Scattering Amplitude from Quantum Computing with Reduction Formula

TL;DR

This paper introduces a quantum computing framework based on the reduction formula for calculating scattering amplitudes in quantum field theory, enabling nonperturbative analysis of bound states and small-particle scatterings.

Contribution

It presents a novel nonperturbative quantum algorithm for scattering amplitudes using the Lehmann-Symanzik-Zimmermann reduction formula, avoiding the need for wave packets.

Findings

Successful simulation of fermion propagator and bound state in the Gross-Neveu model

Demonstration of the pole structure essential for the reduction formula

Framework suitable for exclusive hadron scattering studies

Abstract

Utilizing the Lehmann-Symanzik-Zimmermann reduction formula, we present a new general framework for computing scattering amplitudes in quantum field theory with quantum computers in a fully nonperturbative way. In this framework, one only has to construct one-particle states of zero momentum, and no wave packets of incoming particles are needed. The framework is able to incorporate scatterings of bound states, and is ideal for scatterings involving a small number of particles. We expect this framework to have particular advantages when applied to exclusive hadron scatterings. As a proof of concept, by simulations on classical hardware, we demonstrate that in the one-flavor Gross-Neveu model, the fermion propagator, the connected fermion four-point function, and the propagator of a fermion-antifermion bound state obtained from our proposed quantum algorithm have the desired pole structure crucial to the implementation of the Lehmann-Symanzik-Zimmermann reduction formula.