Related papers: Improved recursive Green's function formalism for …
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function ($G$) framework. This approach is…
Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-form expression necessitates surrogate modeling to guide the…
Non-equilibrium Green's function theory and related methods are widely used to describe transport phenomena in many-body systems, but they often require a costly inversion of a large matrix. We show here that the shift-invert Lanczos method…
The evaluation of elastodynamic Green's functions across numerous source-receiver locations, frequencies, and material properties, particularly in the context of parametric studies or boundary element computations, is computationally…
At low energies, the microscopic characteristics and changes of physical systems as viewed at different distance scales are described by universal scale invariant properties investigated by the Renormalization Group (RG) apparatus, an…
In this work, we propose a quantum unitary downfolding formalism based on the driven similarity renormalization group (QDSRG) that may be combined with quantum algorithms for both noisy and fault-tolerant hardware. The QDSRG is a classical…
We study the nonlinear elastic quantum electronic transport properties of nanoscopic devices using the Nonequilibrium Green's function (NEGF) method. The Green's function method allows us to expand the $I-V$ characteristics of a given…
This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…
Accurate electronic structure calculations are essential in modern materials science, but strongly correlated systems pose a significant challenge due to their computational cost. Traditional methods, such as complete active space…
Recovering a low rank matrix from a subset of its entries, some of which may be corrupted, is known as the robust matrix completion (RMC) problem. Existing RMC methods have several limitations: they require a relatively large number of…
Distortion Risk Measures (DRMs) capture risk preferences in decision-making and serve as general criteria for managing uncertainty. This paper proposes gradient descent algorithms for DRM optimization based on two dual representations: the…
Gradient Boosting Machine (GBM) introduced by Friedman is a powerful supervised learning algorithm that is very widely used in practice---it routinely features as a leading algorithm in machine learning competitions such as Kaggle and the…
We present a detailed comparison of three different methods designed to tackle nonequilibrium quantum transport, namely the functional renormalization group (fRG), the time-dependent density matrix renormalization group (tDMRG), and the…
Recently, we have developed a formalism to evaluate QCD loop diagrams with a single virtual gluon using a running coupling constant at the vertices. This corresponds to an all-order resummation of certain terms (the so-called renormalon…
The problem of the microscopic description of excited states of the even-even open-shell atomic nuclei is considered. A model is formulated which allows one to go beyond the quasiparticle random phase approximation. The physical content of…
Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…
A novel parallel hybrid quantum-classical algorithm for the solution of the quantum-chemical ground-state energy problem on gate-based quantum computers is presented. This approach is based on the reduced density-matrix functional theory…
We develop a density-matrix renormalization group (DMRG) algorithm for the simulation of quantum circuits. This algorithm can be seen as the extension of time-dependent DMRG from the usual situation of hermitian Hamiltonian matrices to…
In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…