Quantifying the sensitivity to errors in analog quantum simulation

TL;DR

This paper introduces a framework to assess how errors affect the reliability of quantum simulators, revealing that macroscopic observables are more robust to imperfections than microscopic ones, with experimental validation on a state-of-the-art device.

Contribution

It links the robustness of quantum expectation values to the spectral properties of observables, providing a universal method to evaluate simulator reliability without detailed imperfection models.

Findings

Macroscopic observables are accurately reproduced despite device imperfections.

Microscopic observables exhibit larger relative errors on average.

Experimental results confirm the universality of the theoretical predictions.

Abstract

Quantum simulators are widely seen as one of the most promising near-term applications of quantum technologies. However, it remains unclear to what extent a noisy device can output reliable results in the presence of unavoidable imperfections. Here we propose a framework to characterize the performance of quantum simulators by linking the robustness of measured quantum expectation values to the spectral properties of the output observable, which in turn can be associated with its macroscopic or microscopic character. We show that, under general assumptions and on average over all states, imperfect devices are able to reproduce the dynamics of macroscopic observables accurately, while the relative error in the expectation value of microscopic observables is much larger on average. We experimentally demonstrate the universality of these features in a state-of-the-art quantum simulator and show that the predicted behavior is generic for a highly accurate device, without assuming any knowledge about the nature of the imperfections.