Scattering Amplitude from Quantum Computing with Reduction Formula
arXiv:2301.04179 · doi:10.1103/PhysRevD.109.036025
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.
arXiv comment9 pages, 3 figures; version published in PRD; Fig. 1 modified, 2 new figures added; estimate on computational complexity modified, example 1 removed, simulations of a four-point function and the propagator of a composite operator added to the study of Gross-Neveu model
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