Condensing an arbitrary algebra of charges in a quantum double model yields a hypergroup-graded extension of the deconfined excitations category whose domain walls act non-invertibly via a Hopf monad.
Universal quantum computation with weakly integral anyons
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
Harnessing non-abelian statistics of anyons to perform quantum computational tasks is getting closer to reality. While the existence of universal anyons by braiding alone such as the Fibonacci anyon is theoretically a possibility, accessible anyons with current technology all belong to a class that is called weakly integral---anyons whose squared quantum dimensions are integers. We analyze the computational power of the first non-abelian anyon system with only integral quantum dimensions---$D(S_3)$, the quantum double of $S_3$. Since all anyons in $D(S_3)$ have finite images of braid group representations, they cannot be universal for quantum computation by braiding alone. Based on our knowledge of the images of the braid group representations, we set up three qutrit computational models. Supplementing braidings with some measurements and ancillary states, we find a universal gate set for each model.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
The paper compiles a curated handbook reference of error-correcting codes, their symbol-based classifications, and interrelations with mathematical objects and physical phases.
citing papers explorer
-
Topological lattice gauge theory enriched by non-invertible symmetry
Condensing an arbitrary algebra of charges in a quantum double model yields a hypergroup-graded extension of the deconfined excitations category whose domain walls act non-invertibly via a Hopf monad.
-
Handbook of Error-Correcting Codes
The paper compiles a curated handbook reference of error-correcting codes, their symbol-based classifications, and interrelations with mathematical objects and physical phases.