Homotopy continuation methods for coupled-cluster theory in quantum chemistry

• URL: http://arxiv.org/abs/2306.13299v1
• Date: Fri, 23 Jun 2023 05:25:45 GMT
• Title: Homotopy continuation methods for coupled-cluster theory in quantum chemistry
• Authors: Fabian M. Faulstich and Andre Laestadius
• Abstract summary: Homotopy methods have proven to be a powerful tool for understanding the multitude of solutions provided by the coupled-cluster equations. New interest in these approaches has emerged using both topological degree theory and algebraically oriented tools.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 pioneered by quantum chemists that have undertaken both elaborate numerical as well as mathematical investigations. Recently, from the perspective of applied mathematics, new interest in these approaches has emerged using both topological degree theory and algebraically oriented tools. This article provides an overview of describing the latter development.

Related papers

• Lie groups for quantum complexity and barren plateau theory [0.0]
  We introduce the theory of Lie groups and their algebras to analyze two fundamental problems in quantum computing.<n> Firstly, we describe the geometric formulation of quantum computational complexity.<n> Secondly, we deal with the barren plateau phenomenon in Variational Quantum Algorithms.
  arXiv  Detail & Related papers  (2025-07-30T11:46:09Z)
• Quantum Many-Body Linear Algebra, Hamiltonian Moments, and a Coupled Cluster Inspired Framework [0.0]
  We introduce a coupled-cluster inspired framework to produce approximate Hamiltonian moments. We demonstrate its application in various linear algebra algorithms for ground state estimation.
  arXiv  Detail & Related papers  (2025-03-28T23:04:33Z)
• Recent Advances in Semiclassical Methods Inspired by Supersymmetric Quantum Mechanics [0.0]
  Recent research has demonstrated a deep connection between supersymmetric quantum mechanics and the exactness of semiclassical methods. Specifically, the mathematical form of conventional shape-invariant potentials guarantees exactness in several related situations.
  arXiv  Detail & Related papers  (2024-08-27T21:57:02Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Symmetry breaking and restoration for many-body problems treated on quantum computers [0.0]
  This thesis explores the application of the Symmetry-Breaking/Symmetry-Restoration methodology on quantum computers. It involves intentionally breaking and restoring the symmetries of the wave function ansatz at different stages of the variational search for the ground state. In the final part, hybrid quantum-classical techniques were introduced to extract an approximation of the low-lying spectrum of a Hamiltonian.
  arXiv  Detail & Related papers  (2023-10-27T09:12:38Z)
• Higher-order topological kernels via quantum computation [68.8204255655161]
  Topological data analysis (TDA) has emerged as a powerful tool for extracting meaningful insights from complex data. We propose a quantum approach to defining Betti kernels, which is based on constructing Betti curves with increasing order.
  arXiv  Detail & Related papers  (2023-07-14T14:48:52Z)
• Coupled-Cluster Theory Revisited. Part II: Analysis of the single-reference Coupled-Cluster equations [0.0]
  We analyze the nonlinear equations of the single-reference Coupled-Cluster method using topological degree theory. For the truncated Coupled-Cluster method, we derive an energy error bound for approximate eigenstates of the Schrodinger equation.
  arXiv  Detail & Related papers  (2023-03-27T11:21:19Z)
• Algebraic structures underlying quantum independences : Theory and Applications [0.0]
  We reconcile two approaches to quantum probabilities: one physical and coming directly from quantum mechanics, the other more algebraic. We provide a unified picture introducing jointly to several fields of applications, many of which are probably not all familiar. We take the opportunity to present various results obtained recently in the various noncommutative probability theories.
  arXiv  Detail & Related papers  (2022-10-17T17:12:04Z)
• Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion [68.8204255655161]
  We present a methodology for simulating multi-dimensional electronic spectra of molecular aggregates with coupling electronic excitation to a structured environment. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space but with the same noise.
  arXiv  Detail & Related papers  (2022-07-06T15:30:38Z)
• A Discrete Variational Derivation of Accelerated Methods in Optimization [68.8204255655161]
  We introduce variational which allow us to derive different methods for optimization. We derive two families of optimization methods in one-to-one correspondence. The preservation of symplecticity of autonomous systems occurs here solely on the fibers.
  arXiv  Detail & Related papers  (2021-06-04T20:21:53Z)
• Coupled-Cluster Theory Revisited. Part I: Discretization [0.0]
  We describe the discretization schemes involved in Coupled-Cluster methods using graph-based concepts. We derive the single-reference and the Jeziorski-Monkhorst multireference Coupled-Cluster equations in a unified and rigorous manner.
  arXiv  Detail & Related papers  (2021-05-19T16:35:49Z)
• Quantum simulation of gauge theory via orbifold lattice [47.28069960496992]
  We propose a new framework for simulating $textU(k)$ Yang-Mills theory on a universal quantum computer. We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories.
  arXiv  Detail & Related papers  (2020-11-12T18:49:11Z)
• Quantum-Inspired Algorithms from Randomized Numerical Linear Algebra [53.46106569419296]
  We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression. We argue that the previous quantum-inspired algorithms for these problems are doing leverage or ridge-leverage score sampling in disguise.
  arXiv  Detail & Related papers  (2020-11-09T01:13:07Z)
• Theoretical methods for ultrastrong light-matter interactions [91.3755431537592]
  This article reviews theoretical methods developed to understand cavity quantum electrodynamics in the ultrastrong-coupling regime. The article gives a broad overview of the recent progress, ranging from analytical estimate of ground-state properties to proper computation of master equations. Most of the article is devoted to effective models, relevant for the various experimental platforms in which the ultrastrong coupling has been reached.
  arXiv  Detail & Related papers  (2020-01-23T18:09:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.