Related papers: Online Quantum State Tomography via Stochastic Gra…

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…

In this work, we propose a stochastic gradient descent (SGD) framework to design data-driven policy gradient descent algorithms for the linear quadratic regulator problem. Two alternative schemes are considered to estimate the policy…

We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a…

Inspired by dynamic programming, we propose Stochastic Virtual Gradient Descent (SVGD) algorithm where the Virtual Gradient is defined by computational graph and automatic differentiation. The method is computationally efficient and has…

This paper focuses on recovering a low-rank tensor from its incomplete measurements. We propose a novel algorithm termed the Single Mode Quasi Riemannian Gradient Descent (SM-QRGD). By exploiting the benefits of both fixed-rank matrix…

Motivated by the problem of online canonical correlation analysis, we propose the \emph{Stochastic Scaled-Gradient Descent} (SSGD) algorithm for minimizing the expectation of a stochastic function over a generic Riemannian manifold. SSGD…

Quantum state tomography, which aims to find the best description of a quantum state -- the density matrix, is an essential building block in quantum computation and communication. Standard techniques for state tomography are incapable of…

Quantum state tomography (QST) aims at estimating a quantum state from averaged quantum measurements made on copies of the state. Most quantum algorithms rely on QST at some point and it is a well explored topic in the literature, mostly…

Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness…

Stochastic gradient descent (SGD) is the main algorithm behind a large body of work in machine learning. In many cases, constraints are enforced via projections, leading to projected stochastic gradient algorithms. In recent years, a large…

Logistic regression, the Support Vector Machine (SVM), and least squares are well-studied methods in the statistical and computer science community, with various practical applications. High-dimensional data arriving on a real-time basis…

We propose LQ-SGD (Low-Rank Quantized Stochastic Gradient Descent), an efficient communication gradient compression algorithm designed for distributed training. LQ-SGD further develops on the basis of PowerSGD by incorporating the low-rank…

The experimental realization of increasingly complex synthetic quantum systems calls for the development of general theoretical methods, to validate and fully exploit quantum resources. Quantum-state tomography (QST) aims at reconstructing…

Quantum state tomography (QST) aims at reconstructing the state of a quantum system. However in conventional QST the number of measurements scales exponentially with the number of qubits. Here we propose a QST protocol, in which the…

We study the Stein Variational Gradient Descent (SVGD) algorithm, which optimises a set of particles to approximate a target probability distribution $\pi\propto e^{-V}$ on $\mathbb{R}^d$. In the population limit, SVGD performs gradient…

This paper studies distributed nonconvex optimization problems with stochastic gradients for a multi-agent system, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. We…

Stochastic Gradient Descent (SGD) has played a central role in machine learning. However, it requires a carefully hand-picked stepsize for fast convergence, which is notoriously tedious and time-consuming to tune. Over the last several…

We propose a new quantum state reconstruction method that combines ideas from compressed sensing, non-convex optimization, and acceleration methods. The algorithm, called Momentum-Inspired Factored Gradient Descent (\texttt{MiFGD}), extends…

We apply deep-neural-network-based techniques to quantum state classification and reconstruction. We demonstrate high classification accuracies and reconstruction fidelities, even in the presence of noise and with little data. Using optical…

With nowadays steadily growing quantum processors, it is required to develop new quantum tomography tools that are tailored for high-dimensional systems. In this work, we describe such a computational tool, based on recent ideas from…