Identify the most informative measurement basis for pretraining in more general quantum many-body systems

Determine, for quantum many-body systems beyond the 2D transverse field Ising model and the 2D dipolar XY model, which measurement basis (for example, the computational Z basis versus a rotated X basis) is more relevant for data-driven pretraining within the hybrid optimization of transformer quantum state ansätze, in order to reliably capture both amplitude and sign structure of the target states.

Background

The paper proposes a hybrid optimization scheme for neural quantum states, specifically transformer quantum states, combining data-driven pretraining with variational Monte Carlo. Pretraining uses projective measurements in the computational Z basis and observables (e.g., local magnetizations or spin-spin correlations) in other bases such as X to capture both amplitude and sign structure.

Empirical results on the 2D transverse field Ising model show that pretraining on both Z and X bases significantly improves convergence and accuracy across parameter regimes, while pretraining on only one basis helps primarily when that basis aligns with the dominant physics (e.g., Z for large J, X for large h). The authors note that for more general systems, it is not known a priori which basis will be most relevant, creating an unresolved question about basis selection for effective pretraining.