Learning fermionic correlations by evolving with random translationally invariant Hamiltonians

TL;DR

This paper introduces a measurement scheme for fermionic quantum devices using translationally invariant evolutions to estimate correlation functions, providing rigorous bounds and feasible implementation methods for analog quantum simulators.

Contribution

It develops a novel classical shadow-like measurement protocol for fermionic systems with translational invariance, including theoretical bounds and practical implementation strategies.

Findings

Estimates second and fourth order correlation functions using free fermionic evolutions.

Provides rigorous sample complexity bounds for the measurement scheme.

Demonstrates approximate implementation with nearest-neighbour hopping quenches.

Abstract

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. On a conceptual level, this work brings the idea of classical shadows to the realm of large scale analog quantum simulators.