Propagating sparsely supported states with time-dependent neural quantum states

• URL: http://arxiv.org/abs/2609.06054v1
• Date: Sat, 05 Sep 2026 12:17:32 GMT
• Title: Propagating sparsely supported states with time-dependent neural quantum states
• Abstract summary: We introduce the sampling method as a novel form of importance sampling, where samples are drawn from a distribution that interpolates between the wave function and its time derivative.<n>We further improve sampling efficiency by introducing (i) a configuration-time joint sampling scheme where spin configurations and time are both treated as random variables, and (ii) a hybrid strategy for sample proposal that incorporates the knowledge of a Krylov subspace.
• Score: 1.4323566945483497
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Neural quantum states (NQSs) have emerged as a powerful ansatz for quantum dynamics. Their high entanglement capacity promises to overcome the entanglement barrier. However, existing time-dependent NQS methods are ill-equipped to propagate sparsely supported initial states due to the inherent mismatch between the supports of such states and their time derivatives. To address this issue, we introduce the interpolation sampling method as a novel form of importance sampling, where samples are drawn from a distribution that interpolates between the wave function and its time derivative. Combined with a global-in-time variational principle, we demonstrate with the example of the two-dimensional transverse-field Ising model that interpolation sampling allows for accurate propagation of extremely peaked states that standard wave function sampling could not tackle. We further improve sampling efficiency by introducing (i) a configuration-time joint sampling scheme where spin configurations and time are both treated as random variables, and (ii) a hybrid strategy for sample proposal that incorporates the knowledge of a Krylov subspace. Our work extends the scope of time-dependent NQS methods to a wider range of physically relevant scenarios, while challenging the prevailing reliance on the Born distribution and its close variants as the default basis for sampling.

Related papers

• A Time-Reparameterized Cumulative Intensity Extrapolation Sampler for Discrete Flow Matching [25.54630601391996]
  TR-CIE aims to improve sampling quality when function evaluations are restricted.<n>We provide a theoretical analysis that bounds the local approximation error of cumulative intensities.<n>Experiments on synthetic tasks, text generation, and text-to-image benchmarks demonstrate that our method improves sampling quality under limited NFE.
  arXiv  Detail & Related papers  (2026-06-23T04:48:45Z)
• TimeAPN: Adaptive Amplitude-Phase Non-Stationarity Normalization for Time Series Forecasting [67.91113180885601]
  TimeAPN explicitly models and predicts non-stationary factors from both the time and frequency domains.<n>TimeAPN consistently improves long-term forecasting accuracy across multiple prediction horizons.<n>It outperforms state-of-the-art reversible normalization methods.
  arXiv  Detail & Related papers  (2026-03-18T07:21:24Z)
• Low-Dimensional Adaptation of Rectified Flow: A New Perspective through the Lens of Diffusion and Stochastic Localization [59.04314685837778]
  Rectified flow (RF) has gained considerable popularity due to its generation efficiency and state-of-the-art performance.<n>In this paper, we investigate the degree to which RF automatically adapts to the intrinsic low dimensionality of the support of the target distribution to accelerate sampling.<n>We show that, using a carefully designed choice of the time-discretization scheme and with sufficiently accurate drift estimates, the RF sampler enjoys an complexity of order $O(k/varepsilon)$.
  arXiv  Detail & Related papers  (2026-01-21T22:09:27Z)
• Time-of-Flow Distributions in Discrete Quantum Systems: From Operational Protocols to Quantum Speed Limits [0.0]
  We propose a framework to quantify transition timing in discrete quantum systems via the time-of-flow (TF) distribution.<n>We apply this framework to optimize time-dependent Hamiltonians, analyze shortcut-to-adiabaticity protocols, study non-adiabatic features in the dynamics of a three-level time-dependent detuning model, and derive a transition-based quantum speed limit (TF-QSL) for both closed and open quantum systems.
  arXiv  Detail & Related papers  (2025-04-13T13:46:01Z)
• Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States [0.0]
  Projected entangled pair states (PEPS) on finite two-dimensional lattices are a natural ansatz for representing ground states of local many-body Hamiltonians.<n>We propose the optimization of PEPS via an improved formulation of the time-dependent variational principle (TDVP)<n>We demonstrate our approach's capability to naturally handle long-range interactions by exploring the phase diagram of Rydberg atom arrays with long-range interactions.
  arXiv  Detail & Related papers  (2025-03-16T16:06:44Z)
• Many-body dynamics with explicitly time-dependent neural quantum states [0.0]
  We introduce the time-dependent neural quantum state (t-NQS)<n>We optimize a single, time-independent set of parameters to solve the time-dependent Schr"odinger equation across an entire time interval.<n>Results establish t-NQS as a powerful framework for exploring quantum dynamics in strongly correlated systems.
  arXiv  Detail & Related papers  (2024-12-16T14:53:26Z)
• Dynamical Measure Transport and Neural PDE Solvers for Sampling [77.38204731939273]
  We tackle the task of sampling from a probability density as transporting a tractable density function to the target. We employ physics-informed neural networks (PINNs) to approximate the respective partial differential equations (PDEs) solutions. PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently.
  arXiv  Detail & Related papers  (2024-07-10T17:39:50Z)
• Stable generative modeling using Schrödinger bridges [0.22499166814992438]
  We propose a generative model combining Schr"odinger bridges and Langevin dynamics. Our framework can be naturally extended to generate conditional samples and to Bayesian inference problems.
  arXiv  Detail & Related papers  (2024-01-09T06:15:45Z)
• DiffuSeq-v2: Bridging Discrete and Continuous Text Spaces for Accelerated Seq2Seq Diffusion Models [58.450152413700586]
  We introduce a soft absorbing state that facilitates the diffusion model in learning to reconstruct discrete mutations based on the underlying Gaussian space. We employ state-of-the-art ODE solvers within the continuous space to expedite the sampling process. Our proposed method effectively accelerates the training convergence by 4x and generates samples of similar quality 800x faster.
  arXiv  Detail & Related papers  (2023-10-09T15:29:10Z)
• Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
  Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution. We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
  arXiv  Detail & Related papers  (2023-06-27T08:15:28Z)
• Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution [44.99833362998488]
  We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate quantum systems classically. We prove that the most used scheme, the time-dependent Variational Monte Carlo (tVMC), is affected by a systematic statistical bias. We show that a different scheme based on the solution of an optimization problem at each time step is free from such problems.
  arXiv  Detail & Related papers  (2023-05-23T17:38:10Z)
• Conditioning Normalizing Flows for Rare Event Sampling [61.005334495264194]
  We propose a transition path sampling scheme based on neural-network generated configurations. We show that this approach enables the resolution of both the thermodynamics and kinetics of the transition region.
  arXiv  Detail & Related papers  (2022-07-29T07:56:10Z)

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.