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This research establishes a formal bridge between topological quantum neural networks and amplituhedra to represent generic universal quantum computation processes. By linking these geometric structures with error-correcting codes, the study advances our theoretical understanding of how topology underpins fundamental scattering phenomena in quantum systems. The work provides new mathematical tools for modeling complex quantum dynamics without relying on traditional circuit-based formalisms.

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Amplituhedra for generic quantum processes via the TQNN representation of UQC

arXiv31 iulie 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2509.19772v3 Announce Type: replace Abstract: We study the relationship between computation and scattering both operationally (hence phenomenologically) and formally. We develop a representation of universal quantum computation (UQC) within the formalism of topological quantum neural networks (TQNNs), using the Reshetikhin-Turaev and Turaev-Viro models to show how TQNNs implement quantum error-correcting codes. We then exhibit a formal correspondence between TQNNs and amplituhedra to support the existence of amplituhedra for representing generic quantum processes. This construction shows how amplituhedra are geometric representations of underlying topological structures. We conclude by pointing to applications areas enabled by these results.

Abstract:We study the relationship between computation and scattering both operationally (hence phenomenologically) and formally. We develop a representation of universal quantum computation (UQC) within the formalism of topological quantum neural networks (TQNNs), using the Reshetikhin-Turaev and Turaev-Viro models to show how TQNNs implement quantum error-correcting codes. We then exhibit a formal correspondence between TQNNs and amplituhedra to support the existence of amplituhedra for representing generic quantum processes. This construction shows how amplituhedra are geometric representations of underlying topological structures. We conclude by pointing to applications areas enabled by these results.

arXiv:2509.19772 [quant-ph]

(or arXiv:2509.19772v3 [quant-ph] for this version)

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