Related papers: Computing a Sparse Approximate Inverse on Quantum …
This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…
The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in…
Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealers that promise to solve certain combinatorial optimization problems of practical relevance faster than their…
Developing quantum algorithms adaptive to specific constraints of near-term devices is an essential step towards practical quantum advantage. In a recent work [Phys. Rev. Lett. 131, 103601(2023)], we show cold atoms in an optical cavity can…
Sparse PCA is one of the most well-studied problems in high-dimensional statistics. In this problem, we are given samples from a distribution with covariance $\Sigma$, whose top eigenvector $v \in R^d$ is $s$-sparse. Existing sparse PCA…
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…
In this paper, we estimate the high dimensional precision matrix under the weak sparsity condition where many entries are nearly zero. We revisit the sparse column-wise inverse operator (SCIO) estimator \cite{liu2015fast} and derive its…
With the advent of quantum computers, researchers are exploring if quantum mechanics can be leveraged to solve important problems in ways that may provide advantages not possible with conventional or classical methods. A previous work by…
Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally…
A black-box optimization algorithm such as Bayesian optimization finds extremum of an unknown function by alternating inference of the underlying function and optimization of an acquisition function. In a high-dimensional space, such…
A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…
Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a…
Variational quantum algorithms offer fascinating prospects for the solution of combinatorial optimization problems using digital quantum computers. However, the achievable performance in such algorithms and the role of quantum correlations…
We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic…
Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present an application level benchmarking framework for near-term quantum…
Commercial quantum annealers from D-Wave Systems make it possible to obtain approximate solutions of high quality for certain NP-hard problems in nearly constant time. Before solving a problem on D-Wave, several pre-processing methods can…
Inverse imaging problems that are ill-posed can be encountered across multiple domains of science and technology, ranging from medical diagnosis to astronomical studies. To reconstruct images from incomplete and distorted data, it is…
Sparse principal component analysis (PCA), an important variant of PCA, attempts to find sparse loading vectors when conducting dimension reduction. This paper considers the nonsmooth Riemannian optimization problem associated with the…
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
Representing signals with sparse vectors has a wide range of applications that range from image and video coding to shape representation and health monitoring. In many applications with real-time requirements, or that deal with…