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The factorization of skew-symmetric matrices is a critically understudied area of dense linear algebra, particularly in comparison to that of general and symmetric matrices. While some algorithms can be adapted from the symmetric case, the…
We derive an automatic procedure for generating a set of highly localized, non-orthogonal orbitals for linear scaling quantum Monte Carlo calculations. We demonstrate the advantage of these orbitals in calculations of the total energy of…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
In recent years, various means of efficiently detecting changepoints in the univariate setting have been proposed, with one popular approach involving minimising a penalised cost function using dynamic programming. In some situations, these…
In this tutorial-style review we discuss basic concepts of coupled cluster theory and recent developments that increase its computational efficiency for calculations of molecules, solids and materials in general. We will touch upon the…
The Harrow-Hassidim-Lloyd (HHL) algorithm is a quantum algorithm for solving systems of linear equations that, in principle, offers an exponential improvement in scaling with the system size compared to classical approaches. In this work,…
Interprocessor communication often dominates the runtime of large matrix computations. We present a parallel algorithm for computing QR decompositions whose bandwidth cost (communication volume) can be decreased at the cost of increasing…
Considering recent advancements and successes in the development of efficient quantum algorithms for electronic structure calculations --- alongside impressive results using machine learning techniques for computation --- hybridizing…
Recent years have witnessed a rapid growth of distributed machine learning (ML) frameworks, which exploit the massive parallelism of computing clusters to expedite ML training. However, the proliferation of distributed ML frameworks also…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
The practical application of quantum technologies to chemical problems faces significant challenges, particularly in the treatment of realistic basis sets and the accurate inclusion of electron correlation effects. A direct approach to…
Pole Expansion and Selected Inversion (PEXSI) is an efficient scheme for evaluating selected entries of functions of large sparse matrices as required e.g. in electronic structure algorithms. We show that the triangular factorizations…
This article empirically examines the computational cost of solving a known hard problem, graph clustering, using novel purpose-built computer hardware. We express the graph clustering problem as an intra-cluster distance or dissimilarity…
We present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use…
Targeting simulations on parallel hardware architectures, this paper presents computational kernels for efficient computations in mortar finite element methods. Mortar methods enable a variationally consistent imposition of coupling…
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…
In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework…
In sensor networks, it is not always practical to set up a fusion center. Therefore, there is need for fully decentralized clustering algorithms. Decentralized clustering algorithms should minimize the amount of data exchanged between…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
A primary objective of quantum computation is to efficiently simulate quantum physics. Scientifically and technologically important quantum Hamiltonians include those with spin-$s$, vibrational, photonic, and other bosonic degrees of…