Related papers: Quantum speedup of leverage score sampling and its…
We create a variety of new quantum algorithms that use Grover's algorithm and similar techniques to give polynomial speedups over their classical counterparts. We begin by introducing a set of tools that carefully minimize the impact of…
Discrete stochastic processes (DSP) are instrumental for modelling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte Carlo methods since the number…
Ridge leverage scores provide a balance between low-rank approximation and regularization, and are ubiquitous in randomized linear algebra and machine learning. Deterministic algorithms are also of interest in the moderately big data…
Leverage scores have become essential in statistics and machine learning, aiding regression analysis, randomized matrix computations, and various other tasks. This paper delves into the inverse problem, aiming to recover the intrinsic model…
Sampling tasks are a natural class of problems for quantum computers due to the probabilistic nature of the Born rule. Sampling from useful distributions on noisy quantum hardware remains a challenging problem. A recent paper [Layden, D. et…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of…
Even after decades of quantum computing development, examples of generally useful quantum algorithms with exponential speedups over classical counterparts are scarce. Recent progress in quantum algorithms for linear-algebra positioned…
Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally…
Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from…
Two-stage stochastic programming is a problem formulation for decision-making under uncertainty. In the first stage, the actor makes a best "here and now" decision in the presence of uncertain quantities that will be resolved in the future,…
Clustering algorithms are of fundamental importance when dealing with large unstructured datasets and discovering new patterns and correlations therein, with applications ranging from scientific research to medical imaging and marketing…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
Quantum computational approaches to some classic target identification and localization algorithms, especially for radar images, are investigated, and are found to raise a number of quantum statistics and quantum measurement issues with…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer,…
Recently, there has been a surge of interest for quantum computation for its ability to exponentially speed up algorithms, including machine learning algorithms. However, Tang suggested that the exponential speed up can also be done on a…
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
We develop an efficient quantum implementation of an important signal processing algorithm for line spectral estimation: the matrix pencil method, which determines the frequencies and damping factors of signals consisting of finite sums of…