Full counting statistics of particle distribution on a digital quantum computer

Full counting statistics (FCS) provides a powerful framework to access the statistical information of a system from the characteristic function. However, applications of FCS for generic interacting quantum systems are often hindered by the intrinsic difficulty of classical simulation of quantum many-body problems. Here we propose a quantum algorithm for FCS that can obtain both the particle distribution and cumulants of interacting systems. The algorithm evaluates the characteristic functions by quantum computing and then extracts the distribution and cumulants with classical postprocessing. With digital signal processing theory, we analyze the dependence of accuracy with the number of sampling points for the characteristic functions. We show that the desired number of sampling points for accurate FCS can be reduced by filtering some components of the quantum state that are not of interest. By numeral simulation, we demonstrate the FCS of domain walls for several representative models. Remarkably, we show that the accuracy of our algorithm does not significantly change with the system size for a given number of measurements. The algorithm suggests an avenue for studying full counting statistics on quantum computers.