Related papers: Computing a Sparse Approximate Inverse on Quantum …

Quantum annealing is a heuristic optimization algorithm that exploits quantum evolution to approximately find lowest energy states. Quantum annealers have scaled up in recent years to tackle increasingly larger and more highly connected…

Compressive sensing is a novel approach that linearly samples sparse or compressible signals at a rate much below the Nyquist-Shannon sampling rate and outperforms traditional signal processing techniques in acquiring and reconstructing…

The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here,…

Inverse problems play a central role for many classical computer vision and image processing tasks. Many inverse problems are ill-posed, and hence require a prior to regularize the solution space. However, many of the existing priors, like…

In this paper, we develop a way to encode several NP-Complete problems in Abstract Argumentation to Quadratic Unconstrained Binary Optimization (QUBO) problems. In this form, a solution for a QUBO problem involves minimizing a quadratic…

Quantum annealing is a powerful tool for solving and approximating combinatorial optimization problems such as graph partitioning, community detection, centrality, routing problems, and more. In this paper we explore the use of quantum…

Quantum annealing aims at solving optimization problems of practical relevance using quantum-computing hardware. Problems of interest are typically formulated in terms of quadratic unconstrained binary optimization (QUBO) Hamiltonians.…

We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…

We consider the problem of computing a sparse binary representation of an image. To be precise, given an image and an overcomplete, non-orthonormal basis, we aim to find a sparse binary vector indicating the minimal set of basis vectors…

In this work we develop theoretical techniques for analysing the performance of the quantum approximate optimization algorithm (QAOA) when applied to random boolean constraint satisfaction problems (CSPs), and use these techniques to…

Quantum Computing allows, in principle, the encoding of the exponentially scaling many-electron wave function onto a linearly scaling qubit register, offering a promising solution to overcome the limitations of traditional quantum chemistry…

In this paper, we propose a simple sparse approximate inverse for triangular matrices (SAIT). Using the Jacobi iteration method, we obtain an expression of the exact inverse of triangular matrix, which is a finite series. The SAIT is…

We propose a novel quasi-Newton method for solving the sparse inverse covariance estimation problem also known as the graphical least absolute shrinkage and selection operator (GLASSO). This problem is often solved using a second-order…

The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…

We consider concave minimization problems over non-convex sets.Optimization problems with this structure arise in sparse principal component analysis. We analyze both a gradient projection algorithm and an approximate Newton algorithm where…

The Quadratic Unconstrained Binary Optimization (QUBO) problems are NP hard; thus, so far, there are no algorithms to solve them efficiently. There are exact methods like the Branch-and-Bound algorithm for smaller problems, and for larger…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

A sparse matrix is called double irregular sparse if it has at least one relatively dense column and row, and it is double regular sparse if all the columns and rows of it are sparse. The sparse approximate inverse preconditioning…

In many problems in Computational Physics and Chemistry, one finds a special kind of sparse matrices, termed "banded matrices". These matrices, which are defined as having non-zero entries only within a given distance from the main…

Quantum annealers (QAs) are specialized quantum computers that minimize objective functions over discrete variables by physically exploiting quantum effects. Current QA platforms allow for the optimization of quadratic objectives defined…