Related papers: i-QLS: Quantum-supported Algorithm for Least Squar…
We introduce a novel optimization algorithm for image recovery under learned sparse and low-rank constraints, which we parameterize as weighted extensions of the $\ell_p^p$-vector and $\mathcal S_p^p$ Schatten-matrix quasi-norms for…
We investigate a hybrid quantum-classical solution method to the mean-variance portfolio optimization problems. Starting from real financial data statistics and following the principles of the Modern Portfolio Theory, we generate…
Quantum annealing is a promising approach for solving combinatorial optimization problems. However, its performance is often limited by the overhead of additional qubits required for embedding logical QUBO models onto quantum annealers.…
Quantum annealing provides a promising route for the development of quantum optimization devices, but the usefulness of such devices will be limited in part by the range of implementable problems as dictated by hardware constraints. To…
Finding solutions to systems of linear equations is a common prob\-lem in many areas of science and engineering, with much potential for a speedup on quantum devices. While the Harrow-Hassidim-Lloyd (HHL) quantum algorithm yields up to an…
Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and…
Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct…
A quantum annealer heuristically minimizes quadratic unconstrained binary optimization (QUBO) problems, but is limited by the physical hardware in the size and density of the problems it can handle. We have developed a meta-heuristic solver…
A major challenge in machine learning is the computational expense of training these models. Model training can be viewed as a form of optimization used to fit a machine learning model to a set of data, which can take up significant amount…
The recovery of sparse data is at the core of many applications in machine learning and signal processing. While such problems can be tackled using $\ell_1$-regularization as in the LASSO estimator and in the Basis Pursuit approach,…
The capability of the quantum approximate optimization algorithm (QAOA) in solving the combinatorial optimization problems has been intensively studied in recent years due to its application in the quantum-classical hybrid regime. Despite…
An iteratively reweighted least squares (IRLS) method is proposed for estimating polyserial and polychoric correlation coefficients in this paper. It iteratively calculates the slopes in a series of weighted linear regression models fitting…
Stochastic Unit Commitment (SUC) has been proposed to manage the uncertainties driven by renewable integration, but it leads to significant computational complexity. When accelerated by Benders Decomposition (BD), the master problem becomes…
Leveraging quantum properties to enhance complex learning tasks has been proven feasible, with excellent recent achievements in the field of unsupervised learning. However, current quantum schemes neglect adaptive adjustments for…
Agile networks with fast adaptation and reconfiguration capabilities are required for on-demand provisioning of various network services. We propose a new methodical framework for short-time network optimization based on quantum computing…
The transition to 100% renewable energy requires new techniques for managing energy networks, such as dividing them into sensible subsets of prosumers called micro-grids. Doing so in an optimal manner is a difficult optimization problem, as…
Given a matrix $A$ of dimension $M \times N$ and a vector $\vec{b}$, the quantum linear system (QLS) problem asks for the preparation of a quantum state $|\vec{y}\rangle$ proportional to the solution of $A\vec{y} = \vec{b}$. Existing QLS…
Linear regression in $\ell_p$-norm is a canonical optimization problem that arises in several applications, including sparse recovery, semi-supervised learning, and signal processing. Generic convex optimization algorithms for solving…
Quantum annealing is getting increasing attention in combinatorial optimization. The quantum processing unit by D-Wave is constructed to approximately solve Ising models on so-called Chimera graphs. Ising models are equivalent to quadratic…
Consider linear regression where the examples are generated by an unknown distribution on $R^d\times R$. Without any assumptions on the noise, the linear least squares solution for any i.i.d. sample will typically be biased w.r.t. the least…