The role of boundary conditions in quantum computations of scattering observables

TL;DR

This paper examines how finite volume effects influence quantum computations of scattering amplitudes in Minkowski space and proposes an averaging method over symmetry-reduced kinematic points to mitigate systematic uncertainties.

Contribution

It quantifies finite volume effects on Minkowski-signature scattering quantities and introduces an averaging strategy to reduce volume-induced distortions in quantum simulations.

Findings

Finite volume effects can significantly distort scattering amplitude calculations.

Averaging over symmetry-reduced kinematic points suppresses volume effects.

The proposed method improves the accuracy of quantum simulation results for scattering observables.

Abstract

Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. This would give access to Minkowski-signature correlators, in contrast to the Euclidean calculations routinely performed at present. However, as with present-day calculations, quantum computation strategies still require the restriction to a finite system size, including a finite, usually periodic, spatial volume. In this work, we investigate the consequences of this in the extraction of hadronic and Compton-like scattering amplitudes. Using the framework presented in Phys. Rev. D101 014509 (2020), we quantify the volume effects for various $1+1$D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty, even for volumes that are very large by the standards of present-day Euclidean calculations. We then present an improvement strategy, based in the fact that the finite volume has a reduced symmetry. This implies that kinematic points, which yield the same Lorentz invariants, may still be physically distinct in the finite-volume system. As we demonstrate, both numerically and analytically, averaging over such sets can significantly suppress the unwanted volume distortions and improve the extraction of the physical scattering amplitudes.