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arXiv · 2202.01973

Toponomic Quantum Computation

C. Chryssomalakos·L. Hanotel·E. Guzmán-González·E. Serrano-Ensástiga
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Abstract

Holonomic quantum computation makes use of non-abelian geometric phases, associated to the evolution of a subspace of quantum states, to encode logical gates. We identify a special class of subspaces, for which a sequence of rotations results in a non-abelian holonomy of a topological nature, so that it is invariant under any $SO(3)$-perturbation. Making use of a Majorana-like stellar representation for subspaces, we give explicit examples of topological-holonomic (or toponomic) NOT and CNOT gates.

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C. Chryssomalakos, L. Hanotel, E. Guzmán-González, E. Serrano-Ensástiga. 2022-02-04. Toponomic Quantum Computation. https://doi.org/10.1142/s021773232250184

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