Simulating dynamics of the two-dimensional transverse-field Ising model: A comparative study of large-scale classical numerics
Abstract
The quantum dynamics of many-qubit systems is an outstanding problem that has recently driven significant advances in both numerical methods and programmable quantum processing units (QPUs). In this work, we employ a comprehensive toolbox of state-of-the-art numerical approaches to classically simulate the dynamics of the two-dimensional transverse-field Ising model. Our methods include three different tensor-network techniques—matrix product states, tree tensor networks, and two-dimensional tensor networks under the belief propagation approximation—as well as time-dependent variational Monte Carlo with neural quantum states. We focus on two paradigmatic dynamical protocols: (1) quantum annealing through a critical point and (2) postquench dynamics. Our extensive results show the quantitative predictions of various state-of-the-art numerical methods providing a benchmark for future numerical investigations and experimental studies with the aim to push the limitations on classical and QPUs. In particular, our work connects classical simulability to different regimes associated with quantum dynamics in Rydberg arrays—namely, quasiadiabatic dynamics, the Kibble-Zurek mechanism, and quantum quenches.
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BibTeX
@article{vovrosh2026simulating,
title = {{Simulating dynamics of the two-dimensional transverse-field Ising model: A comparative study of large-scale classical numerics}},
author = {Joseph Vovrosh and Sergi Julià-Farré and Wladislaw Krinitsin and Michael Kaicher and Fergus Hayes and Emmanuel Gottlob and Augustine Kshetrimayum and Kemal Bidzhiev and Simon Jäger and Markus Schmitt and Joseph Tindall and Constantin Dalyac and Tiago Mendes-Santos and Alexandre Dauphin},
journal = {Physical Review Research},
year = {2026},
month = jun,
doi = {10.1103/x4gs-g63p},
eprint = {2511.19340},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05774049v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - Simulating dynamics of the two-dimensional transverse-field Ising model: A comparative study of large-scale classical numerics
AU - Joseph Vovrosh
AU - Sergi Julià-Farré
AU - Wladislaw Krinitsin
AU - Michael Kaicher
AU - Fergus Hayes
AU - Emmanuel Gottlob
AU - Augustine Kshetrimayum
AU - Kemal Bidzhiev
AU - Simon Jäger
AU - Markus Schmitt
AU - Joseph Tindall
AU - Constantin Dalyac
AU - Tiago Mendes-Santos
AU - Alexandre Dauphin
PY - 2026
DA - 2026/06/17
JO - Physical Review Research
DO - 10.1103/x4gs-g63p
UR - https://hal.science/hal-05774049v1
AB - The quantum dynamics of many-qubit systems is an outstanding problem that has recently driven significant advances in both numerical methods and programmable quantum processing units (QPUs). In this work, we employ a comprehensive toolbox of state-of-the-art numerical approaches to classically simulate the dynamics of the two-dimensional transverse-field Ising model. Our methods include three different tensor-network techniques—matrix product states, tree tensor networks, and two-dimensional tensor networks under the belief propagation approximation—as well as time-dependent variational Monte Carlo with neural quantum states. We focus on two paradigmatic dynamical protocols: (1) quantum annealing through a critical point and (2) postquench dynamics. Our extensive results show the quantitative predictions of various state-of-the-art numerical methods providing a benchmark for future numerical investigations and experimental studies with the aim to push the limitations on classical and QPUs. In particular, our work connects classical simulability to different regimes associated with quantum dynamics in Rydberg arrays—namely, quasiadiabatic dynamics, the Kibble-Zurek mechanism, and quantum quenches.
SN - 2643-1564
SN - 2643-1564
ER -