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 often be 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 post-processing. With digital
signal processing theory, we analyze the dependency 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 FCS of domain walls for the mixed Ising model. The
algorithm suggests an avenue for studying full-counting statistics on quantum
computers