A tensor network representation of path integrals: Implementation and
analysis
- URL: http://arxiv.org/abs/2106.12523v6
- Date: Wed, 22 Mar 2023 14:20:41 GMT
- Title: A tensor network representation of path integrals: Implementation and
analysis
- Authors: Amartya Bose and Peter L. Walters
- Abstract summary: We introduce a novel tensor network-based decomposition of path integral simulations involving Feynman-Vernon influence functional.
The finite temporarily non-local interactions introduced by the influence functional can be captured very efficiently using matrix product state representation.
The flexibility of the AP-TNPI framework makes it a promising new addition to the family of path integral methods for non-equilibrium quantum dynamics.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Tensors with finite correlation afford very compact tensor network
representations. A novel tensor network-based decomposition of real-time path
integral simulations involving Feynman-Vernon influence functional is
introduced. In this tensor network path integral (TNPI) technique, the finite
temporarily non-local interactions introduced by the influence functional can
be captured very efficiently using matrix product state representation for the
path amplitude (PA) tensor. We illustrate this particular TNPI method through
various realistic examples, including a charge transfer reaction and an exciton
transfer in a dimer. We also show how it is readily applied to systems with
greater than two states by simulating a 7-site model of FMO and a molecular
wire model. The augmented propagator (AP) TNPI utilizes the symmetries of the
problem, leading to accelerated convergence and dramatic reductions of
computational effort. We also introduce an approximate method that speeds up
propagation beyond the non-local memory length. Furthermore, the structure
imposed by the tensor network representation of the PA tensor naturally
suggests other factorizations that make simulations for extended systems more
efficient. These factorizations would be the subject of future explorations.
The flexibility of the AP-TNPI framework makes it a promising new addition to
the family of path integral methods for non-equilibrium quantum dynamics.
Related papers
- DimOL: Dimensional Awareness as A New 'Dimension' in Operator Learning [63.5925701087252]
We introduce DimOL (Dimension-aware Operator Learning), drawing insights from dimensional analysis.
To implement DimOL, we propose the ProdLayer, which can be seamlessly integrated into FNO-based and Transformer-based PDE solvers.
Empirically, DimOL models achieve up to 48% performance gain within the PDE datasets.
arXiv Detail & Related papers (2024-10-08T10:48:50Z) - Neural Message Passing Induced by Energy-Constrained Diffusion [79.9193447649011]
We propose an energy-constrained diffusion model as a principled interpretable framework for understanding the mechanism of MPNNs.
We show that the new model can yield promising performance for cases where the data structures are observed (as a graph), partially observed or completely unobserved.
arXiv Detail & Related papers (2024-09-13T17:54:41Z) - Quantum correlation functions through tensor network path integral [0.0]
tensor networks are utilized for calculating equilibrium correlation function for open quantum systems.
The influence of the solvent on the quantum system is incorporated through an influence functional.
The design and implementation of this method is discussed along with illustrations from rate theory, symmetrized spin correlation functions, dynamical susceptibility calculations and quantum thermodynamics.
arXiv Detail & Related papers (2023-08-21T07:46:51Z) - Capturing the Diffusive Behavior of the Multiscale Linear Transport
Equations by Asymptotic-Preserving Convolutional DeepONets [31.88833218777623]
We introduce two types of novel Asymptotic-Preserving Convolutional Deep Operator Networks (APCONs)
We propose a new architecture called Convolutional Deep Operator Networks, which employ multiple local convolution operations instead of a global heat kernel.
Our APCON methods possess a parameter count that is independent of the grid size and are capable of capturing the diffusive behavior of the linear transport problem.
arXiv Detail & Related papers (2023-06-28T03:16:45Z) - Theory on variational high-dimensional tensor networks [2.0307382542339485]
We investigate the emergent statistical properties of random high-dimensional-network states and the trainability of tensoral networks.
We prove that variational high-dimensional networks suffer from barren plateaus for global loss functions.
Our results pave a way for their future theoretical studies and practical applications.
arXiv Detail & Related papers (2023-03-30T15:26:30Z) - 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) - Low-Rank Tensor Function Representation for Multi-Dimensional Data
Recovery [52.21846313876592]
Low-rank tensor function representation (LRTFR) can continuously represent data beyond meshgrid with infinite resolution.
We develop two fundamental concepts for tensor functions, i.e., the tensor function rank and low-rank tensor function factorization.
Our method substantiates the superiority and versatility of our method as compared with state-of-the-art methods.
arXiv Detail & Related papers (2022-12-01T04:00:38Z) - Decimation technique for open quantum systems: a case study with
driven-dissipative bosonic chains [62.997667081978825]
Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics.
We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function.
We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
arXiv Detail & Related papers (2022-02-15T19:00:09Z) - A Multisite Decomposition of the Tensor Network Path Integrals [0.0]
We extend the tensor network path integral (TNPI) framework to efficiently simulate quantum systems with local dissipative environments.
The MS-TNPI method is useful for studying a variety of extended quantum systems coupled with solvents.
arXiv Detail & Related papers (2021-09-20T17:55:53Z) - A Pairwise Connected Tensor Network Representation of Path Integrals [0.0]
It has been recently shown how the tensorial nature of real-time path integrals involving the Feynman-Vernon influence functional can be utilized.
Here, a generalized tensor network is derived and implemented specifically incorporating the pairwise interaction structure of the influence functional.
This pairwise connected tensor network path integral (PCTNPI) is illustrated through applications to typical spin-boson problems and explorations of the differences caused by the exact form of the spectral density.
arXiv Detail & Related papers (2021-06-28T18:30:17Z) - Provably Efficient Neural Estimation of Structural Equation Model: An
Adversarial Approach [144.21892195917758]
We study estimation in a class of generalized Structural equation models (SEMs)
We formulate the linear operator equation as a min-max game, where both players are parameterized by neural networks (NNs), and learn the parameters of these neural networks using a gradient descent.
For the first time we provide a tractable estimation procedure for SEMs based on NNs with provable convergence and without the need for sample splitting.
arXiv Detail & Related papers (2020-07-02T17:55:47Z)
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.