Year: 2025
Type: article
Abstract: As part of a protocol, we braid in a certain way six anyons of topological charges 222211 in the Kauffman-Jones version of SU(2) Chern-Simons theory at level 4. The gate we obtain is a braid for the usual qutrit 2222 but with respect to a different basis than the usual basis. With respect to that basis, the Freedman group of J. Phys. A: Math. Theor. 47, 285203 (2014) is identical to the D-group D(18, 1, 1; 2, 1, 1) from the Blichfeldt classification. We provide a physical realization of each Blichfeldt generator of the SU(3) finite subgroup D(18, 1, 1; 2, 1, 1). The link of this group to elementary particle physics was already well-known by the physicists. This paper uncovers its realization in quantum physics. Inspired by these new techniques for the qutrit, we are able to make new ancillas, namely $$\frac{1}{\sqrt{2}}(|1>\,+|3>)$$ 1 2 ( | 1 > + | 3 > ) and $$\frac{1}{\sqrt{2}}(|1>\,-|3>)$$ 1 2 ( | 1 > - | 3 > ) , for the qubit 1221.
Source: Quantum Information Processing
Author: Claire Levaillant
Institution: University of Southern California
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W4410809338