Related papers: Automatic grid construction for few-body quantum m…
Application of multigrid solvers in shifted linear systems is studied. We focus on accelerating the rational approximation needed for simulating single flavor operators. This is particularly useful, in the case of twisted mass fermions for…
Utilization of a quantum system whose time-development is described by the nonlinear Schrodinger equation in the transformation of qubits would make it possible to construct quantum algorithms which would be useful in a large class of…
We consider a model dissipative quantum-mechanical system realized by coupling a quantum oscillator to a semi-infinite classical string which serves as a means of energy transfer from the oscillator to the infinity and thus plays the role…
Schrieffer-Wolff transformation is extensively used in quantum many-body physics to calculate the low energy effective Hamiltonian. It offers a perturbative method to understand the renormalization effects in the strong coupling regime of…
There is a growing interest in harnessing the potential of the Rydberg-atom system to address complex combinatorial optimization challenges. Here we present an experimental demonstration of how the quadratic unconstrained binary…
To improve the computational efficiencies of the real-space orbital-free density functional theory, this work develops a new single-grid solver by directly providing the closed-form solution to the inner iteration and using an improved…
An important topic in quantum information is the theory of error correction codes. Practical situations often involve quantum systems with states in an infinite dimensional Hilbert space, for example coherent states. Motivated by these…
The QMol-grid package provides a suite of routines for performing quantum-mechanical simulations in atomic and molecular systems, currently implemented in one spatial dimension. It supports ground- and excited-state calculations for the…
Given a multigrid procedure for linear systems with coefficient matrices $A_n$, we discuss the optimality of a related multigrid procedure with the same smoother and the same projector, when applied to properly related algebraic problems…
Implementing high-fidelity quantum control and reducing the effect of the coupling between a quantum system and its environment is a major challenge in developing quantum information technologies. Here, we show that there exists a…
Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small number of pairs of the constituents directly interact. Motivated by advances in…
We present a new computational framework combining coarse-graining techniques with bootstrap methods to study quantum many-body systems. The method efficiently computes rigorous upper and lower bounds on both zero- and finite-temperature…
Unfitted finite element methods have emerged as a popular alternative to classical finite element methods for the solution of partial differential equations and allow modeling arbitrary geometries without the need for a boundary-conforming…
We present a new kind of basis function for discretizing the Schr\"odinger equation in electronic structure calculations, called a gausslet, which has wavelet-like features but is composed of a sum of Gaussians. Gausslets are placed on a…
We aim to explore a more efficient way to simulate few-body dynamics on quantum computers. Instead of mapping the second quantization of the system Hamiltonian to qubit Pauli gates representation via the Jordan-Wigner transform, we propose…
Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…
It is often computationally advantageous to model space as a discrete set of points forming a lattice grid. This technique is particularly useful for computationally difficult problems such as quantum many-body systems. For reasons of…
We present a fully grid-based approach for solving Hartree-Fock and all-electron Kohn-Sham equations based on low-rank approximation of three-dimensional electron orbitals. Due to the low-rank structure the total complexity of the algorithm…
Restricted Boltzmann Machines (RBM) are simple statistical models defined on a bipartite graph which have been successfully used in studying more complicated many-body systems, both classical and quantum. In this work, we exploit the…
The numerical matrix Numerov algorithm is used to solve the stationary Schr\"odinger equation for central Coulomb potentials. An efficient approximation for accelerating the convergence is proposed. The Numerov method is error-prone if the…