Solving coupled Non-linear Schrödinger Equations via Quantum Imaginary Time Evolution

• URL: http://arxiv.org/abs/2402.01623v3
• Date: Mon, 19 Aug 2024 09:44:29 GMT
• Title: Solving coupled Non-linear Schrödinger Equations via Quantum Imaginary Time Evolution
• Authors: Yang Hong Li, Jim Al-Khalili, Paul Stevenson,
• Abstract summary: We present a quantum imaginary time evolution (ITE) algorithm as a solution to such equations in the case of nuclear Hartree-Fock equations. Under a simplified Skyrme interaction model, we calculate the ground state energy of an oxygen-16 nucleus and demonstrate that the result is in agreement with the classical ITE algorithm.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Coupled non-linear Schr\"{o}dinger equations are crucial in describing dynamics of many particle systems. We present a quantum imaginary time evolution (ITE) algorithm as a solution to such equations in the case of nuclear Hartree-Fock equations. Under a simplified Skyrme interaction model, we calculate the ground state energy of an oxygen-16 nucleus and demonstrate that the result is in agreement with the classical ITE algorithm.

Related papers

• A Theory of Quantum Jumps [44.99833362998488]
  We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
  arXiv  Detail & Related papers  (2024-04-16T11:00:46Z)
• Fourier Neural Differential Equations for learning Quantum Field Theories [57.11316818360655]
  A Quantum Field Theory is defined by its interaction Hamiltonian, and linked to experimental data by the scattering matrix. In this paper, NDE models are used to learn theory, Scalar-Yukawa theory and Scalar Quantum Electrodynamics. The interaction Hamiltonian of a theory can be extracted from network parameters.
  arXiv  Detail & Related papers  (2023-11-28T22:11:15Z)
• 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)
• A quantum algorithm for the linear Vlasov equation with collisions [0.0]
  We present a quantum algorithm that simulates the linearized Vlasov equation with and without collisions. We show that a quadratic speedup in system size is attainable.
  arXiv  Detail & Related papers  (2023-03-06T19:19:30Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• Time complexity analysis of quantum algorithms via linear representations for nonlinear ordinary and partial differential equations [31.986350313948435]
  We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations. We compare the quantum linear systems algorithms based methods and the quantum simulation methods arising from different numerical approximations.
  arXiv  Detail & Related papers  (2022-09-18T05:50:23Z)
• Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations [62.81701992551728]
  We present a physics-informed framework for solving time-dependent partial differential equations. Our model utilizes discrete cosine transforms to encode spatial and recurrent neural networks. We show experimental results on the Taylor-Green vortex solution to the Navier-Stokes equations.
  arXiv  Detail & Related papers  (2022-02-24T20:46:52Z)
• Exact Floquet solutions of quantum driven systems [1.0152838128195467]
  We give out the exact Floquet solutions of wave function for three physical models. The idea presented in this paper can be used in mathematics to solve partial differential equations.
  arXiv  Detail & Related papers  (2022-02-02T15:15:05Z)
• Numerical investigation of the logarithmic Schr\"odinger model of quantum decoherence [0.0]
  We present a model of collisional decoherence of the wavefunction of a quantum particle in position-space. The validity of the logarithmic Schr"odinger equation has not yet been investigated numerically for general initial conditions.
  arXiv  Detail & Related papers  (2021-10-11T03:18:03Z)
• Phase-space matrix representation of differential equations for obtaining the energy spectrum of model quantum systems [0.0]
  We develop a method to find the eigenvalues and eigenfunctions of the 1-dimensional time independent Schr"odinger equation for quantum model systems.
  arXiv  Detail & Related papers  (2021-08-25T21:59:16Z)
• The Time-Evolution of States in Quantum Mechanics [77.34726150561087]
  It is argued that the Schr"odinger equation does not yield a correct description of the quantum-mechanical time evolution of states of isolated (open) systems featuring events. A precise general law for the time evolution of states replacing the Schr"odinger equation is formulated within the so-called ETH-Approach to Quantum Mechanics.
  arXiv  Detail & Related papers  (2021-01-04T16:09:10Z)

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.