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To compute models for Water Distribution Networks (WDN), a large system of non-linear equations needs to be solved. The hallmark algorithm for computing these models is the Newton-Raphson Global Gradient Algorithm (NR-GGA), which solves…
We describe the neural-network training framework used in the Kaldi speech recognition toolkit, which is geared towards training DNNs with large amounts of training data using multiple GPU-equipped or multi-core machines. In order to be as…
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…
While quantum computers are a very promising tool for the far future, in their current state of the art they remain limited both in size and quality. This has given rise to hybrid quantum-classical algorithms, where the quantum device…
Variational Quantum Algorithms (VQAs) aim at solving classical or quantum optimization problems by optimizing parametrized trial states on a quantum device, based on the outcomes of noisy projective measurements. The associated optimization…
Gradient based optimization methods are the established state-of-the-art paradigm to study strongly entangled quantum systems in two dimensions with Projected Entangled Pair States. However, the key ingredient, the gradient itself, has…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
We present a collection of optimizers tuned for usage on Noisy Intermediate-Scale Quantum (NISQ) devices. Optimizers have a range of applications in quantum computing, including the Variational Quantum Eigensolver (VQE) and Quantum…
Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…
The variational quantum eigensolver is a hybrid algorithm composed of quantum state driving and classical parameter optimization, for finding the ground state of a given Hamiltonian. The natural gradient method is an optimization method…
For typical quantum subroutines in the gate-based model of quantum computing, explicit decompositions of circuits in terms of single-qubit and two-qubit entangling gates may exist. However, they often lead to large-depth circuits that are…
Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ)…
Recent empirical work on stochastic gradient descent (SGD) applied to over-parameterized deep learning has shown that most gradient components over epochs are quite small. Inspired by such observations, we rigorously study properties of…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…
In this work, we study an optimizer, Grad-Avg to optimize error functions. We establish the convergence of the sequence of iterates of Grad-Avg mathematically to a minimizer (under boundedness assumption). We apply Grad-Avg along with some…
Quantum machine learning aims to release the prowess of quantum computing to improve machine learning methods. By combining quantum computing methods with classical neural network techniques we aim to foster an increase of performance in…
Line-search methods are commonly used to solve optimization problems. The simplest line search method is steepest descent where one always moves in the direction of the negative gradient. Newton's method on the other hand is a second-order…
The natural gradient descent optimisation technique is an efficient optimising protocol for broad classes of classical and quantum systems that takes the underlying geometry of the parameter manifold into account by means of using either…
Variational quantum algorithms (VQAs) are a broad class of algorithms with many applications in science and industry. Applying a VQA to a problem involves optimizing a parameterized quantum circuit by maximizing or minimizing a cost…
Variational quantum algorithms are a leading candidate for early applications on noisy intermediate-scale quantum computers. These algorithms depend on a classical optimization outer-loop that minimizes some function of a parameterized…