Learning fermionic correlations by evolving with random translationally invariant Hamiltonians

Understand

Schemes of classical shadows have been developed to facilitate the read-out of digital quantum devices, but similar tools for analog quantum simulators are scarce and experimentally impractical.

• In this work, we provide a measurement scheme for fermionic quantum devices that estimates second and fourth order correlation functions by means of free fermionic, translationally invariant evolutions - or quenches - and measurements in the mode occupation number basis.
• We precisely characterize what correlation functions can be recovered and equip the estimates with rigorous bounds on sample complexities, a particularly important feature in light of the difficulty of getting good statistics in reasonable experimental platforms, with measurements being slow.
• Finally, we demonstrate how our procedure can be approximately implemented with just nearest-neighbour, translationally invariant hopping quenches, a very plausible procedure under current experimental requirements, and requiring only random time-evolution with respect to a single native Hamiltonian.