Measuring full counting statistics in a trapped-ion quantum simulator

TL;DR

This paper demonstrates how to measure full counting statistics and probability distribution functions of quantum observables in a trapped-ion quantum simulator using classical shadows, enabling comprehensive fluctuation analysis.

Contribution

It introduces a measurement scheme combining classical shadows with random basis measurements to efficiently access FCS and PDF in quantum simulators.

Findings

Successful measurement of FCS and PDF for magnetization in a trapped-ion system

Efficient access to quantum fluctuations of subsystems using the proposed method

Applicable to various operators and subsystem choices in quantum simulations

Abstract

In quantum mechanics, the probability distribution function (PDF) and full counting statistics (FCS) play a fundamental role in characterizing the fluctuations of quantum observables, as they encode the complete information about these fluctuations. In this letter, we measure these two quantities in a trapped-ion quantum simulator for the transverse and longitudinal magnetization within a subsystem. We utilize the toolbox of classical shadows to postprocess the measurements performed in random bases. The measurement scheme efficiently allows access to the FCS and PDF of all possible operators on desired choices of subsystems of an extended quantum system.