Explore advanced numerical methods and algorithms for large-scale quantum mechanical simulations through this comprehensive workshop series from the Institute for Pure & Applied Mathematics. Delve into the computational challenges of simulating very large quantum systems, including solving high-dimensional linear and nonlinear systems of equations and eigenvalue problems that require massive parallelism and rank-reduction methods. Learn about critical error analysis techniques for quantum system simulations, covering model errors, discretization errors, algorithmic errors, implementation errors, and computing errors. Discover how to quantify these error sources to provide guaranteed error bars for simulation results and optimize computational parameters for target accuracy. Examine cutting-edge research presentations covering transport coefficient estimation from molecular dynamics, error bounds in planewave electronic structure calculations, uncertainty quantification in quantum chemical methods, and convergent approximations of Kohn-Sham orbitals. Study contracted quantum eigensolvers, mathematical approaches for predicting superconductors, acceleration techniques for quantum mechanical systems, and black-box optimization of self-consistent field wavefunctions. Investigate planewave approximations for quantum incommensurate systems, sparse compression of matrix product operators, electronic structure calculations of chiral matter, and multi-center decomposition of molecular densities. Master numerical methods for scattering and resonance properties, basis set convergence curing techniques, reference data generation in DFT simulations, and fast algorithms for full configuration interaction excited states. Understand finite-size error corrections in energy calculations, large-scale hybrid DFT functionals, basis-set corrections based on density-functional theory, low rank approximations in electron excitation calculations, and development of a posteriori error estimates for coupled cluster equations.

Syllabus

Stefano Baroni - estimate transport coefficients from short equilibrium molecular-dynamic simulation
Genevieve Dusson - Error bounds for properties in planewave electronic structure calculations
Markus Reiher - Uncertainty Quantification of Quantum Chemical Methods - IPAM at UCLA
Xiaoying Dai - Convergent orthogonality preserving appoximations of the Kohn-Sham orbitals
David Mazziotti - Contracted Quantum Eigensolver for the Quantum Simulation of Many-electron Systems
Julia Contreras-García - Math-chimie: developing approaches for predicting new superconductors
Benjamin Stamm - Acceleration of quantum mechanical systems by exploiting similarity - IPAM at UCLA
Filippo Lipparini - Black-box optimization of self-consistent field wavefunction, closed/open shells
Huajie Chen - Convergence of the Planewave Approximations for Quantum Incommensurate Systems
Mi-Song Dupuy - Sparse and symmetry-preserving compression of matrix product operators
Amartya Banerjee - Electronic Structure Calculations of Chiral Matter - IPAM at UCLA
Virginie Ehrlacher - Multi-center decomposition of molecular densities: a mathematical perspective
Antoine Levitt - Numerical methods for scattering and resonance properties in molecules and solids
Emmanuel Giner - Curing basis set convergence of WFT w/ DFT: overview of framework and some results
Francois Gygi - Generating Reference Data and Controlling Accuracy in DFT and Hybrid DFT Simulations
Yingzhou Li - Fast Algorithms for FCI excited states - IPAM at UCLA
Xin Xing - Finite-size error and its correction in energy calculations for periodic systems
Lin Lin - Large scale hybrid DFT functionals: fast algorithms and finite-size effects - IPAM at UCLA
Julien Toulouse - Basis-set correction based on density-functional theory - IPAM at UCLA
Chao Yang - Low rank approximation in electron excitation calculations - IPAM at UCLA
Muhammad Hassan - Development of a posteriori error estimates for the coupled cluster equations