Adaptive learning for fermionic Gaussian and weakly non-Gaussian states

Determine whether adaptively chosen Gaussian transformations and measurement bases can reduce the sample complexity of learning fermionic Gaussian states relative to non-adaptive single-copy protocols, and establish whether analogous adaptive updates can identify the Gaussian structure of weakly non-Gaussian states while restricting the residual learning problem to a small number of non-Gaussian modes.

Background

The authors propose fermionic Gaussian states and weakly non-Gaussian extensions as a distinct structured setting in which the role of adaptivity can be studied. The analogy with stabilizer learning is that adaptive transformations might progressively simplify the unknown state while preserving structure already identified.

No result is provided for the fermionic setting. The questions concern both a possible sample-complexity advantage for Gaussian states and a structural compression mechanism for weakly non-Gaussian states.

References

Can adaptively chosen Gaussian transformations and measurement bases reduce the sample complexity relative to non-adaptive single-copy protocols? For weakly non-Gaussian states, can such updates progressively identify the Gaussian structure while confining the remaining learning problem to a small number of non-Gaussian modes?

— Adaptivity is all you need: Optimal stabilizer learning using just single-copy measurements  (2610.02031 - Bittel et al., 1 Oct 2026) in Section Conclusions and open questions, item “Fermionic analogues”