Time evolving matrix product operator (TEMPO) method in a non-diagonal basis set based on derivative of the path integral expression

• URL: http://arxiv.org/abs/2410.23877v1
• Date: Thu, 31 Oct 2024 12:38:30 GMT
• Title: Time evolving matrix product operator (TEMPO) method in a non-diagonal basis set based on derivative of the path integral expression
• Authors: Shuocang Zhang, Qiang Shi,
• Abstract summary: The time-evolving matrix product operator (TEMPO) method is a powerful tool for simulating open system quantum dynamics. In this work, we aim to address issues related to off-diagonal coupling by extending the TEMPO algorithm to accommodate arbitrary basis sets.
• Score: 0.0
• License:
• Abstract: The time-evolving matrix product operator (TEMPO) method is a powerful tool for simulating open system quantum dynamics. Typically, it is used in problems with diagonal system-bath coupling, where analytical expressions for discretized influence functional are available. In this work, we aim to address issues related to off-diagonal coupling by extending the TEMPO algorithm to accommodate arbitrary basis sets. The proposed approach is based on computing the derivative of the discretized path integral expression of a generalized influence functional when increasing one time step, which yields an equation of motion valid for non-diagonal basis set and arbitrary number of non-commuting baths. The generalized influence functional is then obtained by integrating the resulting differential equation. Applicability of the the new method is then tested by simulating one- and two- qubit systems coupled to both Z- and X-type baths.

Related papers

• Harmonic Path Integral Diffusion [0.4527270266697462]
  We present a novel approach for sampling from a continuous multivariate probability distribution. Our method constructs a time-dependent bridge from a delta function centered at the origin of the state space.
  arXiv  Detail & Related papers  (2024-09-23T16:20:21Z)
• A Physics-Informed Machine Learning Approach for Solving Distributed Order Fractional Differential Equations [0.0]
  This paper introduces a novel methodology for solving distributed-order fractional differential equations using a physics-informed machine learning framework. By embedding the distributed-order functional equation into the SVR framework, we incorporate physical laws directly into the learning process. The effectiveness of the proposed approach is validated through a series of numerical experiments on Caputo-based distributed-order fractional differential equations.
  arXiv  Detail & Related papers  (2024-09-05T13:20:10Z)
• Accelerating Fractional PINNs using Operational Matrices of Derivative [0.24578723416255746]
  This paper presents a novel operational matrix method to accelerate the training of fractional Physics-Informed Neural Networks (fPINNs) Our approach involves a non-uniform discretization of the fractional Caputo operator, facilitating swift computation of fractional derivatives within Caputo-type fractional differential problems with $0alpha1$. The effectiveness of our proposed method is validated across diverse differential equations, including Delay Differential Equations (DDEs) and Systems of Differential Algebraic Equations (DAEs)
  arXiv  Detail & Related papers  (2024-01-25T11:00:19Z)
• Tree tensor network state approach for solving hierarchical equations of motion [0.0]
  The hierarchical equations of motion (HEOM) method is a numerically exact open quantum system dynamics approach. We show that, the proposed HEOM+TTNS approach yields consistent results with that of the conventional HEOM method. Besides, the simulation with a genuine TTNS is four times faster than a one-dimensional matrix product state decomposition scheme.
  arXiv  Detail & Related papers  (2023-04-11T11:40:15Z)
• Neural Network Verification as Piecewise Linear Optimization: Formulations for the Composition of Staircase Functions [2.088583843514496]
  We present a technique for neural network verification using mixed-integer programming (MIP) formulations. We derive a strong formulation for each neuron in a network using piecewise linear activation functions. We also derive a separation procedure that runs in super-linear time in the input dimension.
  arXiv  Detail & Related papers  (2022-11-27T03:25:48Z)
• Semi-supervised Learning of Partial Differential Operators and Dynamical Flows [68.77595310155365]
  We present a novel method that combines a hyper-network solver with a Fourier Neural Operator architecture. We test our method on various time evolution PDEs, including nonlinear fluid flows in one, two, and three spatial dimensions. The results show that the new method improves the learning accuracy at the time point of supervision point, and is able to interpolate and the solutions to any intermediate time.
  arXiv  Detail & Related papers  (2022-07-28T19:59:14Z)
• An application of the splitting-up method for the computation of a neural network representation for the solution for the filtering equations [68.8204255655161]
  Filtering equations play a central role in many real-life applications, including numerical weather prediction, finance and engineering. One of the classical approaches to approximate the solution of the filtering equations is to use a PDE inspired method, called the splitting-up method. We combine this method with a neural network representation to produce an approximation of the unnormalised conditional distribution of the signal process.
  arXiv  Detail & Related papers  (2022-01-10T11:01:36Z)
• Deep Learning Approximation of Diffeomorphisms via Linear-Control Systems [91.3755431537592]
  We consider a control system of the form $dot x = sum_i=1lF_i(x)u_i$, with linear dependence in the controls. We use the corresponding flow to approximate the action of a diffeomorphism on a compact ensemble of points.
  arXiv  Detail & Related papers  (2021-10-24T08:57:46Z)
• A Discrete Variational Derivation of Accelerated Methods in Optimization [68.8204255655161]
  We introduce variational which allow us to derive different methods for optimization. We derive two families of optimization methods in one-to-one correspondence. The preservation of symplecticity of autonomous systems occurs here solely on the fibers.
  arXiv  Detail & Related papers  (2021-06-04T20:21:53Z)
• The Connection between Discrete- and Continuous-Time Descriptions of Gaussian Continuous Processes [60.35125735474386]
  We show that discretizations yielding consistent estimators have the property of invariance under coarse-graining' This result explains why combining differencing schemes for derivatives reconstruction and local-in-time inference approaches does not work for time series analysis of second or higher order differential equations.
  arXiv  Detail & Related papers  (2021-01-16T17:11:02Z)
• DiffPD: Differentiable Projective Dynamics with Contact [65.88720481593118]
  We present DiffPD, an efficient differentiable soft-body simulator with implicit time integration. We evaluate the performance of DiffPD and observe a speedup of 4-19 times compared to the standard Newton's method in various applications.
  arXiv  Detail & Related papers  (2021-01-15T00:13:33Z)

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.