Related papers: Parallel exact diagonalization solver for quantum-…
An efficient parallelization approach to simulate optical properties of ensembles of quantum emitters in realistic electromagnetic environments is considered. It relies on balancing computing load of utilized processors and is built into…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
Numerical exact diagonalization is the ultimate method of choice in order to discuss static, dynamic, and thermodynamic properties of quantum systems. In this article we consider Heisenberg spin-systems and extend the range of applicability…
It is significant and challenging to solve eigenvalue problems of partial differential operators when many highly accurate eigenpair approximations are required. The adaptive finite element discretization based parallel orbital-updating…
We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…
We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modification of a diagonal matrix. The algorithm computes each eigenvalue and all components of the corresponding eigenvector with…
Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements. Among various approaches, quantum annealing methods effectively…
We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of the dynamic mode decomposition algorithm used in diverse fields such as fluid…
We have used exact numerical diagonalization to study the excitation spectrum and the dynamic spin correlations in the $s=1/2$ next-next-nearest neighbor Heisenberg antiferromagnet on the square lattice, with additional 4-spin ring exchange…
Parallelism of tight-binding molecular dynamics simulations is presented by means of the order-N electronic structure theory with the Wannier states, recently developed (J. Phys. Soc. Jpn. 69,3773 (2000)). An application is tested for…
Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…
We provide algorithms for efficiently addressing quantum memory in parallel. These imply that the standard circuit model can be simulated with low overhead by the more realistic model of a distributed quantum computer. As a result, the…
We present enhancements to the computational efficiency of exact exchange calculations using the density matrix and local support functions. We introduce a numerical method which avoids the explicit calculation the four-center two-electron…
An extremely scalable linear-algebraic algorithm was developed for quantum material simulation (electronic state calculation) with 10$^8$ atoms or 100-nm-scale materials. The mathematical foundation is generalized shifted linear equations…
A one-dimensional model of electrons locally coupled to spin-1/2 degrees of freedom is studied by numerical techniques. The model is one in the class of $dynamic$ $Hubbard$ $models$ that describe the relaxation of an atomic orbital upon…
We present an algorithm for the solution of a simultaneous space-time discretization of linear parabolic evolution equations with a symmetric differential operator in space. Building on earlier work, we recast this discretization into a…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
We study and exactly solve the two-photon and k-photon Jaynes-Cummings models by using a novelty algebraic method. This algebraic method is based on the Pauli matrices realization and the tilting transformation of the $SU(2)$ group and let…
We parallelize density-matrix renormalization group to directly extend it to 2-dimensional ($n$-leg) quantum lattice models. The parallelization is made mainly on the exact diagonalization for the superblock Hamiltonian since the part…
An alternating direction method of multipliers (ADMM) solver is described for optimal resource allocation problems with separable convex quadratic costs and constraints and linear coupling constraints. We describe a parallel implementation…