Related papers: Quantum Divide-and-Conquer Anchoring for Separable…

We present an algorithm for quantum-assisted cluster analysis (QACA) that makes use of the topological properties of a D-Wave 2000Q quantum processing unit (QPU). Clustering is a form of unsupervised machine learning, where instances are…

An efficient integer factorization algorithm would reduce the security of all variants of the RSA cryptographic scheme to zero. Despite the passage of years, no method for efficiently factoring large semiprime numbers in a classical…

We propose a divide-and-conquer approach to filtering which decomposes the state variable into low-dimensional components to which standard particle filtering tools can be successfully applied and recursively merges them to recover the full…

The assumed computationally difficulty of factoring large integers forms the basis of security for RSA public-key cryptography, which specifically relies on products of two large primes or semi-primes. The best-known factoring algorithms…

Classical computing has borne witness to the development of machine learning. The integration of quantum technology into this mix will lead to unimaginable benefits and be regarded as a giant leap forward in mankind's ability to compute.…

In this paper, we consider the symmetric multi-type non-negative matrix tri-factorization problem (SNMTF), which attempts to factorize several symmetric non-negative matrices simultaneously. This can be considered as a generalization of the…

In the Nonnegative Matrix Factorization (NMF) problem we are given an $n \times m$ nonnegative matrix $M$ and an integer $r > 0$. Our goal is to express $M$ as $A W$ where $A$ and $W$ are nonnegative matrices of size $n \times r$ and $r…

Systems of linear equations are employed almost universally across a wide range of disciplines, from physics and engineering to biology, chemistry and statistics. Traditional solution methods such as Gaussian elimination become very time…

Feature selection is a common step in many ranking, classification, or prediction tasks and serves many purposes. By removing redundant or noisy features, the accuracy of ranking or classification can be improved and the computational cost…

Advancements in computing based on qubit networks, and in particular the flux-qubit processor architecture developed by D-Wave System's Inc., have enabled the physical simulation of quantum-dot cellular automata (QCA) networks beyond the…

Motivated by the analysis of nonnegative data objects, a novel Nested Nonnegative Cone Analysis (NNCA) approach is proposed to overcome some drawbacks of existing methods. The application of traditional PCA/SVD method to nonnegative data…

Major obstacles remain to the implementation of macroscopic quantum computing: hardware problems of noise, decoherence, and scaling; software problems of error correction; and, most important, algorithm construction. Finding truly quantum…

Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…

Field-Programmable Gate Arrays (FPGAs) have asserted themselves as vital assets in contemporary computing by offering adaptable, reconfigurable hardware platforms. FPGA-based accelerators incubate opportunities for breakthroughs in areas,…

This paper describes algorithms for nonnegative matrix factorization (NMF) with the beta-divergence (beta-NMF). The beta-divergence is a family of cost functions parametrized by a single shape parameter beta that takes the Euclidean…

Non-negative matrix factorization (NMF) has become a popular machine learning approach to many problems in text mining, speech and image processing, bio-informatics and seismic data analysis to name a few. In NMF, a matrix of non-negative…

We factorize a 48-bit integer using 10 trapped-ion qubits on a Quantinuum's quantum computer. This result outperforms the recent achievement by B. Yan et al., arXiv:2212.12372 (2022), increasing the success probability by a factor of 6 with…

Non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it does not always result in…

In this paper, we propose a provably correct algorithm for convolutive nonnegative matrix factorization (CNMF) under separability assumptions. CNMF is a convolutive variant of nonnegative matrix factorization (NMF), which functions as an…

Quantum integer factorization is a potential quantum computing solution that may revolutionize cryptography. Nevertheless, a scalable and efficient quantum algorithm for noisy intermediate-scale quantum computers looks far-fetched. We…