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Due to the superiority and noteworthy progress of Quantum Computing (QC) in a lot of applications such as cryptography, chemistry, Big data, machine learning, optimization, Internet of Things (IoT), Blockchain, communication, and many more.…

Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration problem, for which a speed-up is shown by quantum computers…

Quantum machine learning (QML) is rapidly transitioning from theoretical promise to practical relevance across data-intensive scientific domains. In this Review, we provide a structured overview of recent advances that bridge foundational…

Quantum machine learning (QML) aims to accelerate machine learning tasks by exploiting quantum computation. Previous work studied a QML algorithm for selecting sparse subnetworks from large shallow neural networks. Instead of directly…

Variational quantum algorithms (VQAs) are leading strategies for using near-term quantum devices, with a well-studied bottleneck being their trainability. Standard expectation-value objectives with expressive circuits frequently encounter…

The $k$-means algorithm (Lloyd's algorithm) is a widely used method for clustering unlabeled data. A key bottleneck of the $k$-means algorithm is that each iteration requires time linear in the number of data points, which can be expensive…

Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practical quantum advantage can be said to exist for such problems when the end-to-end time for…

The power of quantum computers is still somewhat speculative. While they are certainly faster than classical ones at some tasks, the class of problems they can efficiently solve has not been mapped definitively onto known classical…

Although it will be a while before a practical quantum computer is available, there is no need to hold off. Methods and algorithms are being developed to demonstrate the feasibility of running machine learning (ML) pipelines in QC (Quantum…

Data encoding plays a fundamental and distinctive role in Quantum Machine Learning (QML). While classical approaches process data directly as vectors, QML may require transforming classical data into quantum states through encoding…

Quantum machine learning (QML) is a promising field that explores the applications of quantum computing to machine learning tasks. A significant hurdle in the advancement of quantum machine learning lies in the development of efficient and…

Matrices with the displacement structures of circulant, Toeplitz, and Hankel types as well as matrices with structures generalizing these types are omnipresent in computations of sciences and engineering. In this paper, we present efficient…

Many recent investigations conclude, based on asymptotic complexity analyses, that quantum computers could accelerate combinatorial optimization (CO) tasks relative to a purely classical computer. However, asymptotic analysis alone cannot…

Quantum machine learning is considered one of the current research fields with immense potential. In recent years, Havl\'i\v{c}ek et al. [Nature 567, 209-212 (2019)] have proposed a quantum machine learning algorithm with quantum-enhanced…

Feature selection is a common step in many ranking, classification, or prediction tasks and serves many purposes. By removing redundant or noisy features, the accuracy of ranking or classification can be improved and the computational cost…

In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. At the same time, algorithms for quantum computers have been shown to efficiently solve some problems that are intractable on…

Quantum kernel methods (QKMs) have emerged as a prominent framework for supervised quantum machine learning. Unlike variational quantum algorithms, which rely on gradient-based optimisation and may suffer from issues such as barren…

The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent…

Quantum algorithms theoretically outperform classical algorithms in solving problems of increasing size, but computational errors must be kept to a minimum to realize this potential. Despite the development of increasingly capable quantum…

Deep neural network powered artificial intelligence has rapidly changed our daily life with various applications. However, as one of the essential steps of deep neural networks, training a heavily weighted network requires a tremendous…