Quantum Computational Structure of $SU(N)$ Scattering

TL;DR

This paper explores how $SU(N)$ particle scattering processes can be efficiently simulated using quantum algorithms, revealing that all 2-2 scattering amplitudes can be constructed from just three quantum gates, highlighting a fundamental simplicity.

Contribution

It demonstrates that $SU(N)$ scattering amplitudes can be generated from a minimal set of quantum gates and reveals a $bZ_2$ algebra structure underlying the scattering channels.

Findings

All 2-2 scattering amplitudes for fundamental or anti-fundamental particles can be built from three quantum gates.

Scattering channels are governed by a $bZ_2$ algebra, akin to 'bit flips' on internal quantum numbers.

Quantum algorithms based on Linear Combinations of Unitaries effectively describe these scattering processes.

Abstract

We study scattering of particles which obey an $SU(N)$ global symmetry through the lens of quantum computation and quantum algorithms. We show that for scattering between particles which transform in the fundamental or anti-fundamental representations, i.e. qudits, all 2-2 scattering amplitudes can be constructed from only three quantum gates. Further, for any $N$, all 2-2 scattering channels are shown to emerge from the span of a $\mathbb{Z}_{2}$ algebra, suggesting that scattering in this context is fundamentally governed by the action of ``bit flips'' on the internal quantum numbers. We frame these findings in terms of quantum algorithms constructed from Linear Combinations of Unitaries and block encoding.