Differential Equation Based Path Integral for System-Bath Dynamics
- URL: http://arxiv.org/abs/2107.10727v1
- Date: Thu, 22 Jul 2021 15:06:22 GMT
- Title: Differential Equation Based Path Integral for System-Bath Dynamics
- Authors: Geshuo Wang, Zhenning Cai
- Abstract summary: We propose the differential equation based path integral (DEBPI) method to simulate the real-time evolution of open quantum systems.
New numerical schemes can be derived by discretizing these differential equations.
It is numerically verified that in certain cases, by selecting appropriate systems and applying suitable numerical schemes, the memory cost required in the i-QuAPI method can be significantly reduced.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We propose the differential equation based path integral (DEBPI) method to
simulate the real-time evolution of open quantum systems. In this method, a
system of partial differential equations is derived based on the continuation
of a classical numerical method called iterative quasi-adiabatic propagator
path integral (i-QuAPI). While the resulting system has infinite equations, we
introduce a reasonable closure to obtain a series of finite systems. New
numerical schemes can be derived by discretizing these differential equations.
It is numerically verified that in certain cases, by selecting appropriate
systems and applying suitable numerical schemes, the memory cost required in
the i-QuAPI method can be significantly reduced.
Related papers
- Solving Fractional Differential Equations on a Quantum Computer: A Variational Approach [0.1492582382799606]
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations.
Our results indicate that solution fidelity is insensitive to the fractional index and that gradient evaluation cost scales economically with the number of time steps.
arXiv Detail & Related papers (2024-06-13T02:27:16Z) - Parallel-in-Time Probabilistic Numerical ODE Solvers [30.788077484994176]
Probabilistic numerical solvers for ordinary differential equations (ODEs) treat the numerical simulation of dynamical systems as problems of Bayesian state estimation.
We build on the time-parallel formulation of iterated extended Kalman smoothers to formulate a parallel-in-time probabilistic numerical ODE solver.
arXiv Detail & Related papers (2023-10-02T12:32:21Z) - Efficient Quantum Algorithms for Nonlinear Stochastic Dynamical Systems [2.707154152696381]
We propose efficient quantum algorithms for solving nonlinear differential equations (SDE) via the associated Fokker-Planck equation (FPE)
We discretize the FPE in space and time using two well-known numerical schemes, namely Chang-Cooper and implicit finite difference.
We then compute the solution of the resulting system of linear equations using the quantum linear systems.
arXiv Detail & Related papers (2023-03-04T17:40:23Z) - 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) - D-CIPHER: Discovery of Closed-form Partial Differential Equations [80.46395274587098]
We propose D-CIPHER, which is robust to measurement artifacts and can uncover a new and very general class of differential equations.
We further design a novel optimization procedure, CoLLie, to help D-CIPHER search through this class efficiently.
arXiv Detail & Related papers (2022-06-21T17:59:20Z) - Automated differential equation solver based on the parametric
approximation optimization [77.34726150561087]
The article presents a method that uses an optimization algorithm to obtain a solution using the parameterized approximation.
It allows solving the wide class of equations in an automated manner without the algorithm's parameters change.
arXiv Detail & Related papers (2022-05-11T10:06:47Z) - Structure-Preserving Learning Using Gaussian Processes and Variational
Integrators [62.31425348954686]
We propose the combination of a variational integrator for the nominal dynamics of a mechanical system and learning residual dynamics with Gaussian process regression.
We extend our approach to systems with known kinematic constraints and provide formal bounds on the prediction uncertainty.
arXiv Detail & Related papers (2021-12-10T11:09:29Z) - Continuous Convolutional Neural Networks: Coupled Neural PDE and ODE [1.1897857181479061]
This work proposes a variant of Convolutional Neural Networks (CNNs) that can learn the hidden dynamics of a physical system.
Instead of considering the physical system such as image, time -series as a system of multiple layers, this new technique can model a system in the form of Differential Equation (DEs)
arXiv Detail & Related papers (2021-10-30T21:45:00Z) - Multi-objective discovery of PDE systems using evolutionary approach [77.34726150561087]
In the paper, a multi-objective co-evolution algorithm is described.
The single equations within the system and the system itself are evolved simultaneously to obtain the system.
In contrast to the single vector equation, a component-wise system is more suitable for expert interpretation and, therefore, for applications.
arXiv Detail & Related papers (2021-03-11T15:37:52Z) - Linear embedding of nonlinear dynamical systems and prospects for
efficient quantum algorithms [74.17312533172291]
We describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding)
We then explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation)
arXiv Detail & Related papers (2020-12-12T00:01:10Z) - Solving non-linear Kolmogorov equations in large dimensions by using
deep learning: a numerical comparison of discretization schemes [16.067228939231047]
Non-linear partial differential Kolmogorov equations are successfully used to describe a wide range of time dependent phenomena.
Deep learning has been introduced to solve these equations in high-dimensional regimes.
We show that, for some discretization schemes, improvements in the accuracy are possible without affecting the observed computational complexity.
arXiv Detail & Related papers (2020-12-09T07:17:26Z)
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.