Fast Tensor Network Imaginary Time Evolution by Implicit Stepping on Logarithmic Grids

• URL: http://arxiv.org/abs/2606.02930v1
• Date: Mon, 01 Jun 2026 22:25:24 GMT
• Title: Fast Tensor Network Imaginary Time Evolution by Implicit Stepping on Logarithmic Grids
• Abstract summary: We show that logarithmic time grids are sufficient to resolve long imaginary time dynamics.<n>We then show that A-stable implicit time-stepping methods for ordinary differential equations allow stable propagation for any time step size.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a new method for the efficient imaginary time evolution of quantum many-body wavefunctions represented by matrix product states (MPS). We first show that logarithmic time grids are sufficient to resolve long imaginary time dynamics, yielding an exponential reduction in the number of time steps compared with standard approaches. We then show that A-stable implicit time-stepping methods for ordinary differential equations allow stable propagation for any time step size. The resulting scheme requires only matrix-vector products and linear solves, standard operations in the MPS toolbox. We validate our approach with two examples: a Heisenberg spin chain, which we use to demonstrate a speedup of several orders of magnitude over the standard time-dependent variational principle method with uniform time steps, and a single-site Anderson impurity model with a metallic bath, for which propagation to large imaginary times allows one to observe the exponential dependence of the Kondo temperature on the interaction strength.

Related papers

• A Bogoliubov-ratio framework for quantum-information diagnostics of time-dependent two-mode Boson Hamiltonian [10.22413990748989]
  We present a compact and unified framework for quantum-information diagnostics of time-dependent two-mode bosonic systems.<n>We demonstrate the utility of this framework in two distinct non-stationary setups: primordial cosmological perturbations and a chirped-pulse nondegenerate optical parametric amplifier.
  arXiv  Detail & Related papers  (2026-07-27T13:21:40Z)
• Continuous-time quantum control across an exponentially small bottleneck in a frustrated Ising ring model [0.0]
  Continuous-time Quantum Annealing (QA) is a strategy for preparing ground state of nontrivial manybody systems.<n>We show how to implement quantum control over the annealing schedule in a frustrated Ising ring.
  arXiv  Detail & Related papers  (2026-06-05T11:38:11Z)
• Dynamical Simulations of Schrödinger's Equation via Rank-Adaptive Tensor Decompositions [0.0]
  We study low-rank tensor methods for the numerical solution of Schrdinger's equation with time-independent and explicitly time-dependent Hamiltonians.<n>We outline the recent application of the "basis update and Galerkin" (Bug) method for tensor trains, and describe the established TDVP and TDVP-2 algorithms.<n> Numerical experiments on representative time-independent and time-dependent Hamiltonian models quantify the tradeoff between accuracy and compression across methods.
  arXiv  Detail & Related papers  (2026-03-14T15:34:24Z)
• Computing time-dependent reduced models for classical and quantum dynamics [0.0]
  This paper introduces a novel method for approxvolutioning the dynamics of an autonomous system projected onto a fixed subspace.<n>The derivation is based on the Taylor expansion of the exponential map and a new result for computing the time-ordered exponential coupling algorithm of generators.<n>The resulting approximation is accurate for small times, does not require a weak-run assumption, performs better than a truncation of the exponential map at low orders, and guarantees a completely positive and trace-preserving map at the lowest orders.
  arXiv  Detail & Related papers  (2025-10-23T15:51:00Z)
• Overcoming the entanglement barrier with sampled tensor networks [0.0]
  We develop a new hybrid-Network/Monte-Carlo (TN-MC) algorithm that samples and evaluates expectation values of generic local operators.<n>The accurate contraction of wave function amplitudes is a consequence of the favorable scaling with time.<n>Our results show that, when computing expectation values of local operators, the entanglement barrier in one-dimensional Hamiltonian evolution can be bypassed.
  arXiv  Detail & Related papers  (2025-05-14T18:14:47Z)
• IVP-VAE: Modeling EHR Time Series with Initial Value Problem Solvers [20.784780497613557]
  We propose to model time series purely with continuous processes whose state evolution can be approximated directly by IVPs. This eliminates the need for recurrent computation and enables multiple states to evolve in parallel. Experiments on three real-world datasets show that the proposed method can systematically outperform its predecessors, achieve state-of-the-art results, and have significant advantages in terms of data efficiency.
  arXiv  Detail & Related papers  (2023-05-11T11:53:31Z)
• Discovering ordinary differential equations that govern time-series [65.07437364102931]
  We propose a transformer-based sequence-to-sequence model that recovers scalar autonomous ordinary differential equations (ODEs) in symbolic form from time-series data of a single observed solution of the ODE. Our method is efficiently scalable: after one-time pretraining on a large set of ODEs, we can infer the governing laws of a new observed solution in a few forward passes of the model.
  arXiv  Detail & Related papers  (2022-11-05T07:07:58Z)
• 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)
• Time Dependent Hamiltonian Simulation Using Discrete Clock Constructions [42.3779227963298]
  We provide a framework for encoding time dependent dynamics as time independent systems. First, we create a time dependent simulation algorithm based on performing qubitization on the augmented clock system. Second, we define a natural generalization of multiproduct formulas for time-ordered exponentials.
  arXiv  Detail & Related papers  (2022-03-21T21:29:22Z)
• A simple way to incorporate loss when modelling multimode entangled state generation [0.0]
  We show that the light generated via spontaneous four-wave mixing or parametric down conversion in multiple, coupled, lossy cavities is a multimode squeezed thermal state. Requiring this state to be the solution of the Lindblad master equation results in a set of coupled first-order differential equations.
  arXiv  Detail & Related papers  (2021-12-22T17:14:27Z)
• The Variational Method of Moments [65.91730154730905]
  conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables. Motivated by a variational minimax reformulation of OWGMM, we define a very general class of estimators for the conditional moment problem. We provide algorithms for valid statistical inference based on the same kind of variational reformulations.
  arXiv  Detail & Related papers  (2020-12-17T07:21:06Z)
• 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)
• Graph Gamma Process Generalized Linear Dynamical Systems [60.467040479276704]
  We introduce graph gamma process (GGP) linear dynamical systems to model real multivariate time series. For temporal pattern discovery, the latent representation under the model is used to decompose the time series into a parsimonious set of multivariate sub-sequences. We use the generated random graph, whose number of nonzero-degree nodes is finite, to define both the sparsity pattern and dimension of the latent state transition matrix.
  arXiv  Detail & Related papers  (2020-07-25T04:16:34Z)
• Liquid Time-constant Networks [117.57116214802504]
  We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations.
  arXiv  Detail & Related papers  (2020-06-08T09:53:35Z)

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.