On linearity or non-linearity in machine learning for quantum chaotic dynamics

2026-10-07

AI Summary

This study addresses the computational bottleneck arising from entanglement spreading when simulating quantum chaotic many-body dynamics via classical methods by reformulating quantum evolution as a time-series forecasting problem. Using the PXP chain, experimentally realizable with Rydberg atom arrays, as a benchmark, we compare the predictive performance of nonlinear Transformer and linear DLinear models across various initial states. Our results reveal that complex quantum dynamics do not necessarily entail complex prediction tasks: a simple linear mapping suffices to achieve high-accuracy forecasts spanning the entire spectrum from ergodic to scarred states. DLinear maintains robust accuracy across all initial conditions with only minor high-frequency deviations, significantly outperforming Transformers, whose performance degrades in the scar limit. These findings challenge conventional assumptions and validate the feasibility of linear approaches for predicting quantum many-body dynamics.

Abstract

Accurately simulating chaotic quantum many-body dynamics remains a major computational challenge for classical methods, due to the rapid buildup and spatial spreading of entanglement during the evolution. This raises the question of whether machine learning can provide an effective alternative for predicting quantum dynamics. We address this question by formulating quantum dynamics as a time-series forecasting problem, using a few-qubit PXP chain, realizable with Rydberg-atom arrays, as a benchmark. By varying the initial state, the system spans dynamical regimes ranging from ergodic behavior to quantum many-body scarring, providing a controlled setting for testing forecasting models across qualitatively different dynamics. We compare two contrasting architectures: an expressive nonlinear Transformer and DLinear, a simple linear forecasting model. The Transformer accurately predicts dynamics in the more ergodic regime, but its performance progressively deteriorates as the initial state approaches the scarred limit. In contrast, DLinear remains accurate across the entire family of initial states, with its main deviations consisting of small high-frequency oscillations that have little effect on the overall prediction error. Remarkably, these results show that observables generated by complex quantum many-body dynamics can be forecast with high accuracy through a simple linear mapping from past to future observations. This reveals that the complexity of the underlying quantum evolution need not translate into an equally complex forecasting problem.

Problem

• quantum chaotic dynamics
• machine learning
• time-series forecasting
• quantum many-body scarring
• linearity

Innovation

• Quantum chaotic dynamics
• Time-series forecasting
• DLinear
• Transformer
• Quantum many-body scarring