Amplituhedra for generic quantum processes via the TQNN representation of UQC

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.

Comments: 48 pages