Related papers: Implementing scalable matrix-vector products for t…
Exact diagonalization is a powerful numerical method to study isolated quantum many-body systems. This paper provides a review of numerical algorithms to diagonalize the Hamiltonian matrix. Symmetry and the conservation law help us perform…
The increasing number of processing elements and decreas- ing memory to core ratio in modern high-performance platforms makes efficient strong scaling a key requirement for numerical algorithms. In order to achieve efficient scalability on…
We present a parallel computation scheme based on the Arnoldi algorithm for exact diagonalization of quantum-electron models. It contains a selective data transferring method and distributed storage format for efficient computing of the…
The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…
We present algorithmic improvements for fast and memory-efficient use of discrete spatial symmetries in Exact Diagonalization computations of quantum many-body systems. These techniques allow us to work flexibly in the reduced basis of…
For many decades, quantum chemical method development has been dominated by algorithms which involve increasingly complex series of tensor contractions over one-electron orbital spaces. Procedures for their derivation and implementation…
Quantum circuit simulations play a critical role in bridging the gap between theoretical quantum algorithms and their practical realization on physical quantum hardware, yet they face computational challenges due to the exponential growth…
The implicit 2D3V particle-in-cell (PIC) code developed to study the interaction of ultrashort pulse lasers with matter [G. M. Petrov and J. Davis, Computer Phys. Comm. 179, 868 (2008); Phys. Plasmas 18, 073102 (2011)] has been parallelized…
This paper presents an efficient technique for matrix-vector and vector-transpose-matrix multiplication in distributed-memory parallel computing environments, where the matrices are unstructured, sparse, and have a substantially larger…
Boundary value problems involving elliptic PDEs such as the Laplace and the Helmholtz equations are ubiquitous in mathematical physics and engineering. Many such problems can be alternatively formulated as integral equations that are…
Tensor network methods as presented in our open source Matrix Product States software have opened up the possibility to study many-body quantum physics in one and quasi-one-dimensional systems in an easily accessible package similar to…
In quantum embedding theories, a quantum many-body system is divided into localized clusters of sites which are treated with an accurate `high-level' theory and glued together self-consistently by a less accurate `low-level' theory at the…
Exact diagonalization (ED) is one of the most reliable and established numerical methods of quantum many-body theory. The main limiting factor of the method is the exponential scaling of Hilbert space dimension with system size.…
We evaluate optimized parallel sparse matrix-vector operations for two representative application areas on widespread multicore-based cluster configurations. First the single-socket baseline performance is analyzed and modeled with respect…
In this paper we describe, implement, and test the performance of distributed memory simulations of quantum circuits on the MSU Laconia Top500 supercomputer. Using OpenMP and MPI hybrid parallelization, we first use a distributed…
Polynomially filtered exact diagonalization method (POLFED) for large sparse matrices is introduced. The algorithm finds an optimal basis of a subspace spanned by eigenvectors with eigenvalues close to a specified energy target by a…
Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…
The integration of quantum chemical methods with high-performance computing is indispensable for handling large systems with modest accuracy or even small systems but with high accuracy. Continuing with the unified implementation of…
The main computing tasks of a finite element code(FE) for solving partial differential equations (PDE's) are the algebraic system assembly and the iterative solver. This work focuses on the first task, in the context of a hybrid MPI+X…
This article describes algorithms for the hybrid parallelization and SIMD vectorization of molecular dynamics simulations with short-range forces. The parallelization method combines domain decomposition with a thread-based parallelization…