Related papers: A conjugate gradient method for electronic structu…
In atomic, molecular, and nuclear physics, the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states. Here, we propose a novel implementation of this method based on the gradient optimization…
Estimating the ground-state energy of Hamiltonians is a fundamental task for which it is believed that quantum computers can be helpful. Several approaches have been proposed toward this goal, including algorithms based on quantum phase…
We find the ground-state energy of the Ising model using the Cascaded Variational Quantum Eigensolver (CVQE) algorithm with the Guided-Sampling Ansatz (GSA) using up to 63 qubits on a quantum computer. We study a heavy-hex lattice to match…
Efficient methods are proposed, for computing integrals appeaing in electronic structure calculations. The methods consist of two parts: the first part is to represent the integrals as contour integrals and the second one is to evaluate the…
Methods exhibiting linear scaling with respect to the size of the system, so called O(N) methods, are an essential tool for the calculation of the electronic structure of large systems containing many atoms. They are based on algorithms…
We compute the ground state energy of two atoms in a one-dimensional geometry of a harmonic optical trap. We obtain a dependence of the energy on a one-dimensional scattering length, which corresponds to various strengths of the interaction…
Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already for few-atom systems. In this work, we introduce a variational quantum…
This paper analyses the GW method for finite electronic systems. In a first step, we provide a mathematical framework for the usual one-body operators that appear naturally in many-body perturbation theory. We then discuss the GW equations…
In this paper, we propose a Distributed Accumulated Newton Conjugate gradiEnt (DANCE) method in which sample size is gradually increasing to quickly obtain a solution whose empirical loss is under satisfactory statistical accuracy. Our…
Variational Quantum Eigensolvers (VQEs) represent a promising approach to computing molecular ground states and energies on modern quantum computers. These approaches use a classical computer to optimize the parameters of a trial wave…
This paper proposes a conjugate-gradient-based Adam algorithm blending Adam with nonlinear conjugate gradient methods and shows its convergence analysis. Numerical experiments on text classification and image classification show that the…
We have applied the Finite Element Method to the self-consistent electronic structure calculations of molecules and solids for the first time. In this approach all the calculations are performed in "real space" and the use of non-uniform…
A novel Gaussian-Sinc mixed basis set for the calculation of the one-electron electronic structure within a uniform magnetic field in three dimensions is presented. The one-electron system is used to demonstrate the utility of this new…
This Paper conducts a thorough simulation study to assess the effectiveness of various acceleration techniques designed to enhance the conjugate gradient algorithm, which is used for solving large linear systems to accelerate Bayesian…
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…
We investigate Riemannian gradient flows for preparing ground states of a desired Hamiltonian on a quantum device. We show that the number of steps of the corresponding Riemannian gradient descent (RGD) algorithm that prepares a ground…
Estimating ground state energies of many-body Hamiltonians is a central task in many areas of quantum physics. In this work, we give quantum algorithms which, given any $k$-body Hamiltonian $H$, compute an estimate for the ground state…
Force-gradient decomposition methods are used to improve the energy preservation of symplectic schemes applied to Hamiltonian systems. If the potential is composed of different parts with strongly varying dynamics, this multirate potential…
Variational algorithms are promising candidates to be implemented on near-term quantum computers. The variational quantum eigensolver (VQE) is a prominent example, where a parametrized trial state of the quantum mechanical wave function is…
Instanton theory is an established method to calculate rate constants of chemical reactions including atom tunneling. Technical and methodological improvements increased its applicability. Still, a large number of energy and gradient…