Efficient Learning of Fermionic Magic States under Free-Fermion Evolution
The research aims to efficiently learn quantum states belonging to fermionic magic states evolving under an unknown number-conserving free-fermion process. The method uses spectral properties of Particle Reduced Density Matrices (RDMs) and a multi-stage procedure involving Gram splitting and recursive block separation. This approach proves that high-fidelity state reconstruction is possible with polynomial complexity, even for complex systems.