragmented fat. Gender classes were balanced (76 males and 94 females) to mitigate gender bias. A patient with an improvement ≥7 OKS was considered a responder. We trained our QNN classifier on a randomly selected training subset of 113 patients to classify responders from non-responders (73 responders and 40 non-responders) in pain and function at one year. Outliers were hidden from the training dataset but not from the validation set. Results We tested our QNN classifier on a randomly selected test subset of 57 patients (34 responders, 23 non-responders) including outliers. The no information rate was 0.59. Our application correctly classified 28 responders out of 34 and 6 non-responders out of 23 (sensitivity = 0.82, specificity = 0.26, F1 Statistic = 0.71). The positive and negative likelihood ratios were 1.11 and 0.68, respectively. The diagnostic odds ratio was 2. Conclusions Preliminary results on a small validation dataset showed that QML applied to data-driven clinical decisions for the personalized treatment of advanced knee osteoarthritis is a promising technology to reduce computational complexity and improve prognostic performance. Our results need further research validation with larger, real-world unstructured datasets, as well as clinical validation with an artificial intelligence clinical trial to test model efficacy, safety, clinical significance, and relevance at a public health level.

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Background: Cancer is a leading cause of death worldwide. Machine learning (ML) and quantum computers (QCs) have recently advanced significantly. Numerous studies have examined the application of quantum machine learning (QML) in healthcare and validated its superiority over classical ML algorithms. Objectives: This review investigates and reports the oncological applications of QML. Methods: In March 2023, an electronic investigation of PubMed, Scopus, Web of Science, IEEE, and Cochrane databases was performed. The articles were screened based on titles and abstracts, and their full texts were examined. Results: Initially, a total of 207 articles were retrieved. Thereafter, 9 articles were included in the study, most of which were published from 2020 onwards. The results indicated the implementation of various QML techniques in different aspects of oncology, such as reducing mammography image noise, edge detection of breast cancer, clinical decision support in radiotherapy treatment, and cancer classification. Conclusion: These studies revealed that integrating quantum science with ML can significantly improve patient care and clinical outcomes. Future studies should explore the integration of QC and ML and the development of novel algorithms to enhance cancer prognosis, diagnosis, and treatment planning.

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Nearest-neighbour clustering is a simple yet powerful machine learning algorithm that finds natural application in the decoding of signals in classical optical-fibre communication systems. Quantum k-means clustering promises a speed-up over the classical k-means algorithm; however, it has been shown to not currently provide this speed-up for decoding optical-fibre signals due to the embedding of classical data, which introduces inaccuracies and slowdowns. Although still not achieving an exponential speed-up for NISQ implementations, this work proposes the generalised inverse stereographic projection as an improved embedding into the Bloch sphere for quantum distance estimation in k-nearest-neighbour clustering, which allows us to get closer to the classical performance. We also use the generalised inverse stereographic projection to develop an analogous classical clustering algorithm and benchmark its accuracy, runtime and convergence for decoding real-world experimental optical-fibre communication data. This proposed 'quantum-inspired' algorithm provides an improvement in both the accuracy and convergence rate with respect to the k-means algorithm. Hence, this work presents two main contributions. Firstly, we propose the general inverse stereographic projection into the Bloch sphere as a better embedding for quantum machine learning algorithms; here, we use the problem of clustering quadrature amplitude modulated optical-fibre signals as an example. Secondly, as a purely classical contribution inspired by the first contribution, we propose and benchmark the use of the general inverse stereographic projection and spherical centroid for clustering optical-fibre signals, showing that optimizing the radius yields a consistent improvement in accuracy and convergence rate.

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Variational Bayes (VB) inference algorithm is used widely to estimate both the parameters and the unobserved hidden variables in generative statistical models. The algorithm-inspired by variational methods used in computational physics-is iterative and can get easily stuck in local minima, even when classical techniques, such as deterministic annealing (DA), are used. We study a VB inference algorithm based on a nontraditional quantum annealing approach-referred to as quantum annealing variational Bayes (QAVB) inference-and show that there is indeed a quantum advantage to QAVB over its classical counterparts. In particular, we show that such better performance is rooted in key quantum mechanics concepts: i) The ground state of the Hamiltonian of a quantum system-defined from the given data-corresponds to an optimal solution for the minimization problem of the variational free energy at very low temperatures; ii) such a ground state can be achieved by a technique paralleling the quantum annealing process; and iii) starting from this ground state, the optimal solution to the VB problem can be achieved by increasing the heat bath temperature to unity, and thereby avoiding local minima introduced by spontaneous symmetry breaking observed in classical physics based VB algorithms. We also show that the update equations of QAVB can be potentially implemented using ⌈logK⌉ qubits and 𝒪(K) operations per step, where K is the number of values hidden categorical variables can take. Thus, QAVB can match the time complexity of existing VB algorithms, while delivering higher performance.

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In this article, we investigate the applicability of quantum machine learning for classification tasks using two quantum classifiers from the Qiskit Python environment: the variational quantum circuit and the quantum kernel estimator (QKE). We provide a first evaluation on the performance of these classifiers when using a hyperparameter search on six widely known and publicly available benchmark datasets and analyze how their performance varies with the number of samples on two artificially generated test classification datasets. As quantum machine learning is based on unitary transformations, this paper explores data structures and application fields that could be particularly suitable for quantum advantages. Hereby, this paper introduces a novel dataset based on concepts from quantum mechanics using the exponential map of a Lie algebra. This dataset will be made publicly available and contributes a novel contribution to the empirical evaluation of quantum supremacy. We further compared the performance of VQC and QKE on six widely applicable datasets to contextualize our results. Our results demonstrate that the VQC and QKE perform better than basic machine learning algorithms, such as advanced linear regression models (Ridge and Lasso). They do not match the accuracy and runtime performance of sophisticated modern boosting classifiers such as XGBoost, LightGBM, or CatBoost. Therefore, we conclude that while quantum machine learning algorithms have the potential to surpass classical machine learning methods in the future, especially when physical quantum infrastructure becomes widely available, they currently lag behind classical approaches. Our investigations also show that classical machine learning approaches have superior performance classifying datasets based on group structures, compared to quantum approaches that particularly use unitary processes. Furthermore, our findings highlight the significant impact of different quantum simulators, feature maps, and quantum circuits on the performance of the employed quantum estimators. This observation emphasizes the need for researchers to provide detailed explanations of their hyperparameter choices for quantum machine learning algorithms, as this aspect is currently overlooked in many studies within the field. To facilitate further research in this area and ensure the transparency of our study, we have made the complete code available in a linked GitHub repository.

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Adversarial transfer learning is a machine learning method that employs an adversarial training process to learn the datasets of different domains. Recently, this method has attracted attention because it can efficiently decouple the requirements of tasks from insufficient target data. In this study, we introduce the notion of quantum adversarial transfer learning, where data are completely encoded by quantum states. A measurement-based judgment of the data label and a quantum subroutine to compute the gradients are discussed in detail. We also prove that our proposal has an exponential advantage over its classical counterparts in terms of computing resources such as the gate number of the circuits and the size of the storage required for the generated data. Finally, numerical experiments demonstrate that our model can be successfully trained, achieving high accuracy on certain datasets.

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The discovery of quantum algorithms offering provable advantages over the best known classical alternatives, together with the parallel ongoing revolution brought about by classical artificial intelligence, motivates a search for applications of quantum information processing methods to machine learning. Among several proposals in this domain, quantum kernel methods have emerged as particularly promising candidates. However, while some rigorous speedups on certain highly specific problems have been formally proven, only empirical proof-of-principle results have been reported so far for real-world datasets. Moreover, no systematic procedure is known, in general, to fine tune and optimize the performances of kernel-based quantum classification algorithms. At the same time, certain limitations such as kernel concentration effects-hindering the trainability of quantum classifiers-have also been recently pointed out. In this work, we propose several general-purpose optimization methods and best practices designed to enhance the practical usefulness of fidelity-based quantum classification algorithms. Specifically, we first describe a data pre-processing strategy that, by preserving the relevant relationships between data points when processed through quantum feature maps, substantially alleviates the effect of kernel concentration on structured datasets. We also introduce a classical post-processing method that, based on standard fidelity measures estimated on a quantum processor, yields non-linear decision boundaries in the feature Hilbert space, thus achieving the quantum counterpart of the radial basis functions technique that is widely employed in classical kernel methods. Finally, we apply the so-called quantum metric learning protocol to engineer and adjust trainable quantum embeddings, demonstrating substantial performance improvements on several paradigmatic real-world classification tasks.

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Inspired by classical graph neural networks, we discuss a novel quantum graph neural network (QGNN) model to predict the chemical and physical properties of molecules and materials. QGNNs were investigated to predict the energy gap between the highest occupied and lowest unoccupied molecular orbitals of small organic molecules. The models utilize the equivariantly diagonalizable unitary quantum graph circuit (EDU-QGC) framework to allow discrete link features and minimize quantum circuit embedding. The results show QGNNs can achieve lower test loss compared to classical models if a similar number of trainable variables are used, and converge faster in training. This paper also provides a review of classical graph neural network models for materials research and various QGNNs.

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In recent years, drug discovery and life sciences have been revolutionized with machine learning and artificial intelligence (AI) methods. Quantum computing is touted to be the next most significant leap in technology; one of the main early practical applications for quantum computing solutions is predicted to be in quantum chemistry simulations. Here, we review the near-term applications of quantum computing and their advantages for generative chemistry and highlight the challenges that can be addressed with noisy intermediate-scale quantum (NISQ) devices. We also discuss the possible integration of generative systems running on quantum computers into established generative AI platforms.

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