Related papers: Quantum Algorithm for Linear Regression
Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…
Feedback-based quantum algorithms (FQAs) operate by iteratively growing a quantum circuit to optimize a given task. At each step, feedback from qubit measurements is used to inform the next quantum circuit update. In practice, the sampling…
Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…
We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…
We introduce a new approach for quantum linear algebra based on quantum subspace states and present three new quantum machine learning algorithms. The first is a quantum determinant sampling algorithm that samples from the distribution…
Since Harrow, Hassidim, and Lloyd (2009) showed that a system of linear equations with $N$ variables and condition number $\kappa$ can be solved on a quantum computer in $\operatorname{poly}(\log(N), \kappa)$ time, exponentially faster than…
We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine…
This book is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum…
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…
Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over…
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…
Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data. Quantum kernels are able to capture relationships in the data that are not…
Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum…
Quantile regression \parencite{Koenker1978} is a robust and practically useful way to efficiently model quantile varying correlation and predict varied response quantiles of interest. This article constructs and tests MM algorithms, which…
We introduce a quantum algorithm for computing the Ollivier Ricci curvature, a discrete analogue of the Ricci curvature defined via optimal transport on graphs and general metric spaces. This curvature has seen applications ranging from…
We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…
We provide an improved analysis of standard differentially private gradient descent for linear regression under the squared error loss. Under modest assumptions on the input, we characterize the distribution of the iterate at each time…
The encoding of classical to quantum data mapping through trigonometric functions within arithmetic-based quantum computation algorithms leads to the exploitation of multivariate distributions. The studied variational quantum gate learning…
Several quantum algorithms for linear algebra problems, and in particular quantum machine learning problems, have been "dequantized" in the past few years. These dequantization results typically hold when classical algorithms can access the…