Sample-efficient randomized measurements for lattice gauge theories

Randomized measurement techniques provide a versatile framework for extracting a wide range of properties from quantum states. In their most general form, these methods are state-agnostic and particularly effective at estimating generic quantum observables. However, it has been recognized that incorporating prior knowledge—especially in the form of symmetries—can significantly enhance their efficiency, potentially at the cost of deeper randomization circuits. Focusing on the example of the Z2 lattice gauge theory, we study a family of randomized measurement protocols designed to balance the tradeoff between symmetry and circuit complexity. We demonstrate that in a variety of physically relevant settings, the symmetry-informed protocols outperform a symmetry-agnostic approach. We analyze the resulting trade-offs between sample efficiency and circuit depth, and identify specific problem instances where symmetry-tailored protocols yield clear performance advantages over their generic counterparts.