59 citations · 197 across the 26 of their papers we have counts for
27 papers
Reduced scaling implementation of the coupled cluster-based static embedding method, MPCC with density fitting
Avijit Shee, Fabian M. Faulstich, K. Birgitta Whaley +2
An improved algorithm to implement our previously proposed static quantum embedding method MPCC (J. Chem. Phys. 161, 164107 (2024)) is presented. It uses the density-fitting (DF) a…
A robust and efficient solver for coupled cluster equations
Chanaka D. M. Mudiyanselage, Kangbo Li, Fabian M. Faulstich
The coupled-cluster (CC) equations are most frequently solved via fixed-point (FP) iterations. However, when formulated in a non-canonical gauge, as in local correlation CC, the FP…
A quadratic Grassmann manifold optimization problem arising from quantum embedding methods
Thomas Ayral, Eric Cancès, Fabian M. Faulstich +2
This article presents a mathematical analysis and numerical strategies for solving the optimization problem of minimizing the quadratic function $J(P) = \text{Tr}(BP)- \frac{1}{2}…
On the Coupled Cluster Doubles Truncation Variety of Four Electrons
Fabian M. Faulstich, Vincenzo Galgano, Elke Neuhaus +1
We extend recent algebro-geometric results for coupled cluster theory of quantum many-body systems to the truncation varieties arising from the doubles approximation (CCD), focusin…
A CPD-enabled low-scaling environment solver in a coupled cluster based static quantum embedding theory
Karl Pierce, Muhammad Talha Aziz, Avijit Shee +1
We incorporate a canonical polyadic decomposition (CPD) based low-level solver as a means to accelerate the environment-level solver for the recently developed MPCC embedding frame…
Consistent inclusion of triple substitutions within a coupled cluster based static quantum embedding theory
Avijit Shee, Fabian M. Faulstich, K. Birgitta Whaley +2
We incorporate a solver for the fragment problem with accuracy beyond coupled cluster singles and doubles (CCSD) into the previously proposed static embedding framework, MPCC. To t…
Algebraic Geometry for Spin-Adapted Coupled Cluster Theory
Fabian M. Faulstich, Svala Sverrisdóttir
We develop and numerically analyze an algebraic-geometric framework for spin-adapted coupled-cluster (CC) theory. Since the electronic Hamiltonian is SU(2)-invariant, physically re…
From Promise to Practice: Benchmarking Quantum Chemistry on Quantum Hardware
Osama M. Raisuddin, Haimeng Zhang, Mario Motta +1
We provide a systematic evaluation of the sample-based quantum diagonalization (SQD) method for electronic structure based on the W4-11 thermochemistry dataset, comprising 124 tota…
New perspectives on Density-Matrix Embedding Theory
Alicia Negre, Fabian Faulstich, Raehyun Kim +3
Quantum embedding methods enable the study of large, strongly correlated quantum systems by (usually self-consistent) decomposition into computationally manageable subproblems, in…
Exploring Ground and Excited States via Single Reference Coupled-Cluster Theory and Algebraic Geometry
Svala Sverrisdóttir, Fabian M. Faulstich
The exploration of the root structure of coupled cluster equations holds both foundational and practical significance for computational quantum chemistry. This study provides insig…
A static quantum embedding scheme based on coupled cluster theory
Avijit Shee, Fabian M. Faulstich, Birgitta Whaley +2
We develop a static quantum embedding scheme that utilizes different levels of approximations to coupled cluster (CC) theory for an active fragment region and its environment. To r…
Augmented Lagrangian method for coupled-cluster
Fabian M. Faulstich, Yuehaw Khoo, Kangbo Li
We propose to improve the convergence properties of the single-reference coupled cluster (CC) method through an augmented Lagrangian formalism. The conventional CC method changes a…
Recent mathematical advances in coupled cluster theory
Fabian M. Faulstich
This article presents an in-depth educational overview of the latest mathematical developments in coupled cluster (CC) theory, beginning with Schneider's seminal work from 2009 tha…
Algebraic Varieties in Quantum Chemistry
Fabian Faulstich, Bernd Sturmfels, Svala Sverrisdóttir
We develop algebraic geometry for coupled cluster (CC) theory of quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schrödinger equation…
Homotopy continuation methods for coupled-cluster theory in quantum chemistry
Fabian M. Faulstich, Andre Laestadius
Homotopy methods have proven to be a powerful tool for understanding the multitude of solutions provided by the coupled-cluster polynomial equations. This endeavor has been pioneer…
Some mathematical insights on Density Matrix Embedding Theory
Eric Cancès, Fabian M. Faulstich, Alfred Kirsch +2
This article provides the first mathematical analysis of the Density Matrix Embedding Theory (DMET) method. We prove that, under certain assumptions, (i) the exact ground-state den…
The -diagnostic -- an a posteriori error assessment for single-reference coupled-cluster methods
Fabian M. Faulstich, Håkon E. Kristiansen, Mihaly A. Csirik +3
We propose a novel a posteriori error assessment for the single-reference coupled-cluster (SRCC) method called the -diagnostic. We provide a derivation of the -diagnostic tha…
Interacting models for twisted bilayer graphene: a quantum chemistry approach
Fabian M. Faulstich, Kevin D. Stubbs, Qinyi Zhu +7
The nature of correlated states in twisted bilayer graphene (TBG) at the magic angle has received intense attention in recent years. We present a numerical study of an interacting…
Coupled cluster theory: Towards an algebraic geometry formulation
Fabian M. Faulstich, Mathias Oster
Coupled cluster theory produced arguably the most widely used high-accuracy computational quantum chemistry methods. Despite the approach's overall great computational success, its…
On the pure state -representability of density matrix embedding theory
Fabian M. Faulstich, Raehyun Kim, Zhi-Hao Cui +3
Density matrix embedding theory (DMET) formally requires the matching of density matrix blocks obtained from high-level and low-level theories, but this is sometimes not achievable…
Discontinuous Galerkin method with Voronoi partitioning for Quantum Simulation of Chemistry
Fabian M. Faulstich, Xiaojie Wu, Lin Lin
Molecular orbitals based on the linear combination of Gaussian type orbitals are arguably the most employed discretization in quantum chemistry simulations, both on quantum and cla…
One-Dimensional Lieb-Oxford Bounds
Andre Laestadius, Fabian M Faulstich
We investigate and prove Lieb-Oxford bounds in one dimension by studying convex potentials that approximate the ill-defined Coulomb potential. A Lieb-Oxford inequality establishes…
Discontinuous Galerkin discretization for quantum simulation of chemistry
Jarrod R. McClean, Fabian M. Faulstich, Qinyi Zhu +5
Methods for electronic structure based on Gaussian and molecular orbital discretizations offer a well established, compact representation that forms much of the foundation of corre…
Numerical and Theoretical Aspects of the DMRG-TCC Method Exemplified by the Nitrogen Dimer
Fabian M. Faulstich, Mihály Máté, Andre Laestadius +8
In this article, we investigate the numerical and theoretical aspects of the coupled-cluster method tailored by matrix-product states. We investigate chemical properties of the use…