Digital Simulation of Non-Abelian Parafermions in Superconducting Circuits

• URL: http://arxiv.org/abs/2502.20254v4
• Date: Fri, 28 Mar 2025 05:16:39 GMT
• Title: Digital Simulation of Non-Abelian Parafermions in Superconducting Circuits
• Authors: Hong-Yu Wang, Xiong-Jun Liu,
• Abstract summary: Parafermions exhibit profound non-Abelian statistics and emerge in topologically ordered systems.<n>We propose an experimental scheme for the digital simulation of parafermions and their non-Abelian braiding statistics in superconducting (SC) circuits.
• Score: 3.995776518196356
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Parafermions, which can be viewed as a fractionalized version of Majorana modes, exhibit profound non-Abelian statistics and emerge in topologically ordered systems, while their realization in experiment has been challenging. Here we propose an experimental scheme for the digital simulation of parafermions and their non-Abelian braiding statistics in superconducting (SC) circuits by realizing the $\mathbb{Z}_d$ plaquette model on a two-dimensional lattice. Two protocols using quantum circuits and non-destructive measurements are introduced to prepare the ground state, on which parafermion pairs are created by engineering dislocations. We then propose a generalized code deformation approach to realize the fusion and non-Abelian braiding of parafermion modes, and show the application of this approach to the $\mathbb{Z}_3$ parafermions. We also examine the experimental parameter regime to confirm the feasibility of our scheme in SC devices. This work extends previous quantum simulation of twist defects in SC qubits to qudit systems, and opens up a way for parafermion-based high-dimensional topological quantum computing with experimental feasibility.

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