Related papers: Optimization of Fragment State Spaces within the E…
Quadratic programming over orthogonal matrices encompasses a broad class of hard optimization problems that do not have an efficient quantum representation. Such problems are instances of the little noncommutative Grothendieck problem…
We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite…
We consider a model Hamiltonian for a dimer including all the electronic one- and two-body terms consistent with a single orbital per site, a free Einstein phonon term, and an electron-phonon coupling of the Holstein type. The bare…
We describe an algorithm that computes the ground state energy and correlation functions for 2-local Hamiltonians in which interactions between qubits are weak compared to single-qubit terms. The running time of the algorithm is polynomial…
Imposing additional constraints on low-rank optimization has garnered growing interest. However, the geometry of coupled constraints hampers the well-developed low-rank structure and makes the problem intricate. To this end, we propose a…
The configuration interaction (CI) method for calculating the exact eigenstates of a quantum-mechanical few-body system is problematic when applied to particles interacting through contact forces. In dimensions higher than one the approach…
The idea of using fragment embedding to circumvent the high computational scaling of accurate electronic structure methods while retaining high accuracy has been a long-standing goal for quantum chemists. Traditional fragment embedding…
This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to…
We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together…
This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for…
This paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate…
For one-dimensional systems with delta-contact interactions, the convergence of the exact-diagonalization method is tested with a basis of harmonic oscillator eigenfunctions with frequency $\Omega$ optimized through the minimization 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…
In this work, we present an efficiently computational approach for designing material micro-structures by means of topology optimization. The central idea relies on using the isogeometric analysis integrated with the parameterized level set…
In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…
We propose and test several tensor network based algorithms for reconstructing the ground state of an (unknown) local Hamiltonian starting from a random sample of the wavefunction amplitudes. These algorithms, which are based on completing…
Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…
We propose a versatile and efficient algorithmic framework for optimizing fermion-to-qubit mappings by generalizing the idea of randomized block coordinate descent. Our greedy approach, termed Randomized Subsystem Descent, iteratively…
The accurate first-principles description of strongly-correlated materials is an important and challenging problem in condensed matter physics. Ab initio downfolding has emerged as a way of deriving compressed many-body Hamiltonians that…
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be…