Accessing scattering amplitudes using quantum computers

TL;DR

This paper explores how quantum computers could be used to calculate scattering amplitudes, addressing finite-volume effects and proposing solutions to enable future non-perturbative real-time correlation function studies.

Contribution

It introduces a formalism for extracting scattering amplitudes from quantum computer simulations considering finite-volume effects and proposes a practical approach to overcome volume-related challenges.

Findings

Finite-volume effects significantly impact amplitude extraction.

A new method using a non-zero $i \\epsilon$-prescription is proposed.

Potential to study reactions beyond standard lattice QCD capabilities.

Abstract

Future quantum computers may serve as a tool to access non-perturbative real-time correlation functions. In this talk, we discuss the prospects of using these to study Compton scattering for arbitrary kinematics. The restriction to a finite-volume spacetime, unavoidable in foreseeable quantum-computer simulations, must be taken into account in the formalism for extracting scattering observables. One approach is to work with a non-zero $i \epsilon$-prescription in the Fourier transform to definite momentum and then to estimate an ordered double limit, in which the spacetime volume is sent to infinity before $\epsilon$ is sent to $0$. For the amplitudes and parameters considered here, we find that significant volume effects arise, making the required limit very challenging. We present a practical solution to this challenge that may allow for future determinations of deeply virtual Compton scattering amplitudes, as well as many other reactions that are presently outside the scope of standard lattice QCD calculations.