Related papers: Quantum Divide-and-Conquer Anchoring for Separable…
Data compression can be achieved by reducing the dimensionality of high-dimensional but approximately low-rank datasets, which may in fact be described by the variation of a much smaller number of parameters. It often serves as a…
Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
Given a nonnegative matrix factorization, $R$, and a factorization rank, $r$, Exact nonnegative matrix factorization (Exact NMF) decomposes $R$ as the product of two nonnegative matrices, $C$ and $S$ with $r$ columns, such as $R = CS^\top$.…
Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order finding, which quantum mechanics lets us perform…
D-Wave quantum annealers represent a novel computational architecture and have attracted significant interest, but have been used for few real-world computations. Machine learning has been identified as an area where quantum annealing may…
We present here an original application of the non-negative matrix factorization (NMF) method, for the case of extra-financial data. These data are subject to high correlations between co-variables, as well as between observations. NMF…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
Conformation generation, also known as molecular unfolding (MU), is a crucial step in structure-based drug design, remaining a challenging combinatorial optimization problem. Quantum annealing (QA) has shown great potential for solving…
Exploring the potential application of quantum computers in material design and drug discovery has attracted a lot of interest in the age of quantum computing. However, the quantum resource requirement for solving practical electronic…
Quantum data encoding (QDE) enables faster com-putations than classical algorithms through superposition and en-tanglement. Circuit cutting and knitting are effective techniques for ameliorating current noisy quantum processing unit (QPUs)…
We provide an explicit recursive divide and conquer approach for simulating quantum dynamics and derive a discrete first quantized non-relativistic QED Hamiltonian based on the many-particle Pauli Fierz Hamiltonian. We apply this recursive…
The model described in this paper belongs to the family of non-negative matrix factorization methods designed for data representation and dimension reduction. In addition to preserving the data positivity property, it aims also to preserve…
Distributed quantum computing (DQC) is a new paradigm aimed at scaling up quantum computing via the interconnection of smaller quantum processing units (QPUs). Shared entanglement allows teleportation of both states and gates between QPUs.…
Quantum computing holds immense potential for solving classically intractable problems by leveraging the unique properties of quantum mechanics. The scalability of quantum architectures remains a significant challenge. Multi-core quantum…
This study presents a divide-and-conquer (DC) approach based on feature space decomposition for classification. When large-scale datasets are present, typical approaches usually employed truncated kernel methods on the feature space or DC…
Distributed quantum computing (DQC) combines the computing power of multiple networked quantum processing modules, enabling the execution of large quantum circuits without compromising on performance and connectivity. Photonic networks are…
The intrinsic idea of superdense coding is to find as many gates as possible such that they can be perfectly discriminated. In this paper, we consider a new scheme of discrimination of quantum gates, called ancilla-assisted discrimination,…
In this thesis we examine a variety of techniques for reducing the resources required for fault-tolerant quantum computation. First, we show how to simplify universal encoded computation by using only transversal gates and standard error…
Recent quantum algorithms pertaining to electronic structure theory primarily focus on threshold-based dynamic construction of ansatz by selectively including important many-body operators. These methods can be made systematically more…