A quantum algorithm for the n-gluon MHV scattering amplitude

TL;DR

This paper introduces a quantum algorithm to compute n-gluon MHV scattering amplitudes, demonstrating its potential through simulation for four gluons and highlighting its scalability for higher multiplicities.

Contribution

It presents a novel quantum algorithm utilizing unitarisation techniques to efficiently compute gluon scattering amplitudes, with detailed implementation for four gluons.

Findings

Algorithm performs well with parameter optimization

Simulation results validate the approach for n=4

Potential scalability to higher gluon counts

Abstract

We propose a quantum algorithm for computing the n-gluon maximally helicity violating (MHV) tree-level scattering amplitude. We revisit a newly proposed method for unitarisation of non-unitary operations and present how this implementation can be used to create quantum gates responsible for the color and kinematic factors of the gluon scattering amplitude. As a proof-of-concept, we detail the full conceptual algorithm that yields the squared amplitude and implement the corresponding building blocks on simulated noiseless quantum circuits for n = 4 to analyze its performance. The algorithm is found to perform well with parameter optimizations, suggesting it to be a good candidate for implementing on quantum computers also for higher multiplicities.