Related papers: Real-space Hamiltonian method for low-dimensional …
We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd,…
We present a quantum algorithm for simulating rovibrational Hamiltonians on fault-tolerant quantum computers. The method integrates exact curvilinear kinetic energy operators and general-form potential energy surfaces expressed in a hybrid…
We present a new subspace iteration method for computing low-lying eigenpairs (excited states) of high-dimensional quantum many-body Hamiltonians with nearest neighbor interactions on two-dimensional lattices. The method is based on a new…
The Hamiltonian Monte Carlo method generates samples by introducing a mechanical system that explores the target density. For distributions on manifolds it is not always simple to perform the mechanics as a result of the lack of global…
The spurious states found in numerical implementations of envelope function models for semiconductor heterostructures and nanostructures are artifacts of the use of the centered-difference formula. They are readily removed by employing a…
Highly excited vibrational states of an isolated molecule encode the vibrational energy flow pathways in the molecule. Recent studies have had spectacular success in understanding the nature of the excited states mainly due to the extensive…
Using quantum systems to efficiently solve quantum chemistry problems is one of the long-sought applications of near-future quantum technologies. In a recent work, ultra-cold fermionic atoms have been proposed for these purposes by showing…
To overcome the limitations of existing algorithms for solving self-bound quantum many-body problems -- such as those encountered in nuclear and particle physics -- that access only a restricted subset of energy levels and provide limited…
We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use…
We provide a novel approach for characterization of quantum Hamiltonian systems via utilizing a single measurement device. Specifically, we demonstrate how external quantum correlations can be used for Hamiltonian identification tasks. We…
One-neutron halo nuclei, composed by a weakly-bound particle coupled to a core nucleus, are studied within a particle-plus-core model. A semi-microscopic method to generate the two-body Hamiltonian of such a system, including core…
We propose a linearly implicit structure-preserving numerical method for semilinear Hamiltonian systems with polynomial nonlinearities, combining Kahan's method and exponential integrator. This approach efficiently balances computational…
Advantages of using a low-energy effective theory to study bound state properties are briefly discussed, and a nonperturbative implementation of such an effective theory is described within the context of nonrelativistic quantum mechanics.…
These lecture notes introduce some simple effective Hamiltonians (also known as semi-empirical models) that have widespread applications to solid state and molecular systems. They are aimed as an introduction to a beginning graduate…
We discuss how to construct a tight binding model Hamiltonan for the simplest possible solid, composed of hydrogen-like atoms. A single orbital per atom is not sufficient because the on-site electron-electron repulsion mixes in higher…
We introduce a generic method for computing groundstates that is applicable to a wide range of spatially anisotropic 2D many-body quantum systems. By representing the 2D system using a low-energy 1D basis set, we obtain an effective 1D…
We describe a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods provide effective convergence acceleration and preconditioning on all…
An approximate diagonalization method is proposed that combines exact diagonalization and perturbation expansion to calculate low energy eigenvalues and eigenfunctions of a Hamiltonian. The method involves deriving an effective Hamiltonian…
We present a detailed formalism of the microscopic particle-rotor model for hypernuclear low-lying states based on a covariant density functional theory. In this method, the hypernuclear states are constructed by coupling a hyperon to…
Several methodologies are developed for large-scale atomistic simulations with fully quantum mechanical description of electron systems. The important methodological concepts are (i) generalized Wannier state, (ii) Krylov subspace and (iii)…