Linear models outperform Transformers on scarred quantum dynamics in PXP chains
Simple linear mappings from past to future observables suffice to forecast PXP dynamics across ergodic and scarred regimes. The finding implies that quantum many-body complexity does not automatically demand expressive nonlinear architectures for prediction tasks. Follow-up work should test whether this linearity persists at larger system sizes and in two-dimensional Rydberg arrays.
The authors cast quantum evolution as multivariate time-series prediction on local observables of a 1D PXP model. They trained both a full Transformer and the parameter-light DLinear architecture on trajectories starting from product states tuned from volume-law entanglement to scar eigenstates. Training used exact diagonalization data for N=8-12 sites with 10^4-10^5 time steps per trajectory. DLinear achieved mean-squared errors below 0.01 even at long horizons in the scarred limit, whereas Transformer errors rose above 0.1 once scarring dominated. The linear model’s residuals were confined to rapid oscillations that averaged out in integrated observables. This indicates the underlying map from past to future expectation values remains approximately linear despite exponential Hilbert-space growth. The result aligns with earlier observations that scarred dynamics exhibit long-lived revivals and reduced operator spreading, lowering the effective degrees of freedom that any forecaster must capture.
Perciavalle et al.: DLinear will maintain sub-0.02 MSE on N=16 PXP chains with scar initial states when tested at 2027 benchmarks.
Sources (3)
- [1]Primary Source(https://arxiv.org/abs/2610.10697)
- [2]Supporting Source(https://arxiv.org/abs/2207.01663)
- [3]Supporting Source(https://arxiv.org/abs/2303.06006)