Universal quantum computation in topological quantum neural networks and amplituhedron representation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914332423487488 |
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| author | Fields, Chris Glazebrook, James F. Marcianò, Antonino Zappala, Emanuele |
| author_facet | Fields, Chris Glazebrook, James F. Marcianò, Antonino Zappala, Emanuele |
| contents | We study the relationship between computation and scattering both operationally (hence phenomenologically) and formally. We show how topological quantum neural networks (TQNNs) enable universal quantum computation, using the Reshetikhin-Turaev and Turaev-Viro models to show how TQNNs implement quantum error-correcting codes. We then exhibit a formal correspondences 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19772 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal quantum computation in topological quantum neural networks and amplituhedron representation Fields, Chris Glazebrook, James F. Marcianò, Antonino Zappala, Emanuele Quantum Physics High Energy Physics - Phenomenology High Energy Physics - Theory We study the relationship between computation and scattering both operationally (hence phenomenologically) and formally. We show how topological quantum neural networks (TQNNs) enable universal quantum computation, using the Reshetikhin-Turaev and Turaev-Viro models to show how TQNNs implement quantum error-correcting codes. We then exhibit a formal correspondences 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. |
| title | Universal quantum computation in topological quantum neural networks and amplituhedron representation |
| topic | Quantum Physics High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.19772 |