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Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is that of quantum process…
Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the…
In recent years, variational quantum algorithms have garnered significant attention as a candidate approach for near-term quantum advantage using noisy intermediate-scale quantum (NISQ) devices. In this article we introduce kernel descent,…
Gaussian Process Regression (GPR) is a nonparametric supervised learning method, widely valued for its ability to quantify uncertainty. Despite its advantages and broad applications, classical GPR implementations face significant…
The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks, which is an optimization algorithm for finding a local minimum of an objective function. The quantum versions of gradient…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
Accurate quantum tomography is a vital tool in both fundamental and applied quantum science. It is a task that involves processing a noisy measurement record in order to construct a reliable estimate of an unknown quantum state, and is…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
Quantum machine learning and optimization are exciting new areas that have been brought forward by the breakthrough quantum algorithm of Harrow, Hassidim and Lloyd for solving systems of linear equations. The utility of {classical} linear…
Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…
The gradient descent method aims at finding local minima of a given multivariate function by moving along the direction of its gradient, and hence, the algorithm typically involves computing all partial derivatives of a given function,…
Gradient descent methods have long been the de facto standard for training deep neural networks. Millions of training samples are fed into models with billions of parameters, which are slowly updated over hundreds of epochs. Recently, it's…
We consider a generic framework of optimization algorithms based on gradient descent. We develop a quantum algorithm that computes the gradient of a multi-variate real-valued function $f:\mathbb{R}^d\rightarrow \mathbb{R}$ by evaluating it…
An algorithm and associated strategy for solving polynomial systems within the optimization framework is presented. The algorithm and strategy are named, respectively, the penetrating gradient algorithm and the deepest descent strategy. The…
Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
In this article we introduce an algorithm for mitigating the adverse effects of noise on gradient descent in variational quantum algorithms. This is accomplished by computing a {\emph{regularized}} local classical approximation to the…
A programmable quantum processor is a fundamental model of quantum computation. In this model, any quantum channel can be approximated by applying a fixed universal quantum operation onto an input state and a quantum `program' state, whose…
The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are…