Kohn-Sham inversion with mathematical guarantees

• URL: http://arxiv.org/abs/2409.04372v2
• Date: Mon, 03 Mar 2025 20:24:48 GMT
• Title: Kohn-Sham inversion with mathematical guarantees
• Authors: Michael F. Herbst, Vebjørn H. Bakkestuen, Andre Laestadius,
• Abstract summary: We use an exact Moreau-Yosida regularized formulation to obtain the exchange-correlation potential for periodic systems.<n>We reveal a profound connection between rigorous mathematical principles and efficient numerical implementation.<n>We develop a mathematically rigorous inversion algorithm which is demonstrated for representative bulk materials.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We use an exact Moreau-Yosida regularized formulation to obtain the exchange-correlation potential for periodic systems. We reveal a profound connection between rigorous mathematical principles and efficient numerical implementation, which marks the first computation of a Moreau-Yosida-based inversion for physical systems. We develop a mathematically rigorous inversion algorithm which is demonstrated for representative bulk materials, specifically bulk silicon, gallium arsenide, and potassium chloride. This inversion algorithm allows the construction of rigorous error bounds that we are able to verify numerically. This unlocks a new pathway to analyze Kohn-Sham inversion methods, which we expect in turn to foster mathematical approaches for developing approximate functionals.

Related papers

• Classical simulation of parity-preserving quantum circuits [0.0]
  We present a classical simulation method for fermionic quantum systems without loss of generality. We map such circuits to a fermionic tensor network and introduce a novel decomposition of non-Matchgate gates. Our algorithm significantly lowers resource requirements for simulating parity-preserving circuits while retaining high accuracy.
  arXiv  Detail & Related papers  (2025-04-27T17:42:39Z)
• Explicit near-optimal quantum algorithm for solving the advection-diffusion equation [0.0]
  An explicit quantum algorithm is proposed for modeling dissipative initial-value problems. We propose a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. The proposed algorithm can be used for modeling a wide class of nonunitary initial-value problems.
  arXiv  Detail & Related papers  (2025-01-19T19:03:29Z)
• Efficient Representation of Gaussian Fermionic Pure States in Non-Computational Bases [0.0]
  This paper introduces an innovative approach for representing Gaussian fermionic states, pivotal in quantum spin systems and fermionic models. We focus on transitioning these states from the conventional computational (sigmaz) basis to more complex bases, such as (phi, fracpi2, alpha) We present a novel algorithm that not only simplifies the basis transformation but also reduces computational complexity.
  arXiv  Detail & Related papers  (2024-03-05T19:43:33Z)
• Moment expansion method for composite open quantum systems including a damped oscillator mode [0.0]
  We develop a numerical method to compute the reduced density matrix of the target system and the low-order moments of the quadrature operators. The application to an optomechanical setting shows that the new method can compute the correlation functions accurately with a significant reduction in the computational cost.
  arXiv  Detail & Related papers  (2023-11-10T15:29:34Z)
• Deep Stochastic Mechanics [17.598067133568062]
  This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schr"odinger equation. Our method allows us to adapt to the latent low-dimensional structure of the wave function by sampling from the Markovian diffusion.
  arXiv  Detail & Related papers  (2023-05-31T09:28:03Z)
• Non-Parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence [65.63201894457404]
  We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of non-linear differential equations. The key idea essentially consists of fitting a RKHS-based approximation of the corresponding Fokker-Planck equation to such observations.
  arXiv  Detail & Related papers  (2023-05-24T20:43:47Z)
• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory [79.50644650795012]
  We propose a deep learning approach to solve Kohn-Sham Density Functional Theory (KS-DFT) We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity. In addition, we show that our approach enables us to explore more complex neural-based wave functions.
  arXiv  Detail & Related papers  (2023-03-01T10:38:10Z)
• Exploring the role of parameters in variational quantum algorithms [59.20947681019466]
  We introduce a quantum-control-inspired method for the characterization of variational quantum circuits using the rank of the dynamical Lie algebra. A promising connection is found between the Lie rank, the accuracy of calculated energies, and the requisite depth to attain target states via a given circuit architecture.
  arXiv  Detail & Related papers  (2022-09-28T20:24:53Z)
• Bayesian Recurrent Units and the Forward-Backward Algorithm [91.39701446828144]
  Using Bayes's theorem, we derive a unit-wise recurrence as well as a backward recursion similar to the forward-backward algorithm. The resulting Bayesian recurrent units can be integrated as recurrent neural networks within deep learning frameworks. Experiments on speech recognition indicate that adding the derived units at the end of state-of-the-art recurrent architectures can improve the performance at a very low cost in terms of trainable parameters.
  arXiv  Detail & Related papers  (2022-07-21T14:00:52Z)
• The Bold-Thin-Bold Diagrammatic Monte Carlo Method for Open Quantum Systems [0.0]
  We present two diagrammatic Monte Carlo methods for quantum systems coupled with harmonic baths. The underlying mechanism of the governing equations associated with the two methods lies in the recurrence relation of the path integrals. Compared with the algorithms therein, our methods show better performance in terms of computational efficiency and memory cost.
  arXiv  Detail & Related papers  (2022-05-22T18:17:23Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• 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)
• Efficient construction of tensor-network representations of many-body Gaussian states [59.94347858883343]
  We present a procedure to construct tensor-network representations of many-body Gaussian states efficiently and with a controllable error. These states include the ground and thermal states of bosonic and fermionic quadratic Hamiltonians, which are essential in the study of quantum many-body systems.
  arXiv  Detail & Related papers  (2020-08-12T11:30:23Z)
• Quantum Algorithm for Smoothed Particle Hydrodynamics [0.0]
  We present a quantum computing algorithm for the smoothed particle hydrodynamics (SPH) method. Error convergence is exponentially fast in the number of qubits. We extend the method to solve the one-dimensional advection and partial diffusion differential equations.
  arXiv  Detail & Related papers  (2020-06-11T18:28:24Z)

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.