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## "Universality of Z3 parafermions via edge-mode interaction and quantum simulation of topological space evolution with Rydberg atoms", Asmae Benhemou et al., 2023

*Reviewed December 29, 2023*

*Citation:* Benhemou, Asmae, et al. "Universality of Z3 parafermions via edge-mode interaction and quantum simulation of topological space evolution with Rydberg atoms." Physical Review Research 5.2 (2023): 023076.

*Web:* https://arxiv.org/abs/2111.04132

*Tags:* Abelian-anyons, Hardware, Universal-scheme

This paper discusses a proposal for non-topologically protected universal quantum computation
using Z3 parafermions. The proposal is extremely similar to the Majorana fermion idea,
where two quasiparticles are brought close together for a short amount of time to execute a gate.
The new contribution of this paper is to extend these results to Z3, and to explicitly work out
the calculations for the effective Hamiltonians which describe Rydberg atom arrays.

One thing to note about Z3 parafermions is that they are deeply related to the 3-state Potts model:

> Mong, Roger SK, et al. "Parafermionic conformal field theory on the lattice." Journal of Physics A: Mathematical and Theoretical 47.45 (2014): 452001.

> Vanhove, Robijn, et al. "Topological aspects of the critical three-state Potts model." Journal of Physics A: Mathematical and Theoretical 55.23 (2022): 235002.

Thus, since this model is so well known, Z3 parafermions have attracted a lot of attention
from physicists for a very long time - especially those in conformal field theory.