Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation

• URL: http://arxiv.org/abs/2504.07344v2
• Date: Sat, 19 Apr 2025 20:59:56 GMT
• Title: Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• Authors: Gunhee Park, Johnnie Gray, Garnet Kin-Lic Chan,
• Abstract summary: We extend the applicability of the TN-IF method to two-dimensional lattices by demonstrating its construction on tree lattices and proposing a belief propagation (BP) algorithm for the TN-IF.<n>We demonstrate the power of the cluster expansion of IF-BP in quench the quantum dynamics of the 2D transverse field Ising model, obtaining numerical results that improve on the state-of-the-art.
• Score: 1.4132765964347058
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Describing nonequilibrium quantum dynamics remains a significant computational challenge due to the growth of spatial entanglement. The tensor network influence functional (TN-IF) approach mitigates this problem for computing the time evolution of local observables by encoding the subsystem's influence functional path integral as a matrix product state (MPS), thereby shifting the resource governing computational cost from spatial entanglement to temporal entanglement. We extend the applicability of the TN-IF method to two-dimensional lattices by demonstrating its construction on tree lattices and proposing a belief propagation (BP) algorithm for the TN-IF, termed influence functional BP (IF-BP), to simulate local observable dynamics on arbitrary graphs. Even though the BP algorithm introduces uncontrolled approximation errors on arbitrary graphs, it provides an accurate description for locally tree-like lattices. Numerical simulations of the kicked Ising model on a heavy-hex lattice, motivated by a recent quantum experiment, highlight the effectiveness of the IF-BP method, which demonstrates superior performance in capturing long-time dynamics where traditional tensor network state-based methods struggle. Our results further reveal that the temporal entanglement entropy (TEE) only grows logarithmically with time for this model, resulting in a polynomial computational cost for the whole method. We further construct a cluster expansion of IF-BP to introduce loop correlations beyond the BP approximation, providing a systematic correction to the IF-BP estimate. We demonstrate the power of the cluster expansion of the IF-BP in simulating the quantum quench dynamics of the 2D transverse field Ising model, obtaining numerical results that improve on the state-of-the-art.

Related papers

• Towards robust variational quantum simulation of Lindblad dynamics via stochastic Magnus expansion [10.144001671935907]
  We introduce a novel and general framework for the variational quantum simulation of Lindblad equations. We demonstrate the effectiveness of our algorithm through numerical examples.
  arXiv  Detail & Related papers  (2025-03-28T02:37:56Z)
• Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems [49.819436680336786]
  Gaussian process state-space models (GPSSMs) have emerged as a powerful framework for modeling dynamical systems.<n>We propose an efficient transformed Gaussian process state-space model (ETGPSSM) to address these limitations.<n>Our approach leverages a single shared Gaussian process (GP) combined with normalizing flows and Bayesian neural networks, enabling efficient modeling of complex, high-dimensional state transitions.
  arXiv  Detail & Related papers  (2025-03-24T03:19:45Z)
• Time-dependent Neural Galerkin Method for Quantum Dynamics [42.81677042059531]
  We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle.<n>We showcase the method's effectiveness simulating global quantum quenches in the paradigmatic Transverse-Field Ising model in both 1D and 2D.<n>Overall, the method presented here shows competitive performance compared to state-of-the-art time-dependent variational approaches.
  arXiv  Detail & Related papers  (2024-12-16T13:48:54Z)
• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces novel deep dynamical models designed to represent continuous-time sequences. We train the model using maximum likelihood estimation with Markov chain Monte Carlo. Experimental results on oscillating systems, videos and real-world state sequences (MuJoCo) demonstrate that our model with the learnable energy-based prior outperforms existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Tensor network influence functionals in the continuous-time limit: connections to quantum embedding, bath discretization, and higher-order time propagation [2.368662284133926]
  We implement higher-order time propagators for the quench dynamics of the Anderson impurity model within the boundary IF-MPS formalism. We show the advantages of IF-MPS dynamics, with its associated highly compact effective bath dynamics, over state vector propagation with a static bath discretization.
  arXiv  Detail & Related papers  (2024-01-23T03:01:04Z)
• Gibbs-Duhem-Informed Neural Networks for Binary Activity Coefficient Prediction [45.84205238554709]
  We propose Gibbs-Duhem-informed neural networks for the prediction of binary activity coefficients at varying compositions. We include the Gibbs-Duhem equation explicitly in the loss function for training neural networks.
  arXiv  Detail & Related papers  (2023-05-31T07:36:45Z)
• Dynamic Causal Explanation Based Diffusion-Variational Graph Neural Network for Spatio-temporal Forecasting [60.03169701753824]
  We propose a novel Dynamic Diffusion-al Graph Neural Network (DVGNN) fortemporal forecasting. The proposed DVGNN model outperforms state-of-the-art approaches and achieves outstanding Root Mean Squared Error result.
  arXiv  Detail & Related papers  (2023-05-16T11:38:19Z)
• Convex Analysis of the Mean Field Langevin Dynamics [49.66486092259375]
  convergence rate analysis of the mean field Langevin dynamics is presented. $p_q$ associated with the dynamics allows us to develop a convergence theory parallel to classical results in convex optimization.
  arXiv  Detail & Related papers  (2022-01-25T17:13:56Z)
• 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)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• A tensor network representation of path integrals: Implementation and analysis [0.0]
  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.
  arXiv  Detail & Related papers  (2021-06-23T16:41:54Z)
• Constructing Tensor Network Influence Functionals for General Quantum Dynamics [0.0]
  We use a space-time tensor network representation of the influence functional and investigate its approximability in terms of the bond dimensions and time-like entanglement. We find that the influence functional and the intermediates involved in its construction can be efficiently approximated by low bond dimension tensor networks in certain dynamical regimes. As one iteratively integrates out the bath, the correlations in the influence functional can first increase before decreasing, indicating that the final compressibility of the influence functional is achieved via non-trivial cancellation.
  arXiv  Detail & Related papers  (2021-01-14T05:42:25Z)

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.