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Schemes of classical shadows have been developed to facilitate the read-outof digital quantum devices, but similar tools for analog quantum simulators arescarce and experimentally impractical. In this work, we provide a measurementscheme for fermionic quantum devices that estimates second and fourth ordercorrelation functions by means of free fermionic, translationally invariantevolutions - or quenches - and measurements in the mode occupation numberbasis. We precisely characterize what correlation functions can be recoveredand equip the estimates with rigorous bounds on sample complexities, aparticularly important feature in light of the difficulty of getting goodstatistics in reasonable experimental platforms, with measurements being slow.Finally, we demonstrate how our procedure can be approximately implemented withjust nearest-neighbour, translationally invariant hopping quenches, a veryplausible procedure under current experimental requirements, and requiring onlyrandom time-evolution with respect to a single native Hamiltonian. On aconceptual level, this work brings the idea of classical shadows to the realmof large scale analog quantum simulators.

Learning fermionic correlations by evolving with random translationally invariant Hamiltonians