Universal gates from braiding and fusing anyons on quantum hardware.

Abstract

A quantum computer requires the ability to store and manipulate information globally to protect against local noise. Topologically ordered phases^1,2 offer two routes: encoding information in the ground-state subspace³ or in anyonic excitations^1,4,5. The toric code¹ exemplifies the first approach but does not intrinsically support a universal gate set. The latter-topological quantum computation-implements gates by braiding non-Abelian anyons⁶ around each other. However, the simplest non-Abelian generalizations of the toric code cannot achieve universality by braiding alone^7-9. Here we demonstrate that anyon fusion, used as a computational primitive, renders these minimally non-Abelian topologically ordered states universal. We prepare a 54-qubit ground state of the quantum double of S₃, the smallest non-Abelian group, on the H2 processor of Quantinuum. We encode logical information in the global fusion space of non-Abelian anyons, and by combining braiding with fusion, we realize a universal topological gate set and read-out, which we demonstrate by topologically preparing a magic state. This demonstrates that the S₃ topologically ordered state is scalably preparable, yet rich enough to support a universal gate set. More broadly, this work opens up new pathways for harnessing the intrinsic properties of quantum matter to manipulate quantum information.