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arXiv:2511.10550

Quantum Computational Structure of $SU(N)$ Scattering

Navin McGinnis

quant-phSubmitted Nov 13, 2025• Announced Nov 14, 2025• 0 citations
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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.

Comments
5 pages, 2 figures, comments welcome!

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