Learning properties of interacting fermionic systems with limited hardware

Interacting fermionic systems can model real world physical phenomenon directly. Many people are working on finding efficient and practical ways to determine properties of these quantum simulators. Specifically, estimating correlation functions, that reveal important properties such as coulomb-coulomb interaction strength and entanglement spreading, is a crucial goal. The well know classical shadows formalism allows one to find linear properties of a quantum state by reusing outcomes from simple basis measurements. For analog quantum simulators (like our fermions) there have been fewer applications of classical shadows and those are generally experimentally impractical. In this talk, I will present our results so far on estimating second and fourth order correlation functions by means of free fermionic translationally invariant evolutions and measurements in the mode occupation number basis. We chsracterise what correlation functions can be recovered under what circumstances and provide sample complexities. I will also demonstrate numerically that our scheme can be implemented approximately with only nearest-neighbour translationally invariant hopping quenches, a more plausible design under current experimental requirements.