Necessity of fermionic magic for sampling hardness

Determine whether fermionic magic is necessary for computational hardness in fixed-basis computational-basis sampling of fermionic states and their dynamics.

Background

The paper constructs antisymmetrized products of strongly orthogonal geminals whose one-body and higher-order fermionic AntiFlatness measures grow without bound while the states remain efficiently representable and sampleable as low-bond-dimension tensor networks. This demonstrates that large fermionic magic is not sufficient for hardness and does not determine the sampling cost.

The construction does not resolve the converse direction. Although the authors identify generic high-rank non-Gaussianity in the operative sampling basis as a possible source of hardness, they explicitly leave unanswered whether some form of fermionic magic is required for hardness.

References

The construction is silent on whether magic is necessary for hardness (it may well be, and the paired stratum's residual structure is where locates tractability); it refutes only that magic is sufficient for, or determines, the cost---the coefficient-insensitivity of Prop.~\ref{prop:obstruction} made constructive.

— Dynamical spectral functions from bitstring-sampled quantum subspaces: entanglement, not one-body magic, tracks the sampling cost  (2608.16436 - Vargas, 17 Aug 2026) in Appendix B, subsection “A provably-simulable witness: magic without cost”