Simulating dynamics of the two-dimensional transverse-field Ising model: a comparative study of large-scale classical numerics

TL;DR

This paper compares multiple advanced classical numerical methods to simulate the complex quantum dynamics of the two-dimensional transverse-field Ising model, providing benchmarks and insights relevant for quantum computing and experimental physics.

Contribution

It introduces a comprehensive comparison of tensor network techniques and Monte Carlo methods for simulating 2D quantum dynamics, highlighting their effectiveness and limitations.

Findings

Tensor network methods show varying accuracy depending on the dynamical regime.

The study establishes benchmarks for classical simulation of 2D quantum dynamics.

Results connect classical simulability with regimes like quasi-adiabatic dynamics and quantum quenches.

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. 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: (i) quantum annealing through a critical point and (ii) post-quench 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, quasi-adiabatic dynamics, the Kibble-Zurek mechanism, and quantum quenches.