Full-counting statistics of particle distribution on a digital quantum computer

TL;DR

This paper introduces a quantum algorithm for calculating full-counting statistics in interacting quantum systems, enabling efficient extraction of particle distributions and cumulants via quantum computing and classical post-processing.

Contribution

It presents a novel quantum algorithm for FCS that reduces sampling requirements and applies digital signal processing to improve accuracy in quantum simulations.

Findings

Demonstrated FCS of domain walls in the mixed Ising model

Reduced the number of sampling points needed for accurate FCS

Showed potential for studying quantum many-body systems on quantum computers

Abstract

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.