Geometric inflation of deviations challenges neural quantum states in dynamics of quantum Ising models
Abstract
Neural quantum states (NQS) have emerged as a powerful framework for simulating non-equilibrium dynamics in strongly correlated quantum systems, offering scalable variational representations of highly entangled states. Yet, accurate NQS simulations have been found to be surprisingly challenging in some physical regimes of limited complexity. Here, we address paradigmatic quench dynamics of a one-dimensional quantum Ising model as a controlled benchmark. Through supervised state reconstruction we establish substantially tighter empirical upper bounds on the required parameter count than previous estimates, ruling out representational limitations as the key obstruction. Instead, we uncover a geometric inflation of small deviations as a hitherto overlooked challenge for accurate solutions of the infinitesimal time-dependent variational principle (TDVP): the dynamical rotation of the kernel of the quantum geometric tensor (QGT) can suddenly lend physical significance to previously irrelevant parameter deviations. The stability of matrix product state solutions of the same TDVP suggests that the non-linearity of the neural network ansatz is the origin of the sensitivity. These results identify QGT-null-space rotation as a geometric diagnostic of sensitive NQS dynamics and as a concrete target for improving TDVP algorithms.
Related
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BibTeX
@misc{krinitsin2026geometric,
title = {{Geometric inflation of deviations challenges neural quantum states in dynamics of quantum Ising models}},
author = {Wladislaw Krinitsin and Jonas B. Rigo and Mohammad Abedi and Markus Schmitt},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.07645},
eprint = {2609.07645},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07645},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometric inflation of deviations challenges neural quantum states in dynamics of quantum Ising models
AU - Wladislaw Krinitsin
AU - Jonas B. Rigo
AU - Mohammad Abedi
AU - Markus Schmitt
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2609.07645
UR - https://arxiv.org/abs/2609.07645
AB - Neural quantum states (NQS) have emerged as a powerful framework for simulating non-equilibrium dynamics in strongly correlated quantum systems, offering scalable variational representations of highly entangled states. Yet, accurate NQS simulations have been found to be surprisingly challenging in some physical regimes of limited complexity. Here, we address paradigmatic quench dynamics of a one-dimensional quantum Ising model as a controlled benchmark. Through supervised state reconstruction we establish substantially tighter empirical upper bounds on the required parameter count than previous estimates, ruling out representational limitations as the key obstruction. Instead, we uncover a geometric inflation of small deviations as a hitherto overlooked challenge for accurate solutions of the infinitesimal time-dependent variational principle (TDVP): the dynamical rotation of the kernel of the quantum geometric tensor (QGT) can suddenly lend physical significance to previously irrelevant parameter deviations. The stability of matrix product state solutions of the same TDVP suggests that the non-linearity of the neural network ansatz is the origin of the sensitivity. These results identify QGT-null-space rotation as a geometric diagnostic of sensitive NQS dynamics and as a concrete target for improving TDVP algorithms.
ER -