LUQPI with classical shadows as privileged information

Investigate whether Learning Under Quantum Privileged Information can circumvent the need for known order parameters by using classical-shadow measurements of ground states as privileged training information, and determine whether such shadows suffice to realize LUQPI advantages for phase classification without prior knowledge of order parameters.

Background

In the empirical study, privileged information consists of ground-state order parameters, which presupposes prior knowledge of suitable observables. The authors propose replacing this with classical-shadow measurements of ground states to avoid dependence on predefined order parameters.

They explicitly conjecture that such an approach could work, motivating investigation into whether shadows can serve as effective privileged information to train classical predictors within LUQPI.