Quantum machine learning (QML) is a rapidly growing field that combines quantum computing principles with traditional machine learning. It seeks to revolutionize machine learning by harnessing the unique capabilities of quantum mechanics and employs machine learning techniques to advance quantum computing research. This paper introduces quantum computing for the machine learning paradigm, where variational quantum circuits (VQC) are used to develop QML architectures on noisy intermediate-scale quantum (NISQ) devices. We discuss machine learning for the quantum computing paradigm, showcasing our recent theoretical and empirical findings. In particular, we delve into future directions for studying QML, exploring the potential industrial impacts of QML research.

Quantum Machine Learning (QML) offers tremendous potential but is currently limited by the availability of qubits. We introduce an innovative approach that utilizes pre-trained neural networks to enhance Variational Quantum Circuits (VQC). This technique effectively separates approximation error from qubit count and removes the need for restrictive conditions, making QML more viable for real-world applications. Our method significantly improves parameter optimization for VQC while delivering notable gains in representation and generalization capabilities, as evidenced by rigorous theoretical analysis and extensive empirical testing on quantum dot classification tasks. Moreover, our results extend to applications such as human genome analysis, demonstrating the broad applicability of our approach. By addressing the constraints of current quantum hardware, our work paves the way for a new era of advanced QML applications, unlocking the full potential of quantum computing in fields such as machine learning, materials science, medicine, mimetics, and various interdisciplinary areas.

Identifying and utilising various biomarkers for tracking Alzheimer's disease (AD) progression have received many recent attentions and enable helping clinicians make the prompt decisions. Traditional progression models focus on extracting morphological biomarkers in regions of interest (ROIs) from MRI/PET images, such as regional average cortical thickness and regional volume. They are effective but ignore the relationships between brain ROIs over time, which would lead to synergistic deterioration. For exploring the synergistic deteriorating relationship between these biomarkers, in this paper, we propose a novel spatio-temporal similarity measure based multi-task learning approach for effectively predicting AD progression and sensitively capturing the critical relationships between biomarkers. Specifically, we firstly define a temporal measure for estimating the magnitude and velocity of biomarker change over time, which indicate a changing trend(temporal). Converting this trend into the vector, we then compare this variability between biomarkers in a unified vector space(spatial). The experimental results show that compared with directly ROI based learning, our proposed method is more effective in predicting disease progression. Our method also enables performing longitudinal stability selection to identify the changing relationships between biomarkers, which play a key role in disease progression. We prove that the synergistic deteriorating biomarkers between cortical volumes or surface areas have a significant effect on the cognitive prediction.

Variational quantum circuit (VQC) is a promising approach for implementing quantum neural networks on noisy intermediate-scale quantum (NISQ) devices. Recent studies have shown that a tensor-train network (TTN) for VQC, namely TTN-VQC, can improve the representation and generalization powers of VQC. However, the Barren Plateau problem leads to the gradients of the cost function vanishing exponentially small as the number of qubits increases, making it difficult to find the optimal parameters for the VQC. To address this issue, we put forth a new learning approach called Pre+TTN-VQC that builds upon the TTN-VQC architecture by incorporating a pre-trained TTN to alleviate the Barren Plateau problem. The pre-trained TTN allows for efficient fine-tuning of target data, which reduces the depth of the VQC required to achieve good empirical performance and potentially alleviates the training obstacles posed by the Barren Plateau landscape. Furthermore, we highlight the advantages of Pre+TTN-VQC in terms of representation and generalization powers by exploiting the error performance analysis. Moreover, we characterize the optimization performance of Pre+TTN-VQC without the need for the Polyak-Lojasiewicz condition, thereby enhancing the practicality of implementing quantum neural networks on NISQ devices. We conduct experiments on a handwritten digit classification dataset to corroborate our proposed methods and theorems.

Quantum federated learning (QFL) is a quantum extension of the classical federated learning model across multiple local quantum devices. An efficient optimization algorithm is always expected to minimize the communication overhead among different quantum participants. In this work, we propose an efficient optimization algorithm, namely federated quantum natural gradient descent (FQNGD), and further, apply it to a QFL framework that is composed of a variational quantum circuit (VQC)-based quantum neural networks (QNN). Compared with stochastic gradient descent methods like Adam and Adagrad, the FQNGD algorithm admits much fewer training iterations for the QFL to get converged. Moreover, it can significantly reduce the total communication overhead among local quantum devices. Our experiments on a handwritten digit classification dataset justify the effectiveness of the FQNGD for the QFL framework in terms of a faster convergence rate on the training set and higher accuracy on the test set.

This work investigates an extension of transfer learning applied in machine learning algorithms to the emerging hybrid end-to-end quantum neural network (QNN) for spoken command recognition (SCR). Our QNN-based SCR system is composed of classical and quantum components: (1) the classical part mainly relies on a 1D convolutional neural network (CNN) to extract speech features; (2) the quantum part is built upon the variational quantum circuit with a few learnable parameters. Since it is inefficient to train the hybrid end-to-end QNN from scratch on a noisy intermediate-scale quantum (NISQ) device, we put forth a hybrid transfer learning algorithm that allows a pre-trained classical network to be transferred to the classical part of the hybrid QNN model. The pre-trained classical network is further modified and augmented through jointly fine-tuning with a variational quantum circuit (VQC). The hybrid transfer learning methodology is particularly attractive for the task of QNN-based SCR because low-dimensional classical features are expected to be encoded into quantum states. We assess the hybrid transfer learning algorithm applied to the hybrid classical-quantum QNN for SCR on the Google speech command dataset, and our classical simulation results suggest that the hybrid transfer learning can boost our baseline performance on the SCR task.

The state-of-the-art machine learning (ML), particularly based on deep neural networks (DNN), has enabled a wide spectrum of successful applications ranging from the everyday deployment of speech recognition [1] and computer vision [2] through to the frontier of scientific research in synthetic biology [8]. Despite rapid theoretical and empirical progress in DNN based regression and classification [9], DNN training algorithms are computationally expensive for many new scientific applications, such as new drug discovery [10], which requires computational resources that are beyond the computational limits of classical hardwares [11]. Fortunately, the imminent advent of quantum computing devices opens up new possibilities of exploiting quantum machine learning (QML) [12, 13, 14, 15, 16, 17] to improve the computational efficiency of ML algorithms in the new scientific domains. Although the exploitation of quantum computing devices to carry out QML is still in its initial exploratory stages, the rapid development in quantum hardware has motivated advances in quantum neural networks (QNN) to run in noisy intermediate-scale quantum (NISQ) devices [18, 19, 20, 21]. A NISQ device means that not enough qubits could be spared for quantum error correction, and the imperfect qubits have to be directly used at the physical layer.

In this paper, we exploit the properties of mean absolute error (MAE) as a loss function for the deep neural network (DNN) based vector-to-vector regression. The goal of this work is two-fold: (i) presenting performance bounds of MAE, and (ii) demonstrating new properties of MAE that make it more appropriate than mean squared error (MSE) as a loss function for DNN based vector-to-vector regression. First, we show that a generalized upper-bound for DNN-based vector- to-vector regression can be ensured by leveraging the known Lipschitz continuity property of MAE. Next, we derive a new generalized upper bound in the presence of additive noise. Finally, in contrast to conventional MSE commonly adopted to approximate Gaussian errors for regression, we show that MAE can be interpreted as an error modeled by Laplacian distribution. Speech enhancement experiments are conducted to corroborate our proposed theorems and validate the performance advantages of MAE over MSE for DNN based regression.

In this paper, we show that, in vector-to-vector regression utilizing deep neural networks (DNNs), a generalized loss of mean absolute error (MAE) between the predicted and expected feature vectors is upper bounded by the sum of an approximation error, an estimation error, and an optimization error. Leveraging upon error decomposition techniques in statistical learning theory and non-convex optimization theory, we derive upper bounds for each of the three aforementioned errors and impose necessary constraints on DNN models. Moreover, we assess our theoretical results through a set of image de-noising and speech enhancement experiments. Our proposed upper bounds of MAE for DNN based vector-to-vector regression are corroborated by the experimental results and the upper bounds are valid with and without the "over-parametrization" technique.