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In this work, multi-variable derivative-free optimization algorithms for unconstrained optimization problems are developed. A novel procedure for approximating the gradient of multi-variable objective functions based on non-commutative maps…
In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…
The growing interest in using x-ray spectroscopy for refined materials characterization calls for accurate electronic-structure theory to interpret x-ray near-edge fine structure. In this work, we propose an efficient and unified framework…
We present a second-order formulation of multi-reference algebraic diagrammatic construction theory [Sokolov, A. Yu. J. Chem. Phys. 2018, 149, 204113] for simulating photoelectron spectra of strongly correlated systems (MR-ADC(2)). The…
Analytic energy gradients are presented for a variational two-electron reduced-density-matrix-driven complete active space self-consistent field (v2RDM-CASSCF) procedure that employs the density-fitting (DF) approximation to the…
Multiconfiguration pair-density functional theory (MC-PFDT) has previously been applied successfully to carry out ground-state and excited-state calculations. However, because it includes no interaction between electronic states, MC-PDFT…
We report a new implementation of multireference algebraic diagrammatic construction theory (MR-ADC) for simulations of electron attachment and ionization in strongly correlated molecular systems (EA/IP-MR-ADC). Following our recent work on…
We consider monotone variational inequality (VI) problems in multi-GPU settings where multiple processors/workers/clients have access to local stochastic dual vectors. This setting includes a broad range of important problems from…
We introduce a quantum-inspired approximation algorithm for MaxCut based on low-depth Clifford circuits. We start by showing that the solution unitaries found by the adaptive quantum approximation optimization algorithm (ADAPT-QAOA) for the…
In the accompanying paper of arXiv:2505.00697, we have presented a generalized scheme of adaptive quantum gradient estimation (QGE) algorithm, and further proposed two practical variants which not only achieve doubly quantum enhancement in…
We propose a mixed-configuration approximation based on single-band impurity solvers to efficiently study nonequilibrium multi-orbital systems at moderate computational cost. In this work, we merge the approach with the so-called auxiliary…
We introduce two quantum algorithms for solving structured prediction problems. We first show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the…
The calibration of CALPHAD (CALculation of PHAse Diagrams) models involves the solution of a very challenging high-dimensional multiobjective optimization problem. Traditional approaches to parameter fitting predominantly rely on…
An efficient perturbational treatment of spin-orbit coupling within the framework of high-level multi-reference techniques has been implemented in the most recent version of the COLUMBUS quantum chemistry package, extending the existing…
Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the…
Configuration-interaction-type calculations on electronic and vibrational structure are often the method of choice for the reliable approximation of many-particle wave functions and energies. The exponential scaling, however, limits their…
Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational…
Policy gradient methods are among the most effective methods in challenging reinforcement learning problems with large state and/or action spaces. However, little is known about even their most basic theoretical convergence properties,…
Data representation techniques have made a substantial contribution to advancing data processing and machine learning (ML). Improving predictive power was the focus of previous representation techniques, which unfortunately perform rather…
We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…