Related papers: Factorization in large-scale many-body calculation…
In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…
We consider energetics and structural properties of a many particle system in one dimension with pairwise contact interactions confined in a parabolic external potential. To render the problem analytically solvable, we use the harmonic…
A self-consistent many-body approach is proposed to build a first-principles crystal field theory, where crystal field parameters are calculated ab initio. Many-body theory is used to write the energy of the interacting system as a function…
One of the useful and practical methods for solving quantum-mechanical many-body systems is to recast the full problem into a form of the effective interaction acting within a model space of tractable size. Many of the effective-interaction…
We present a scalable framework for accurately modeling many-body interactions in surface-code quantum processor units (QPUs). Combining a concise diagrammatic formalism with high-precision numerical methods, our approach efficiently…
The integrability of one dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) $\delta$-function interaction there is another…
The partitioning of a system model will condition the structure of the controller as well as its design. In order to partition a system model, one has to know what states and inputs to group together to define subsystem models. For a given…
Many matrices associated with fast transforms posess a certain low-rank property characterized by the existence of several block partitionings of the matrix, where each block is of low rank. Provided that these partitionings are known,…
We examine the relation between inter-particle interactions and real-time equilibration in one-dimensional lattice systems with hard-core constraints. Focusing on the roles of interactions, our results demonstrate that in the presence of…
Group theoretic method for the systematic study of multi-quark states is developed. The calculation of matrix elements of many body Hamiltonian is simplified by transforming the physical bases (quark cluster bases) to symmetry bases (group…
The simulation of open quantum systems coupled to a reservoir through multiple channels remains a substantial challenge. This kind of open quantum system arises when considering the radiationless decay of excited states that are coupled to…
Recent successes in Monte Carlo methods for simulating fermionic quantum impurity models have been based on diagrammatic resummation techniques, but are restricted by the need to sum over factorially large classes of diagrams individually.…
Factorization Machine (FM) is a widely used supervised learning approach by effectively modeling of feature interactions. Despite the successful application of FM and its many deep learning variants, treating every feature interaction…
In the age of big data and interpretable machine learning, approaches need to work at scale and at the same time allow for a clear mathematical understanding of the method's inner workings. While there exist inherently interpretable…
Characterization of qubit couplings in many-body quantum systems is essential for benchmarking quantum computation and simulation. We propose a tomographic measurement scheme to determine all the coupling terms in a general many-body…
Achieving an accurate description of fermionic systems typically requires considerably many more orbitals than fermions. Previous resource analyses of quantum chemistry simulation often failed to exploit this low fermionic number…
A variational formulation for the calculation of interacting fermion systems based on the density-matrix functional theory is presented. Our formalism provides for a natural integration of explicit many-particle effects into standard…
Quantum Monte Carlo (QMC) methods are one of the most important tools for studying interacting quantum many-body systems. The vast majority of QMC calculations in interacting fermion systems require a constraint to control the sign problem.…
We present a novel input scheme for general second-quantized Hamiltonians of relativistic or non-relativistic many-fermion systems. This input scheme incorporates the fermionic anticommutation relations, particle number variations, and…
Matrix factorization is a very common machine learning technique in recommender systems. Bayesian Matrix Factorization (BMF) algorithms would be attractive because of their ability to quantify uncertainty in their predictions and avoid…