Non-Stationary Long-Term Dynamics via Selected Incomplete Dual Bases

• URL: http://arxiv.org/abs/2306.07407v2
• Date: Tue, 22 Oct 2024 17:00:36 GMT
• Title: Non-Stationary Long-Term Dynamics via Selected Incomplete Dual Bases
• Authors: Hsiao-Han Chuang, Abhijit Pendse,
• Abstract summary: We propose an SU(2) coherent state basis and deriving equations of motion for both time-independent and time-dependent Hamiltonian. We evaluate this method through numerical simulations of a seven-qubit system. Our conclusion suggests that the selected incomplete dual basis method can efficiently capture both short-term and long-term dynamics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Simulating the dynamics of non-stationary, long-term many-body quantum systems poses significant challenges due to the large size of the state space. We are examining how traditional basis sets struggle to accurately represent long-term dynamics when using incomplete sets. To address this issue, we propose using an SU(2) coherent state basis and deriving equations of motion for both time-independent and time-dependent Hamiltonian. This methodology involves a sampling approach, where a subset of relevant configurations is chosen based on energy criteria, and a projection method is used to enhance the accuracy of wavefunction propagation while reducing computational cost. We evaluate this method through numerical simulations of a seven-qubit system, calculating key physical observables such as state probabilities and domain-wall densities. Our results indicate that while complete basis sets offer accurate dynamics, selected incomplete sets can recover essential features, especially with the assistance of a projector. Our conclusion suggests that the selected incomplete dual basis method can efficiently capture both short-term and long-term dynamics.

Related papers

• Generative System Dynamics in Recurrent Neural Networks [56.958984970518564]
  We investigate the continuous time dynamics of Recurrent Neural Networks (RNNs) We show that skew-symmetric weight matrices are fundamental to enable stable limit cycles in both linear and nonlinear configurations. Numerical simulations showcase how nonlinear activation functions not only maintain limit cycles, but also enhance the numerical stability of the system integration process.
  arXiv  Detail & Related papers  (2025-04-16T10:39:43Z)
• Photonic Simulation of Localization Phenomena Using Boson Sampling [0.0]
  We propose boson sampling as an alternative compact synthetic platform performing at room temperature. By mapping the time-evolution unitary of a Hamiltonian onto an interferometer via continuous-variable gate decompositions, we present proof-of-principle results of localization characteristics of a single particle.
  arXiv  Detail & Related papers  (2024-10-17T18:00:05Z)
• Truncated Gaussian basis approach for simulating many-body dynamics [0.0]
  The approach constructs an effective Hamiltonian within a reduced subspace, spanned by fermionic Gaussian states, and diagonalizes it to obtain approximate eigenstates and eigenenergies. Symmetries can be exploited to perform parallel computation, enabling to simulate systems with much larger sizes. For quench dynamics we observe that time-evolving wave functions in the truncated subspace facilitates the simulation of long-time dynamics.
  arXiv  Detail & Related papers  (2024-10-05T15:47:01Z)
• Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
  We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations. We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2024-10-04T18:06:12Z)
• Space and Time Continuous Physics Simulation From Partial Observations [0.0]
  Data-driven methods based on large-scale machine learning promise high adaptivity by integrating long-range dependencies more directly and efficiently. We focus on fluid dynamics and address the shortcomings of a large part of the literature, which are based on fixed support for computations and predictions in the form of regular or irregular grids. We propose a novel setup to perform predictions in a continuous spatial and temporal domain while being trained on sparse observations.
  arXiv  Detail & Related papers  (2024-01-17T13:24:04Z)
• Neural Time-Reversed Generalized Riccati Equation [60.92253836775246]
  Hamiltonian equations offer an interpretation of optimality through auxiliary variables known as costates. This paper introduces a novel neural-based approach to optimal control, with the aim of working forward-in-time.
  arXiv  Detail & Related papers  (2023-12-14T19:29:37Z)
• Stochastic parameter optimization analysis of dynamical quantum critical phenomena in long-range transverse-field Ising chain [0.0]
  We explore the quantum phase transition of the one-dimensional long-range transverse-field Ising model. In our simulations, the simulator automatically determines the parameters to sample from, even without prior knowledge of the critical point and universality class. We successfully obtained numerical evidence supporting $sigma = 7/4$ as the universality boundary between the latter two.
  arXiv  Detail & Related papers  (2023-05-23T14:46:16Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Quantifying spatio-temporal patterns in classical and quantum systems out of equilibrium [0.0]
  A rich variety of non-equilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques. By the example of the discrete time crystal realized in non-equilibrium quantum systems we provide a complete low-level characterization of this nontrivial dynamical phase with only processing bitstrings.
  arXiv  Detail & Related papers  (2023-02-28T13:27:45Z)
• A two stages Deep Learning Architecture for Model Reduction of Parametric Time-Dependent Problems [0.0]
  Parametric time-dependent systems are of crucial importance in modeling real phenomena. We present a general two-stages deep learning framework able to perform that generalization with low computational effort in time. Results are obtained applying the framework to incompressible Navier-Stokes equations in a cavity.
  arXiv  Detail & Related papers  (2023-01-24T11:24:18Z)
• Predicting the State of Synchronization of Financial Time Series using Cross Recurrence Plots [75.20174445166997]
  This study introduces a new method for predicting the future state of synchronization of the dynamics of two financial time series. We adopt a deep learning framework for methodologically addressing the prediction of the synchronization state. We find that the task of predicting the state of synchronization of two time series is in general rather difficult, but for certain pairs of stocks attainable with very satisfactory performance.
  arXiv  Detail & Related papers  (2022-10-26T10:22:28Z)
• On optimization of coherent and incoherent controls for two-level quantum systems [77.34726150561087]
  This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr"odinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
  arXiv  Detail & Related papers  (2022-05-05T09:08:03Z)
• 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)
• Long-time integration of parametric evolution equations with physics-informed DeepONets [0.0]
  We introduce an effective framework for learning infinite-dimensional operators that map random initial conditions to associated PDE solutions within a short time interval. Global long-time predictions across a range of initial conditions can be then obtained by iteratively evaluating the trained model. This introduces a new approach to temporal domain decomposition that is shown to be effective in performing accurate long-time simulations.
  arXiv  Detail & Related papers  (2021-06-09T20:46:17Z)
• Realistic simulations of spin squeezing and cooperative coupling effects in large ensembles of interacting two-level systems [0.0]
  We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay. This opens up the possibility to perform accurate real-scale simulations of a diverse range of experiments in quantum optics or with solid-state spin ensembles under realistic laboratory conditions.
  arXiv  Detail & Related papers  (2021-04-30T18:00:00Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Probing the topological Anderson transition with quantum walks [48.7576911714538]
  We consider one-dimensional quantum walks in optical linear networks with synthetically introduced disorder and tunable system parameters. The option to directly monitor the walker's probability distribution makes this optical platform ideally suited for the experimental observation of the unique signatures of the one-dimensional topological Anderson transition.
  arXiv  Detail & Related papers  (2021-02-01T21:19:15Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)
• Quantum relaxation in a system of harmonic oscillators with time-dependent coupling [0.0]
  We analyze the relaxation of nonequilibrium initial distributions for a system of coupled one-dimensional harmonic oscillators. We show that in general the system studied here tends to equilibrium, but the relaxation can be retarded depending on the values of the parameters.
  arXiv  Detail & Related papers  (2020-07-06T12:57:18Z)
• Supporting Optimal Phase Space Reconstructions Using Neural Network Architecture for Time Series Modeling [68.8204255655161]
  We propose an artificial neural network with a mechanism to implicitly learn the phase spaces properties. Our approach is either as competitive as or better than most state-of-the-art strategies.
  arXiv  Detail & Related papers  (2020-06-19T21:04:47Z)

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.