Related papers: Quantum Algorithms and Lower Bounds for Finite-Sum…
We study the optimal lower and upper complexity bounds for finding approximate solutions to the composite problem $\min_x\ f(x)+h(Ax-b)$, where $f$ is smooth and $h$ is convex. Given access to the proximal operator of $h$, for strongly…
We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
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…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
We explore the potential for quantum speedups in convex optimization using discrete simulations of the Quantum Hamiltonian Descent (QHD) framework, as proposed by Leng et al., and establish the first rigorous query complexity bounds. We…
We consider the SUBSET SUM problem and its important variants in this paper. In the SUBSET SUM problem, a (multi-)set $X$ of $n$ positive numbers and a target number $t$ are given, and the task is to find a subset of $X$ with the maximal…
Finite-sum optimization plays an important role in the area of machine learning, and hence has triggered a surge of interest in recent years. To address this optimization problem, various randomized incremental gradient methods have been…
Quantum algorithms for optimization problems are of general interest. Despite recent progress in classical lower bounds for nonconvex optimization under different settings and quantum lower bounds for convex optimization, quantum lower…
We propose a first order algorithm, a modified version of FISTA, to solve an optimization problem with an objective function that is a sum of a possibly nonconvex function, with Lipschitz continuous gradient, and a convex function which can…
This paper considers the projection-free sparse convex optimization problem for the vector domain and the matrix domain, which covers a large number of important applications in machine learning and data science. For the vector domain…
We study finite-sum non-convex optimization $\min_{x\in\mathbb{R}^d} F(x) \;=\; \frac{1}{n}\sum_{i=1}^n f_i(x)$ and analyze a variance-reduced cubic Newton method based on EMA-smoothed SARAH estimators for both gradient and Hessian…
We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…
This paper studies stochastic optimization for a sum of compositional functions, where the inner-level function of each summand is coupled with the corresponding summation index. We refer to this family of problems as finite-sum coupled…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
The thesis deals with Quantum Algorithms for solving Hard Constrained Optimization Problems. It shows how quantum computers can solve difficult everyday problems such as finding the best schedule for social workers or the path of a robot…
Computational fluid dynamics (CFD) is a cornerstone of classical scientific computing, and there is growing interest in whether quantum computers can accelerate such simulations. To date, the existing proposals for fault-tolerant quantum…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…