Real-time Estimators for Scattering Observables: A full account of finite volume errors for quantum simulation

TL;DR

This paper proves that real-time estimators for scattering observables in quantum field theories have exponentially suppressed finite-volume errors, enabling more accurate quantum simulations of particle interactions.

Contribution

It establishes the universal applicability of real-time estimators for scattering observables and quantifies finite-volume error suppression in quantum simulations.

Findings

Finite-volume errors are exponentially suppressed.

Averages over boosts further reduce errors.

Results apply to wavepacket scattering simulations.

Abstract

The real-time correlators of quantum field theories can be directly probed through new approaches to simulation, such as quantum computing and tensor networks. This provides a new framework for computing scattering observables in lattice formulations of strongly interacting theories, such as lattice quantum chromodynamics. In this paper, we prove that the proposal of real-time estimators of scattering observables is universally applicable to all scattering observables of gapped quantum field theories. All finite-volume errors are exponentially suppressed, and the rate of this suppression is controlled by the regulator considered, namely, a displacement of the spectrum of the theory into the complex plane. A partial restoration of Lorentz symmetry by averaging over different boosts gives an additional suppression of finite volume errors. Our results also apply to the simulation of wavepacket scattering, where a similar averaging is performed to construct the wavepackets that regulate the finite volume effects. This result represents a necessary key step towards determining a broad class of scattering observables via quantum computing that are currently inaccessible via classical computing. Such observables are relevant for various applications, including hadron spectroscopy, hadron structure, and precision tests of the Standard Model. We also comment on potential applications of our results to traditional computational schemes.