Abstract In this paper we develop methods to solve two problems related to time series (TS) analysis using quantum computing: reconstruction and classification. We formulate the task of reconstructing a given TS from a training set of data as an unconstrained binary optimization (QUBO) problem, which can be solved by both quantum annealers and gate-model quantum processors. We accomplish this by discretizing the TS and converting the reconstruction to a set cover problem, allowing us to perform a one-versus-all method of reconstruction. Using the solution to the reconstruction problem, we show how to extend this method to perform semi-supervised classification of TS data. We present results indicating our method is competitive with current semi- and unsupervised classification techniques, but using less data than classical techniques.
Abstract In this paper we develop methods to solve two problems related to time series (TS) analysis using quantum computing: reconstruction and classification. We formulate the task of reconstructing a given TS from a training set of data as an unconstrained binary optimization (QUBO) problem, which can be solved by both quantum annealers and gate-model quantum processors. We accomplish this by discretizing the TS and converting the reconstruction to a set cover problem, allowing us to perform a one-versus-all method of reconstruction. Using the solution to the reconstruction problem, we show how to extend this method to perform semi-supervised classification of TS data. We present results indicating our method is competitive with current semi- and unsupervised classification techniques, but using less data than classical techniques.
Recent advances in quantum technology have led to the development and the manufacturing of programmable quantum annealers that promise to solve certain combinatorial optimization problems faster than their classical counterparts. Semi-supervised learning is a machine learning technique that makes use of both labeled and unlabeled data for training, which enables a good classifier with only a small amount of labeled data. In this paper, we propose and theoretically analyze a graph-based semi-supervised learning method with the aid of the quantum annealing technique, which efficiently utilizes the quantum resources while maintaining good accuracy. We illustrate two classification examples, suggesting the feasibility of this method even with a small portion (30%) of labeled data involved.
This study focuses on the integration of quantum computing and artificial intelligence, proposing a multi-task optimisation framework based on the quantum annealing algorithm to address the bottlenecks in computational efficiency and model optimisation in traditional machine learning. The study converts problems such as time series prediction, Support Vector Machine (SVM) classification, and Convolutional Neural Network (CNN) training into Quadratic Unconstrained Binary Optimisation (QUBO) models and achieves parameter optimisation through the simulated annealing algorithm. In time series prediction, an autoregressive model is constructed based on historical data. The problem of minimising prediction error is mapped to a binary optimisation problem through QUBO transformation, and the model parameters are solved using the simulated annealing algorithm to achieve trend prediction of the target variable, validating the effectiveness of quantum optimisation in time series analysis. For classification tasks, the hinge loss and regularisation terms of SVM are converted into a QUBO matrix to optimise the classification hyperplane parameters, thereby enhancing the model's classification performance in the feature space. The results demonstrate that this method exhibits strong geometric interpretability and generalisation capabilities in binary classification problems. In the field of deep learning, L2 regularisation is introduced into the weight optimisation of CNNs, and a QUBO model is constructed to explore the application of quantum optimisation in image feature extraction and network training. Although limited by the scale of variables, this demonstrates the potential value of combining quantum computing with deep learning. The study shows that the quantum optimisation framework can effectively improve solution efficiency in small- to medium-scale problems, providing new technical pathways for time series analysis, classification tasks, and deep learning optimisation.
We study the problem of supervised binary classification from the perspective of deploying adiabatic quantum optimization in training. A vast body of prior academic work consisting of both theoretical and numerical studies has indicated that quantum technology promises to provide computational power that may be fundamentally superior to any classical computing methods. Given the abundance of NP-hard optimization problems that naturally arise in learning, it is clear that machine learning can immensely benefit from such an optimization tool. We describe a series of increasingly complex designs that result in computationally hard training problems of combinatorial nature. In return for accepting classical computational hardness, we retain theoretical properties such as maximal sparsity and robustness to label noise, which are otherwise sacrificed by convex methods for the sake of computational efficiency and sound theoretical footing. In order to be compatible with emerging quantum hardware technology, we formalize the training problem as quadratic unconstrained binary optimization. Our initial investigations focus on a simple training formulation with non-convex regularization that conforms to the architecture of existing quantum hardware and makes frugal use of a limited number of available physical qubits. Next, we extend this baseline formulation to a scalable algorithm, QBoost, which is able to train incrementally large-scale classifiers on data sets of practical interest. Further, we derive another algorithm, TotalQBoost, as a theoretically motivated totally corrective boosting algorithm with cardinality penalization that also makes use of quantum optimization. Both QBoost and TotalQBoost perform explicit cardinality regularization, which is the only known way of achieving maximal sparsity in the trained classifiers. We apply QBoost and TotalQBoost to three different real-world computer vision problems and make use of a quantum processor for solving the sequence of discrete optimization problems generated by one of them. Finally, we study a learning formulation with convex regularization and a non-convex loss function, q-loss, specifically designed for robust supervised learning in the presence of label noise as it occurs in practice. For compatibility with quantum hardware we derive the corresponding quadratic binary problem via variational approximation. For all proposed algorithms we compare results on a variety of popular synthetic and natural data sets against a rich selection of existing rival learning formulations.
We propose an enhanced hybrid quantum-classical framework for time series anomaly detection. Building on our previous formulation of the problem as a Quadratic Unconstrained Binary Optimization solved via the Quantum Approximate Optimization Algorithm, we extend the methodology with a statistical model selector and a refined set-covering inference scheme that accounts for temporal-value asymmetries. We analyze scalability in terms of qubit resources, assess feasibility on current quantum devices, and validate the approach on a benchmark of over one hundred heterogeneous time series. The results demonstrate interpretable decisions, robust precision, and competitive performance against both shallow classical local detectors and deep global classical architectures, highlighting the potential of the proposed methodology.
This work focuses on quantum machine learning and analyzes the power of one single qubit to solve classical machine learning problems. We explore possible strategies to address traditional supervised, unsupervised, and reinforcement learning tasks. In particular, we study binary and multinomial classification, regression problems, time series forecasting, clustering, and quantum reinforcement learning. Our results suggest that the same methodology could be used to address all three types of learning with different measurement strategies and, despite the strong limitation of reduced data dimensionality of the candidate problems, a single qubit can achieve similar or even improved performance with respect to state-of-the-art classic machine learning methods in many cases. As simulating the evolution of one qubit state is computationally efficient, our study enables the possibility to use the qubit model as a candidate solution to implement simple decision-making machine learning models in hardware with extremely low memory resources such as embedded systems or edge devices. The outcomes provided could be also of interest in academia and for the construction of demonstrators using low-scale contemporary quantum hardware.
Abstract Quantum machine learning recently gained prominence due to the promise of quantum computers in solving machine learning problems that are intractable on a classical computer. Nevertheless, several studies on problems which remain challenging for classical computing algorithms are emerging. One of these is classifying continuously incoming data instances in incremental fashion, which is studied in this paper through a hybrid computational solution that combines classical and quantum techniques. Hybrid approaches represents one of the current ways for the use of quantum computation in practical applications. In this paper, we show how typical issues of domain-incremental learning can be equally addressed with the properties of quantum mechanics, until to offer often better results. We propose the framework QUARTA to combine algorithms of quantum supervised learning, that is, variational quantum circuits, and techniques used in quantum unsupervised learning, that is, distance estimation. We aim at keeping the classification capabilities, which have learned on previously processed data instances, preserved as much as possible, and then acquiring new knowledge on new data instances. Experiments are performed on real-world datasets with quantum simulators.