Heat semigroup representation of Laplacian

• URL: http://arxiv.org/abs/2501.08820v1
• Date: Wed, 15 Jan 2025 14:17:13 GMT
• Title: Heat semigroup representation of Laplacian
• Authors: Evgueni Dinvay,
• Abstract summary: This work introduces novel numerical algorithms for computational quantum mechanics. The key advantage of this approach lies in its computational efficiency. The proposed multiwavelet-based Laplacian approximation is tested through two fundamental quantum chemistry applications.
• Score: 0.0
• License:
• Abstract: This work introduces novel numerical algorithms for computational quantum mechanics, grounded in a representation of the Laplace operator -- frequently used to model kinetic energy in quantum systems -- via the heat semigroup. The key advantage of this approach lies in its computational efficiency, particularly within the framework of multiresolution analysis, where the heat equation can be solved rapidly. This results in an effective and scalable method for evaluating kinetic energy in quantum systems. The proposed multiwavelet-based Laplacian approximation is tested through two fundamental quantum chemistry applications: self-consistent field calculations and the time evolution of Schr\"odinger-type equations.

Related papers

• A variational quantum algorithm for tackling multi-dimensional Poisson equations with inhomogeneous boundary conditions [1.8174852547661968]
  We design a variational quantum algorithm to solve multi-dimensional Poisson equations with mixed boundary conditions. We employ the proposed algorithm to calculate bias-dependent spatial distributions of electric fields in semiconductor systems.
  arXiv  Detail & Related papers  (2024-11-05T11:15:05Z)
• Dynamical quantum Ansatz tree approach for the heat equation [0.0]
  We consider a discretized version of the heat equation and address its solution on quantum computer. We extend this method originally proposed for the system of linear equations to tackle full time dependent heat equation.
  arXiv  Detail & Related papers  (2024-04-22T11:44:48Z)
• A novel scheme for modelling dissipation or thermalization in open quantum systems [0.0]
  We introduce a novel method for investigating dissipation (gain) and thermalization in an open quantum system. To demonstrate the efficiency and significance of the method, we apply it to some ubiquitous open quantum systems.
  arXiv  Detail & Related papers  (2024-04-16T05:20:30Z)
• Quantum Circuits for partial differential equations via Schrödingerisation [26.7034263292622]
  We present implementation of a quantum algorithm for general PDEs using Schr"odingerisation techniques. We provide examples of the heat equation, and the advection equation approximated by the upwind scheme.
  arXiv  Detail & Related papers  (2024-03-15T05:42:03Z)
• Reweight-annealing method for evaluating the partition function via quantum Monte Carlo calculations [4.595034707642593]
  We present an unbiased but low-technical-barrier algorithm within the quantum Monte Carlo framework, which has exceptionally high accuracy and no systemic error. This method can be widely used in both classical and quantum Monte Carlo simulations and is easy to be parallelized on computer.
  arXiv  Detail & Related papers  (2024-03-13T15:54:57Z)
• Implementation of a two-stroke quantum heat engine with a collisional model [50.591267188664666]
  We put forth a quantum simulation of a stroboscopic two-stroke thermal engine in the IBMQ processor. The system consists of a quantum spin chain connected to two baths at their boundaries, prepared at different temperatures using the variational quantum thermalizer algorithm.
  arXiv  Detail & Related papers  (2022-03-25T16:55:08Z)
• 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-Classical Hybrid Algorithm for the Simulation of All-Electron Correlation [58.720142291102135]
  We present a novel hybrid-classical algorithm that computes a molecule's all-electron energy and properties on the classical computer. We demonstrate the ability of the quantum-classical hybrid algorithms to achieve chemically relevant results and accuracy on currently available quantum computers.
  arXiv  Detail & Related papers  (2021-06-22T18:00:00Z)
• Experimental verification of fluctuation relations with a quantum computer [68.8204255655161]
  We use a quantum processor to experimentally validate a number of theoretical results in non-equilibrium quantum thermodynamics. Our experiments constitute the experimental basis for the understanding of the non-equilibrium energetics of quantum computation.
  arXiv  Detail & Related papers  (2021-06-08T14:16:12Z)
• Method of spectral Green functions in driven open quantum dynamics [77.34726150561087]
  A novel method based on spectral Green functions is presented for the simulation of driven open quantum dynamics. The formalism shows remarkable analogies to the use of Green functions in quantum field theory. The method dramatically reduces computational cost compared with simulations based on solving the full master equation.
  arXiv  Detail & Related papers  (2020-06-04T09:41:08Z)
• Quantum computation of thermal averages in the presence of a sign problem [45.82374977939355]
  We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system. We show how quantum algorithms completely solve the problem, and discuss how this can apply to more complex systems of physical interest.
  arXiv  Detail & Related papers  (2020-01-15T14:01:11Z)

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.