Provably Efficient Learning of Fermionic Correlations under Particle-Number Symmetry
This research develops a provably efficient method for learning fermionic correlations in $N$-mode $\eta$-particle states that respects particle-number symmetry. By using random orbital rotations, the authors introduce a number-conserving shadow tomography technique. This method achieves optimal sample complexity, scaling favorably with the state's particle number and precision while remaining independent of total system size.